Find the perimeter of this figure to the nearest tenth. Use 3.1 to approximate
Answers
Since the diameter and height of both shapes are the same, we know that the equation to solve for the semi circle is:
πr = 3.1*8 = 24.8
16 + 20 = 36
36 + 24.8 = 60.8
The perimeter of the shape is 60.8 ft
Related Questions
Lily takes a train each day to work that averages 35 miles per hour . On her way home her train ride follows the same path and averages 45 miles per hour . If the total trip takes 2.5 hours , what equation can be used to find n, the number of miles Lilly's homes is for work
Answers
Answer:
49.2 miles
Step-by-step explanation:
The distance remains the same. d
The time spent on the outbound trip is t1 = -------------
35 mph
and that on the inbound (return) trip is
d
t2 = -------------
45 mph
We combine these two fractions and set the sum = to 2.5 hours:
d(1/35 + 1/45) = 5/2
We wish to solve for d, the distance between home and work.
The LCD of 35, 45 and 2 is 630.
1/35 becomes 18/630; 1/45 becomes 14/630, and 5/2 becomes 1575/630. Then we have the simpler equation d(18 + 14) = 1575, or
d(32) = 1575, and d is then
d = 1575/32 = 49.2 miles
Solve the system by using a matrix equation
3x-5y=3
3x-4y=3
Answers
Answer:
The correct answer is B. (1,0).
Answer: B. (1,0)
Step-by-step explanation:
1. We will use the matrix method to solve this problem.
3 -5 3
3 -4 3
2. Apply to Row2 : Row2 - Row1.
3 -5 3
0 1 0
3. Simplify rows.
3 -5 3
0 1 0
Note: The matrix is now in row echelon form.
The steps below are for back substitution.
4. Apply to Row1 : Row1 + 5 Row2.
3 0 3
0 1 0
5. Simplify rows.
1 0 1
0 1 0
Note: The matrix is now in reduced row echelon form.
6. Therefore,
x=1
y=0
or (1,0).
solve on the interval [0, 2pi] 2 sec x+5 = 1
Answers
Move the 5 to the other side:
[tex]2\sec(x)=1-5=-4[/tex]
Divide both sides by 2:
[tex]\sec(x) = -2[/tex]
Recall the definition:
[tex]\sec(x)=-2 \iff \dfrac{1}{\cos(x)}=-2[/tex]
Invert both sides
[tex]\cos(x) = -\dfrac{1}{2}[/tex]
This is true when
[tex]x=\pm \dfrac{\pi}{3}[/tex]
If you need both angles to be in [0,2pi], you can recall
[tex]\cos\left(-\dfrac{\pi}{3}\right) = \cos\left(-\dfrac{\pi}{3}+2\pi\right) = \cos\left(\dfrac{5\pi}{3}\right)[/tex]
So, the solutions are
[tex]x=\dfrac{\pi}{3},\quad x=\dfrac{5\pi}{3}[/tex]
Answer:
2pi/3 and 4pi/3
Step-by-step explanation:
this is the answer according to apex
Which of these statements are true?
A. Both graphs have exactly one asymptote
B. Both graphs have been shifted and flipped.
C. Both graphs are logarithmic functions.
D. Both graphs are exponential functions.
Answers
Answer:
Step-by-step explanation:
Given are two graphs. f(x) will have x axis as asymptote while x=2 is asymptote for g(x).
Hence both graphs have exactly one asymptote
First graph passes through (0,2)
f(x) is exponential while g(x) is log.
Both graphs are shifted because f(x) is vertically shifted by 1, while g(x) is horizontally shifted by 3 units to left
The expression f(x) = 12(1.035)x models the monthly growth of membership in the new drama club at a school. According to the function, what is the monthly growth rate?
A.
0.35%
B.
1.035%
C.
3.5%
D.
12%
Answers
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
The expression is defined as
[tex]f(x)=12(1.035)^x------------------------(1)[/tex]
As we know the general form of exponential function:
[tex]f(x)=a(1+r)^x--------------------------(2)[/tex]
Here, a denotes the initial amount.
r denotes the growth rate.
On comparing, we get that
[tex]1+r=1.035\\\\r=1.035-1\\\\r=0.035\\\\r=0.035\times 100\%\\\\r=3.5\%[/tex]
Hence, option 'C' is correct.
Answer:
C) 3.5%
Step-by-step explanation:
Which of the following points is not on the graph of y=-3x^2+6x-4 ?
