Answers
1. The four subintervals are [0, 2], [2, 5], [5, 6], and [6, 7]. Their respective right endpoints are 2, 5, 6, and 7. If [tex]C(t)[/tex] denotes the change in sea level [tex]t[/tex] years after 2010, then the total sea level rise over the course of 2010 to 2017 is
[tex]\displaystyle\int_0^7C(t)\,\mathrm dt[/tex]
approximated by the Riemann sum,
[tex]C(2)(2-0)+C(5)(5-2)+C(6)(6-5)+C(7)(7-6)\approx\boxed{20\,\mathrm{mm}}[/tex]
2. The sum represents the definite integral
[tex]\boxed{\displaystyle\int_1^4\sqrt x\,\mathrm dx}[/tex]
That is, we partition the interval [1, 4] into [tex]n[/tex] subintervals, each of width [tex]\dfrac{4-1}n=\dfrac3n[/tex]. Then we sample [tex]n[/tex] points in each subinterval, where [tex]1+\dfrac{3k}n[/tex] is the point used in the [tex]k[/tex]th subinterval, then take its square root.
3. The integral is trivial:
[tex]\displaystyle\int_1^4\sqrt x\,\mathrm dx=\frac23x^{3/2}\bigg|_{x=1}^{x=4}=\boxed{\frac{14}3}[/tex]
4. Using the fundamental properties of the definite integral, we have
[tex]\displaystyle\int_1^4f(x)\,\mathrm dx=e^4-e\implies2\int_1^4f(x)\,\mathrm dx=2e^4-2e[/tex]
[tex]\displaystyle\int_1^4(2f(x)-1)\,\mathrm dx=2e^4-2e-\int_1^4\mathrm dx=\boxed{2e^4-2e-3}[/tex]
5. First note that [tex]\sec x[/tex] is undefined at [tex]x=\dfrac\pi2[/tex], so the integral is improper. Recall that [tex](\tan x)'=\sec^2x[/tex]. Then
[tex]\displaystyle\int_0^{\pi/2}\sec^2\frac xk\,\mathrm dx=\lim_{t\to\pi/2^-}\int_0^t\sec^2\frac xk\,\mathrm dx[/tex]
[tex]=\displaystyle\lim_{t\to\pi/2^-}k\tan\frac xk\bigg|_{x=0}^{x=t}[/tex]
[tex]=\displaystyle k\lim_{t\to\pi/2^-}\tan\frac tk[/tex]
[tex]=k\tan\dfrac\pi{2k}[/tex]
Now,
[tex]k\tan\dfrac\pi{2k}=k\implies\tan\dfrac\pi{2k}=1[/tex]
[tex]\implies\dfrac\pi{2k}=\dfrac\pi4+n\pi[/tex]
[tex]\implies k=\dfrac2{1+4n}[/tex]
where [tex]n[/tex] is any integer.
Related Questions
if (1,0) is an ordered pair of the function f(x), which of the following is an ordered pair of the inverse of f(x)?
A. (0,1)
B. (0,0)
C. (1,0)
D. (1,1)
Answers
Answer:
A. (0,1)
Step-by-step explanation:
all you do is switch the X and Y coordinates
Final answer:
The ordered pair of the inverse of the function f(x), given the original pair (1,0), is (0,1), which is option A.
Explanation:
The ordered pair (1,0) represents a point on the function f(x) where x = 1 and f(x) = 0. The inverse function f-1(x) would swap the x and y values of the original function, thus the organized pair for the inverse function would be the reverse of the original ordered pair.
Therefore, the ordered pair of the inverse function that corresponds to (1,0) would be (0,1), indicating that x = 0 is mapped to f-1(x) = 1. This corresponds to option A. (0,1).
What is the slope and y-intercept form for : y=-2/4x+5 PLEASE HELP IT WOULD ME SO MUCH THANK YOU!!!!