(6, -70)
(4, -28)
(-8, -244)
(12, -364)
Answers
Answer:
(6, -70) is not on the graph
Step-by-step explanation:
we have
[tex]y=-3x^{2}+6x-4[/tex]
we know that
If a ordered pair is on the graph of the quadratic equation, then the ordered pair must satisfy the quadratic equation
Verify each case
Substitute the x-coordinate of the ordered pair in the quadratic equation to find the value of y and then compare the results
case 1) (6, -70)
For x=-6
[tex]y=-3(-6)^{2}+6(-6)-4=-148[/tex]
[tex]-148\neq-70[/tex]
therefore
the ordered pair is not on the graph
case 2) (4, -28)
For x=4
[tex]y=-3(4)^{2}+6(4)-4=-28[/tex]
[tex]-28=-28[/tex]
therefore
the ordered pair is on the graph
case 3) (-8,-244)
For x=-8
[tex]y=-3(-8)^{2}+6(-8)-4=-148[/tex]
[tex]-244=-244[/tex]
therefore
the ordered pair is on the graph
case 4) (12,-364)
For x=12
[tex]y=-3(12)^{2}+6(12)-4=-148[/tex]
[tex]-364=-364[/tex]
therefore
the ordered pair is on the graph
Determine whether the relationship between the circumference of a circle and its diameter is a direct variation. If so, identify the constant of proportionality. Justify your response.
Answers
Answer:
The relationship between the circumference of a circle and its diameter represent a direct variation
The constant of proportionality is equal to [tex]\pi[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
Let
C=y
D=x
substitute
[tex]y=\pi x[/tex]
therefore
The relationship between the circumference of a circle and its diameter represent a direct variation
The constant of proportionality is equal to [tex]\pi[/tex]
AP CALC HELP!!! Worth 38 points. AP Calc AB differental FRQ
Answers
Answer:
5a. approximately 6 grams remain after 2 seconds
5b. The graph shown cannot be a solution. The solution has negative slope everywhere.
5c. y = 50/(t+5)
5d. The amount is changing at a decreasing rate. (As y gets smaller, so does the magnitude of dy/dt.)
Step-by-step explanation:
5a. The tangent line has the equation ...
y = f'(0)t +f(0)
Here, that is
y = -0.02·10²·t +10 = 10 -2t
Then at t=2, the value is ...
y = 10 -2·2 = 6 . . . . grams remaining
__
5b. y² is always positive (or zero), so -0.02y² will be negative. This is dy/dt, the slope of the curve with respect to time, so any curve with positive slope somewhere cannot be a solution.
__
5c. The equation is separable so can be solved by integrating ...
∫y^-2·dy = -0.02∫dt
-y^-1 = -0.02t +c . . . . for some arbitrary constant c
Multiplying by -50 gives ...
50/y = t + c . . . . for some constant c
We can find the value of c by invoking the initial condition. At t=0, y=10, so we have ...
50/10 = 0 +c = 5
Then, solving for y, we get ...
y = 50/(t+5)
__
5d. As noted above (and as described by the differential equation), the magnitude of the rate of change is proportional to the square of y. As y decreases, its rate of change will also decrease (faster). You can see that the curve for y flattens out as t increases. The amount of the substance is changing at a decreasing rate.
A gym instructer has a total of 60 hand weights in her studio. Some of the hand weights are 3 pound weights and the rest are 5 pound weights. If their are 10 more 5-lb weights , than how many of each kind does she have?
Answers
Answer:
Let's imagine that x is the number of 3 pound weights that the gym instructer has.
Since we know that there are 10 more 5 pound weights, which tells us that the number of 5 pound weight is x + 10, and the total amount is 60 hand weights, we have:
x + x + 10 = 60
2x = 60 - 10
2x = 50
x = 50/2 = 25
So there are 25 3 pound weights at the gym.
From the number we have just found, we also know that the number of the 5 pound weights should be:
60 - 25 = 35 (hand weights)
Which strategy would not correctly solve this story problem? Mellie ran for 30 minutes on Monday, for 45 minutes on Tuesday, and for 25 minutes on Wednesday. How long did Mellie run if she kept up this plan for 8 weeks? A. Translate into an equation. (30 + 45 + 25) × 8 = m B. Use logical reasoning. Add together the number of minutes Mellie exercises each week: 30 + 45 + 25 = 100. Multiply 100 by the number of weeks Mellie keeps up with this plan. C. Draw a diagram. Draw 4 groups of dots to show the 3 types of exercise and the weeks. Write 30, 45, 25, and 8 in each circle. Add the four numbers. D. Make a table. Week 1 2 3 4 5 6 7 8 Total (minutes) 100 200 300 400 500 600 700
Answers
Answer:
C. Draw a diagram. Draw 4 groups of dots to show the 3 types of exercise and the weeks. Write 30, 45, 25, and 8 in each circle. Add the four numbers.
Step-by-step explanation:
You might be able to get there starting with strategy C, but it is incomplete as written and will not solve the problem.
I need help please :-)
Answers
Answer:
A. 1
B. slope: 1/2 mile/minute; the slope represents the speed of the car
C. correlation
Step-by-step explanation:
A. The points in the table lie on a straight line, so the correlation coefficient is exactly 1.
__
B. The ratio of distance to time is speed. That ratio for this data is 10 miles/20 minutes = 1/2 mile/minute. This is the slope of the graph.
__
C. Passage of time does not cause the car to go any particular distance, nor does the car's traveling cause time to pass. The best that can be said is that the car's distance traveled is strongly correlated with the time it takes. (The reason the car goes some distance is likely due to a cause not mentioned in the problem statement, for example, it was switched on and the motor started.)
Use the diagram to complete the statements.
The measure of angle EJB is (equal to, one-half, twice, 180 minus) the measure of angle BOE.
The measure of angle BDE is (equal to, one-half, twice, 180 minus) the measure of angle BOE.
The measure of angle OED is (equal to, one-half, twice, 180 minus) the measure of angle OBD.
Answers
Answer:
m < EJB = half of m < OBE.
m < BDE = 180 minus m < BOE.
m < OED = m<OBD.
Step-by-step explanation:
First part : Because angled subtended by an arc at the circumference = half of angle at the center.
Second: Because The 2 angles OBD and OED = 90 degrees.
Third: DB and DE are both tangents to the circle, and OE and OB are both radii. So m < OED = m<OBD = 90 degrees.
Answer:
1. B. one-half
2. D. 180 minus
3. A. equal to
You have no more than $65 to spend after paying your bills. You want a drink that costs
$2.25 including tax, and you want to buy a pair of shoes, which will have 7% sales tax.
What is the inequality that represents the amount of money you have to spend?
a. x + 0.07x + 2.25 > 65
b. x + 0.07x + 2.25 ≤ 65
c. x + 0.07x + 2.25 < 65
d. x + 0.07x + 2.25 ≥ 65
Answers
Answer: B
Step-by-step explanation: You have no more than $65 which means you will want to spend equal to or less. Since you have $65, you will be able to spend up to that amount but you will not be able to spend any more than that. So, you will need to make sure the final price remains under or equal to your amount.
State the y-coordinate of the y-intercept for the function below.
[tex]f(x)=x^{3} -x^2-x+1[/tex]
Answers
Answer:
1
Step-by-step explanation:
y-intercept is defined as the point where the graph crosses the y-axis. The value of x coordinate at this point is zero, as along entire y-axis, the value of x coordinate is always zero. So substituting x = 0 in the function will give us the y-coordinate of the y-intercept of the given function.
[tex]f(x)=x^{3}-x^{2} -x+1[/tex]
Substituting x = 0 in this function, we get:
[tex]f(0)=0^{3}-0^{2}-0+1=1[/tex]
Thus, the y-coordinate of the y-intercept is 1. Therefore the y-intercept of the function in ordered pair will be: (0, 1)
On a world globe, the distance between City A and City B, two cities that are actually 10 comma 480 kilometers apart, is 13.9 inches. The actual distance between City C and City D is 1590 kilometers. How far apart are City C and City D on this globe?
City C and City D are
nothing inches apart on this globe.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
Answer:
[tex]2.1\ in[/tex]
Step-by-step explanation:
we know that
The scale of the world globe is equal to
[tex]\frac{13.9}{10,480}\frac{in}{km}= 0.0013\frac{in}{km}[/tex]
To find the distance between City C and City D on the globe, multiply the actual distance by the scale
[tex]0.0013\frac{in}{km}*(1,590\ km)=2.1\ in[/tex]
Jina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Jina drove home, there was no traffic and the trip only took
4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Jina live from the mountains?
Do not do any rounding.