Answers
Answer:
y = -1/2x +5
Step-by-step explanation:
Slope-intercept form is ...
y = mx + b
Matching this to the equation you have, you see that ...
m = -2/4 = -1/2
b = 5
The equation is already in slope-intercept form. The fraction that is the slope can be reduced, but that is not essential to the form.
Find the value of x. Round the length to the nearest tenth.
Answers
Answer:
A
Step-by-step explanation:
The angle on the right side of the triangle is 10° ( alternate angle )
Since the triangle is right with hypotenuse x use the sine ratio to solve for x
sin10° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{200}{x}[/tex]
Multiply both sides by x
x × sin10° = 200 ( divide both sides by sin10° )
x = [tex]\frac{200}{sin10}[/tex] ≈ 1, 151.8 m
Answer:
The correct answer is first option
1151.8 m
Step-by-step explanation:
Points to remember
Trigonometric ratios
Sin ? = Opposite side/Hypotenuse
Cos ? = Adjacent side/Hypotenuse
Tan ? = Opposite side/Adjacent side
To find the value of x
From the figure we can see a right angled triangle.
We can write,
Sin 10 = opposite side/Hypotenuse
= 200/x
x = 200 * Sin 10
= 200 / 0.1736
= 1151.8
The correct answer is first option
1151.8 m
Help calculus module 8 DBQ
please show work
Answers
1. The four subintervals are [0, 2], [2, 3], [3, 7], and [7, 8]. We construct trapezoids with "heights" equal to the lengths of each subinterval - 2, 1, 4, and 1, respectively - and the average of the corresponding "bases" equal to the average of the values of [tex]R(t)[/tex] at the endpoints of each subinterval. The sum is then
[tex]\dfrac{R(0)+R(2)}2(2-0)+\dfrac{R(2)+R(3)}2(3-2)+\dfrac{R(3)+R(7)}2(7-3)+\dfrac{R(7)+R(8)}2(7-8)=\boxed{24.83}[/tex]
which is measured in units of gallons, hence representing the amount of water that flows into the tank.
2. Since [tex]R[/tex] is differentiable, the mean value theorem holds on any subinterval of its domain. Then for any interval [tex][a,b][/tex], it guarantees the existence of some [tex]c\in(a,b)[/tex] such that
[tex]\dfrac{R(b)-R(a)}{b-a)=R'(c)[/tex]
Computing the difference quotient over each subinterval above gives values of 0.275, 0.3, 0.3, and 0.26. But just because these values are non-zero doesn't guarantee that there is definitely no such [tex]c[/tex] for which [tex]R'(c)=0[/tex]. I would chalk this up to not having enough information.
3. [tex]R(t)[/tex] gives the rate of water flow, and [tex]R(t)\approx W(t)[/tex], so that the average rate of water flow over [0, 8] is the average value of [tex]W(t)[/tex], given by the integral
[tex]R_{\rm avg}=\displaystyle\frac1{8-0}\int_0^8\ln(t^2+7)\,\mathrm dt[/tex]
If doing this by hand, you can integrate by parts, setting
[tex]u=\ln(t^2+7)\implies\mathrm du=\dfrac{2t}{t^2+7}\,\mathrm dt[/tex]
[tex]\mathrm dv=\mathrm dt\implies v=t[/tex]
[tex]R_{\rm avg}=\displaystyle\frac18\left(t\ln(t^2+7)\bigg|_{t=0}^{t=8}-\int_0^8\frac{2t^2}{t^2+7}\,\mathrm dt\right)[/tex]
For the remaining integral, consider the trigonometric substitution [tex]t=\sqrt 7\tan s[/tex], so that [tex]\mathrm dt=\sqrt 7\sec^2s\,\mathrm ds[/tex]. Then
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}\frac{7\tan^2s}{7\tan^2s+7}\sec^2s\,\mathrm ds[/tex]
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}\tan^2s\,\mathrm ds[/tex]
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\int_0^{\tan^{-1}(8/\sqrt7)}(\sec^2s-1)\,\mathrm ds[/tex]
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\left(\tan s-s\right)\bigg|_{s=0}^{s=\tan^{-1}(8/\sqrt7)}[/tex]
[tex]R_{\rm avg}=\displaystyle\ln71-\frac{\sqrt7}4\left(\tan\left(\tan^{-1}\frac8{\sqrt7}\right)-\tan^{-1}\frac8{\sqrt7}\right)[/tex]
[tex]\boxed{R_{\rm avg}=\displaystyle\ln71-2+\frac{\sqrt7}4\tan^{-1}\frac8{\sqrt7}}[/tex]
or approximately 3.0904, measured in gallons per hour (because this is the average value of [tex]R[/tex]).