Answers
Answer:
264 miles
Step-by-step explanation:
Using the relation ...
distance = speed · time
we can rearrange to get ...
speed = distance/time
We can choose to let d represent the distance we want to find. Then Jina's speed going to the mountains is d/6. Her speed coming home is then d/6+22. It takes Jina 4 hours at that speed to cover the same distance, so we have ...
d = 4(d/6 +22)
d = 2/3d +88 . . . . eliminate parentheses
1/3d = 88 . . . . . . . subtract 2/3d
d = 264 . . . . . . . . . multiply by 3
Jina lives 264 miles from the mountains.
I need a clear understanding....
Margaret makes a square frame out of four pieces of wood. Each piece of wood is a rectangular prism with a length of 40 centimeters, a height of 4 centimeters, and a depth of 6 centimeters. What is the total volume of the wood used in the frame?
Answers
V= 3,840 cm
Volume is L x W x H
and W is the same as Depth
So you would multiply those and multiply it again by four to make up for the other pieces of wood.
Final answer:
The total volume of wood used in making the square frame is 3840 cubic centimeters, which is calculated by finding the volume of one piece (960 cm³) and multiplying it by the number of pieces (4).
Explanation:
The question concerns the calculation of the total volume of wood used in making a square frame. Each piece of wood is a rectangular prism with given dimensions. To find the total volume, one must multiply the length, height, and depth of a single piece and then multiply the result by the number of pieces.
To calculate the volume of a single piece of wood, we use the formula for the volume of a rectangular prism, which is length × width × height. For one piece of wood:
Length = 40 cm
Width (depth) = 6 cm
Height = 4 cm
The volume of one piece of wood is therefore 40 cm × 6 cm × 4 cm = 960 cm³.
Since there are four pieces that make up the frame, the total volume of wood used is:
960 cm³/piece × 4 pieces = 3840 cm³
Thus, the total volume of the wood used in the frame is 3840 cubic centimeters.
Fill in the blank to complete the following sentence.
The two roots a+√b and a-√b are called _______ radicals.
Answers
Answer:
Conjugate radicals.
Step-by-step explanation:
The two roots a+√b and a-√b are called Conjugate radicals.
Just like in the complex number system where we have complex conjugates such as of 4+7i and 4 - 7i, the radicals also have their conjugate radicals. The conjugate radical of a+√b is simply obtained by changing the sign of the radical part of the expression to obtain a-√b. Therefore, the two expressions given are conjugate radicals
Answer:
Conjugate.
Step-by-step explanation:
The difference is in the signs. They are conjugate radicals.
Distribute and combine like terms. Please show all of your work.
-5(3x + 7) - 4(x - 4) + 11
Answers
For this case we have the following expression:
[tex]-5 (3x + 7) -4 (x-4) +11[/tex]
For simplicity we follow the steps:
We apply distributive property to the terms within the parenthesis, bearing in mind that:
[tex]- * + = -\\- * - = +\\-15x-35-4x + 16 + 11 =[/tex]
We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.
[tex]-15x-4x-35 + 16 + 11 =\\-19x-8[/tex]
ANswer:
[tex]-19x-8[/tex]
Answer: 19x - 8
Steps-5(3x + 7)
Apply the distributive law: a( b + c ) = ab + ac
a = -5, b = 3x, c = 7
= -5 * 3x + (-5) x 7
Apply minus - plus rules
+(-a) = -a
= -5 * 3x - 5 x 7
Simplify
-5 * 3x - 5 x 7
Multiply the numbers: 5 x 3 = 15
= -15x - 5 x 7
Multiply the numbers: 5 x 7 = 35
= -15x - 35
Plug in the values
-15x - 35 - 4(x - 4) + 11
------------------------------------------------------------------
-4(x - 4)
Apply the distributive law: a( b - c ) = ab - ac
a = -4, b = x, c = 4
= -4x - (-4) * 4
Apply minus - plus rules
-(-a) = a
= -4x + 4 * 4
Multiply the numbers: 4 * 4 = 16
= -4x + 16
Plug in the values
-15x - 35 - 4x + 16 + 11
------------------------------------------------------------------
Simplify
-15x - 35 - 4x + 16 + 11
Group like terms
= -15x - 4x - 35 + 16 + 11
Add similar elements: -15x - 4x = -19x
= -19x - 35 + 16 + 11
Add/Subtract the numbers: -35 + 16 + 11 = -8
= 19x - 8
Using the quadratic formula to solve 2x^2 = 4x - 7, what are the values of x?
Answers
Explaining the quadratic formula application in solving an equation.
The quadratic formula:
Given equation: [tex]2x^2 = 4x - 7[/tex]Rearrange into a quadratic equation: [tex]2x^2 - 4x + 7 = 0[/tex]Using the quadratic formula, a=2, b=-4, c=7Substitute into the formula to get x = 1 or x = -3/2A 25-foot ladder leans against a wall. The base of the ladder is 15 feet from the bottom of the wall. How far up the wall does the top of the ladder reach?
Answers
Answer: 20 feet.
Step-by-step explanation:
Observe the right triangle attached.
You need to find the value of "x".
Then, you can use the Pythagorean Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse of the triangle, and "b" and "c" are the legs.
In this case, you can identify that:
[tex]a=25ft\\b=15ft\\c=x[/tex]
Substitute these values into [tex]a^2=b^2+c^2[/tex]:
[tex](25ft)^2=(15ft)^2+x^2[/tex]
Now, you need to solve for x to find how far up the wall the top of the ladder reaches. Then you get:
[tex]x^2=(25ft)^2-(15ft)^2[/tex]
[tex]x=\sqrt{(25ft)^2-(15ft)^2}[/tex]
[tex]x=20ft[/tex]
ANSWER
20ft
EXPLANATION
The ladder, the wall and the ground formed a right triangle.
Let how far up the wall does the top of the ladder reached be x units.
The 25ft ladder is the hypotenuse.
The shorter legs are, 15ft and x ft
Then from Pythagoras Theorem,
[tex] {x}^{2} + {15}^{2} = {25}^{2} [/tex]
[tex] {x}^{2} + 225 = 625[/tex]
[tex] {x}^{2}= 625 - 225[/tex]
[tex]{x}^{2}= 400[/tex]
[tex]x = \sqrt{400} [/tex]
[tex]x = 20ft[/tex]
Therefore the ladder is 20 ft up the wall.
A department store is haveing 30% off sale on all pair of jeans. If you have an coupon for an additional 15% off any items price, how much will a $60.00 pair of Jeans cost? (hint: first find the scale price of the jeans and then take the coupon discount off the sale price)
Answers
then jeans will cost $38.25
Answer:
the answer would be $35.70
Step-by-step explanation:
0.70 x $60 = $42
0.85 x $42 = $35.70
This is using multipliers so the amount off will be taken away from 1 and that answer times amount needed to found from will give the answer you are looking for
Jenny must peel 300 oranges for kitchen duty. She peeled 30% of them in the morning and 45% of them in the afternoon.How many oranges are left for her to peel in the evening?
Answers
Final answer:
To find the number of oranges left for Jenny to peel in the evening, subtract the number of oranges she already peeled from the total number of oranges.
Explanation:
To find the number of oranges left for Jenny to peel in the evening, we need to subtract the number of oranges she already peeled in the morning and afternoon from the total number of oranges.
Jenny peeled 30% of the oranges in the morning, which is (30/100) * 300 = 90 oranges.
Jenny peeled 45% of the oranges in the afternoon, which is (45/100) * 300 = 135 oranges.
Therefore, the number of oranges left for Jenny to peel in the evening is 300 - 90 - 135 = 75 oranges.
A father who is 42 years old has a son and a daughter. The daughter is three times as old as the son. In 10 years the sum of all their ages will be 100 years. How old are the two siblings at present?
Answers
Answer:
The ages at present are:
Age of the son: 7 years oldAge of the daughter: 21 years oldExplanation:
Translate the word language to algebraic expressions.
1) A father who is 42 years old has a son and a daughter.
Age of the father: 422) The daughter is three times as old as the son.
Age of the son: x (this is the variable chosen, x = present age of the son)Age of the dagther: 3x (three times as old as the son, x)3) In 10 years the sum of all their ages will be 100 years
(42 + 10) + (x + 10) + (3x + 10) = 100↑ ↑ ↑ ↑
age of the father age of the son age of the daughter sum
4) How old are the two siblings at present:
Solve the equation
Delete the parenthesis: 42 + 10 + x + 10 + 3x + 10 = 100Combine like terms: 72 + 4x = 100Subtraction property of equalities (subtract 72 from each side)4x = 100 - 72
4x = 28
Division property of equalities (dive both sides by 4)x = 28 / 4
x = 7
5) Answers:
Age of the son: x = 7Age of the daughter: 3x = 3(7) = 216) Verification:
In ten years:age of the son: 7 + 10 = 17
age of the daughter: 21 + 10 = 31
age of the father: 42 + 10 = 52
sum of the ages: 17 + 31 + 52 = 100 ⇒ correct.
Answer: Son’s age:7 Daughter’s age:21
Step-by-step explanation:
1. The daughter is 3 times older than the son. Son will be x. Then the daughter will be 3x
2. In ten years the sum of their ages will be 100. Father+Son+Daughter=(42+10)+(x+10)+(3x+10)=100
3. Solve the equation:
72+4x=100
x=7
4. You have found the age of the son, 7. Now find the daughter. 3*7=21. The daughter is 21.
Success.!
which of the following formulas would find the lateral area of a right cylinder where h is the height and r is the radius
Answers
Answer:
B. [tex]LA=2\pi rh[/tex]
Step-by-step explanation:
The lateral area of the right cylinder refers to the curved surface area.
The lateral area of the right cylinder does not include the two circular bases.
The lateral area is given by the formula;
[tex]LA=2\pi rh[/tex]
The correct choice is B.
Answer:
thats the correct answer =B
Step-by-step explanation:
Researchers in a local area found that the population of rabbits with an initial population of 20 grew continuously at the rate of 5% per month the fox population had an initial value of 30 and grew continuously at the rate of 3% per month. Find, to the nearest tenth of a month, how long it takes for these populations to be equal
Answers
The answer is:
It will take 20.5 months to the populations to be equal.
Why?Since from the statement we know that both populations are growing, we need to use the formula to calculate the exponential growth.
The exponential growth is defined by the following equation:
[tex]P(t)=StartPopulation*e^{\frac{growthpercent}{100}*t}[/tex]
Now,
Calculating for the rabbits, we have:
[tex]StartPopulation=20\\GrowthPercent=5\\[/tex]
So, writing the equation for the rabbits, we have:
[tex]P(t)=20*e^{\frac{5}{100}*t}[/tex]
[tex]P(t)=20*e{0.05}*t}[/tex]
Calculating for the fox, we have:
[tex]StartPopulation=30\\GrowthPercent=3\\[/tex]
So, writing the equation for the fox, we have:
[tex]P(t)=30*e{\frac{3}{100}*t}[/tex]
[tex]P(t)=30*e^{0.03}*t}[/tex]
Then, if we want to calculate how long does it takes for these populations to be equal, we need to make their equations equal, so:
[tex]20*e^{0.05}*{t}=30*e^{0.03}*{t}\\\\\frac{20}{30}=\frac{e^{0.03}*{t}}{e^{0.05}*t}}\\\\0.66=e^{0.03t-0.05t}=e^{-0.02t}\\\\0.66=e^{-0.02t}\\\\ln(0.66)=ln(e^{-0.02t})\\\\-0.41=-0.02t\\\\t=\frac{-0.41}{-0.02}=20.5[/tex]
Hence, we have that it will take 20.5 months to the populations to be equal.
To find out how long it takes for the populations to be equal, set up and solve an equation using the growth rates of the rabbit and fox populations.
Explanation:To find out how long it takes for the rabbit population and the fox population to be equal, we can set up and solve an equation. Let's start by setting up an equation for each population growth:
Rabbit population: P(t) = 20 * (1 + 0.05)^t
Fox population: P(t) = 30 * (1 + 0.03)^t
We want to find the value of t when the two populations are equal, so we set the equations equal to each other and solve for t:
20 * (1 + 0.05)^t = 30 * (1 + 0.03)^t
Divide both sides by 20:
(1 + 0.05)^t = 1.5 * (1 + 0.03)^t
Now take the natural logarithm of both sides:
t * ln(1 + 0.05) = ln(1.5 * (1 + 0.03)^t)
Divide both sides by ln(1 + 0.05):
t = ln(1.5 * (1 + 0.03)^t) / ln(1 + 0.05)
Using a calculator, we can approximate the value of t to the nearest tenth of a month.
Learn more about Population Growth here:https://brainly.com/question/18415071
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SOMEONE HELP MEEEEEE 75 POINTS TO THE PERSON THAT HELPS
1. Indicate the equation of the given line in standard form.
The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5).
2. Indicate the equation of the given line in standard form.
The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).
3. Indicate the equation of the given line in standard form.
The line containing the midpoints of the legs of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.
4. Indicate the equation of the given line in standard form.
The line containing the hypotenuse of right triangle ABC where A(-5, 5), B(1, 1), and C(3, 4) are the vertices.
5. Indicate the equation of the given line in standard form.
The line containing the longer diagonal of a quadrilateral whose vertices are A (2, 2), B(-2, -2), C(1, -1), and D(6, 4).
6. Indicate the equation of the given line in standard form.
The line containing the median of the trapezoid whose vertices are R(-1, 5) , S(1, 8), T(7, -2), and U(2, 0).
7. Indicate the equation of the given line in standard form.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
8. Indicate the equation of the given line in standard form.
The line containing the diagonal of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.
Answers
Answer:
Part 1) [tex]9x-7y=-25[/tex]
Part 2) [tex]2x-y=2[/tex]
Part 3) [tex]x+8y=22[/tex]
Part 4) [tex]x+8y=35[/tex]
Part 5) [tex]3x-4y=2[/tex]
Part 6) [tex]10x+6y=39[/tex]
Part 7) [tex]x-5y=-6[/tex]
Part 8)
case A) The equation of the diagonal AC is [tex]x+y=0[/tex]
case B) The equation of the diagonal BD is [tex]x-y=0[/tex]
Step-by-step explanation:
Part 1)
step 1
Find the midpoint
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M=(\frac{2-6}{2},\frac{-3+5}{2})[/tex]
[tex]M=(-2,1)[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-1=\frac{9}{7}(x+2)\\ \\y=\frac{9}{7}x+\frac{18}{7}+1\\ \\y=\frac{9}{7}x+\frac{25}{7}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=\frac{9}{7}x+\frac{25}{7}[/tex]
Multiply by 7 both sides
[tex]7y=9x+25[/tex]
[tex]9x-7y=-25[/tex]
Part 2)
step 1
Find the midpoint
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M=(\frac{1+5}{2},\frac{0-2}{2})[/tex]
[tex]M=(3,-1)[/tex]
step 2
Find the slope
The slope between two points is equal to
[tex]m=\frac{-2-0}{5-1}=-\frac{1}{2}[/tex]
step 3
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
Find the slope of the line perpendicular to the segment joining the given points
[tex]m1=-\frac{1}{2}[/tex]
[tex]m1*m2=-1[/tex]
therefore
[tex]m2=2[/tex]
step 4
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=2[/tex] and point [tex](1,0)[/tex]
[tex]y-0=2(x-1)\\ \\y=2x-2[/tex]
step 5
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=2x-2[/tex]
[tex]2x-y=2[/tex]
Part 3)
In this problem AB and BC are the legs of the right triangle (plot the figure)
step 1
Find the midpoint AB
[tex]M1=(\frac{-5+1}{2},\frac{5+1}{2})[/tex]
[tex]M1=(-2,3)[/tex]
step 2
Find the midpoint BC
[tex]M2=(\frac{1+3}{2},\frac{1+4}{2})[/tex]
[tex]M2=(2,2.5)[/tex]
step 3
Find the slope M1M2
The slope between two points is equal to
[tex]m=\frac{2.5-3}{2+2}=-\frac{1}{8}[/tex]
step 4
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{8}[/tex] and point [tex](-2,3)[/tex]
[tex]y-3=-\frac{1}{8}(x+2)\\ \\y=-\frac{1}{8}x-\frac{1}{4}+3\\ \\y=-\frac{1}{8}x+\frac{11}{4}[/tex]
step 5
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=-\frac{1}{8}x+\frac{11}{4}[/tex]
Multiply by 8 both sides
[tex]8y=-x+22[/tex]
[tex]x+8y=22[/tex]
Part 4)
In this problem the hypotenuse is AC (plot the figure)
step 1
Find the slope AC
The slope between two points is equal to
[tex]m=\frac{4-5}{3+5}=-\frac{1}{8}[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{8}[/tex] and point [tex](3,4)[/tex]
[tex]y-4=-\frac{1}{8}(x-3)[/tex]
[tex]y=-\frac{1}{8}x+\frac{3}{8}+4[/tex]
[tex]y=-\frac{1}{8}x+\frac{35}{8}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=-\frac{1}{8}x+\frac{35}{8}[/tex]
Multiply by 8 both sides
[tex]8y=-x+35[/tex]
[tex]x+8y=35[/tex]
Part 5)
The longer diagonal is the segment BD (plot the figure)
step 1
Find the slope BD
The slope between two points is equal to
[tex]m=\frac{4+2}{6+2}=\frac{3}{4}[/tex]
step 2
The equation of the line into point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{4}[/tex] and point [tex](-2,-2)[/tex]
[tex]y+2=\frac{3}{4}(x+2)[/tex]
[tex]y=\frac{3}{4}x+\frac{6}{4}-2[/tex]
[tex]y=\frac{3}{4}x-\frac{2}{4}[/tex]
step 3
Convert to standard form
Remember that the equation of the line into standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer, and B, and C are integers
[tex]y=\frac{3}{4}x-\frac{2}{4}[/tex]
Multiply by 4 both sides
[tex]4y=3x-2[/tex]
[tex]3x-4y=2[/tex]
Note The complete answers in the attached file
the variable used to show correlation is r, which is also known as the correlation constant?
A. True
B. False
Answers
Answer:
FALSE
Correlations tell us the strength and the direction of the relationship between two variables. The main result of a correlation is called the correlation coefficient (or "r").
Hope this helps and have a great day!!
[tex]Sofia[/tex]
Answer:false
Step-by-step explanation:
What is the length of the conjugate axis?
[tex]\frac{(x-2)^2}{36} - \frac{(y+1)^2}{64} =1[/tex]
Answers
Answer:
the length of the conjugate axis is 16
Step-by-step explanation:
We know that the general equation of a hyperbola with transverse horizontal axis has the form:
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1[/tex]
Where the point (h, k) are the coordinates of the center of the ellipse
2a is the length of the transverse horizontal axis
2b is the length of the conjugate axis
In this case the equation of the ellipse is:
[tex]\frac{(x-2)^2}{36} + \frac{(y+1)^2}{64} = 1[/tex]
Then
[tex]b^2 = 64\\\\b = \sqrt{64}\\\\b = 8\\\\2b = 16[/tex]
Finally the length of the conjugate axis is 16
Final answer:
The length of the conjugate axis of the given hyperbola \(\frac{(x-2)²}{36} - \frac{(y+1)²}{64} =1\) is 16 units.
Explanation:
The question asks to find the length of the conjugate axis of a hyperbola given by the equation:
\(\frac{(x-2)²}{36} - \frac{(y+1)²}{64} =1\)
In the equation of a hyperbola of the form \(\frac{(x-h)²}{a²} - \frac{(y-k)²}{b²} = 1\), where \((h,k)\) is the center of the hyperbola, \(a²\) is the denominator under the \(x\)-term, and \(b^2\) is the denominator under the \(y\)-term, the length of the transverse axis is \(2a\) and the length of the conjugate axis is \(2b\).
For the given hyperbola:
a² = 36, so \(a = 6\)
b² = 64, so \(b = 8\)
Therefore, the length of the conjugate axis is \(2 \times 8 = 16\) units.
how to find the derivative of x + y2 = ln(x/y) ? please show all workings and simplify!
the answer is supposed to be y^2-x/xy
Answers
Answer:
Step-by-step explanation:
If your function is
[tex]x+y^2=ln(\frac{x}{y} )[/tex], that is definitely not the answer you should get after taking the derivative implicitely. Rewrite your function to simplify a bit:
[tex]x+y^2=ln(x)-ln(y)[/tex]
Take the derivative of x terms like "normal", but taking the derivative of y with respect to x has to be offset by dy/dx. Doing that gives you:
[tex]1+2y\frac{dy}{dx}=\frac{1}{x}-\frac{1}{y}\frac{dy}{dx}[/tex]
Collect the terms with dy/dx on one side and everything else on the other side:
[tex]2y\frac{dy}{dx}+\frac{1}{y}\frac{dy}{dx}=\frac{1}{x}-1[/tex]
Now factor out the common dy/dx term, leaving this:
[tex]\frac{dy}{dx}(2y+\frac{1}{y})=\frac{1}{x}-1[/tex]Now divide on the left to get dy/dx alone:
[tex]\frac{dy}{dx}=\frac{\frac{1}{x}-1 }{2y+\frac{1}{y} }[/tex]
Simplify each set of fractions to get:
[tex]\frac{dy}{dx}=\frac{\frac{1-x}{x} }{\frac{2y^2+1}{y} }[/tex]
Bring the lower fraction up next to the top one and flip it upside down to multiply:
[tex]\frac{dy}{dx}=\frac{1-x}{x}[/tex]×[tex]\frac{y}{2y^2+1}[/tex]
Simplifying that gives you the final result:
[tex]\frac{dy}{dx}=\frac{y-xy}{x(2y^2+1)}[/tex]
or you could multiply in the x on the bottom, as well. Same difference as far as the solution goes. You'd use this formula to find the slope of a function at a point by subbing in both the x and the y coordinates so it doesn't matter if you do the distribution at the very end or not. You'll still get the same value for the slope.