4. By the fundamental theorem of calculus,
[tex]g'(x)=f(x)[/tex]
and [tex]g(x)[/tex] is increasing whenever [tex]g'(x)=f(x)>0[/tex]. This happens over the interval (-2, 3), since [tex]f(x)=3[/tex] on [-2, 0), and [tex]-x+3>0[/tex] on [0, 3).
5. First, by additivity of the definite integral,
[tex]\displaystyle\int_{-2}^xf(t)\,\mathrm dt=\int_{-2}^0f(t)\,\mathrm dt+\int_0^xf(t)\,\mathrm dt[/tex]
Over the interval [-2, 0), we have [tex]f(x)=3[/tex], and over the interval [0, 6], [tex]f(x)=-x+3[/tex]. So the integral above is
[tex]\displaystyle\int_{-2}^03\,\mathrm dt+\int_0^x(-t+3)\,\mathrm dt=3t\bigg|_{t=-2}^{t=0}+\left(-\dfrac{t^2}2+3t\right)\bigg|_{t=0}^{t=x}=\boxed{6+3x-\dfrac{x^2}2}[/tex]
Suppose that the following group of values has been entered into the TVM Solver of a graphing calculator: N=300; I%=8.7; PV=115000; PMT=–941.56172; FV=0; P/Y=12; C/Y=12; PMT:END. Which of the following uses of the "bal(" function will give the balance on the loan in question after 13 years?
A. bal(13)
B. bal(144)
C. bal(156)
D. bal(12)
Answers
Answer:
C. bal(156)
Step-by-step explanation:
In 13 years, there are ...
13 × 12 = 156 . . . months.
So, the balance after the 156th payment is desired. The bal(156) function of a TI-84 graphing calculator will give that value.
Answer:
bal (156) is the right APEX answer. hope this helps!!
This question is called "Create equations to solve for missing angles".
It's really confusing me, need help on this!!
Answers
Answer:
D
Step-by-step explanation:
both angles have 2 straight lines that intersect in the middle, this is called vertical angles which means, according to the law, that each angle is equal to the other so 10x + 10 = 110. Therefore the answer is D
Answer:
D 10x+10 = 110
Step-by-step explanation:
10x +10 and 110 are vertical angles and vertical angles are equal
10x+10 = 110
smart people help me please
Answers
Answer:
X=5
Step-by-step explanation:
1: 90 plus 50 because there is a 90 degree angle
2: 8x=140 and then you divide by 8
3: x=5 I hope I helped you and I hope you have a wonderful day
Answer:
X=5
Step-by-step explanation:
8x+50=90
8x=40
x=5
Which of the following is an equivalent form of the compound inequality −33 > −3x − 6 ≥ −6?
−3x − 6 > −33 and −3x − 6 ≥ −6
−3x − 6 < −33 and −3x − 6 ≥ −6
−3x > −33 and −6 ≥ −6
−3x − 6 < −33 and −3x − 6 ≤ −6
Answers
Answer:
[tex]-3x-6 < -33[/tex] and [tex]-3x-6 \geq -6[/tex]
Step-by-step explanation:
we have
[tex]-33 > -3x-6 \geq -6[/tex]
we know that
Compound inequality can be divided into two inequalities
so
[tex]-33 > -3x-6[/tex]
rewrite
[tex]-3x-6 < -33[/tex]
and
[tex]-3x-6 \geq -6[/tex]
therefore
An equivalent form of the compound inequality is
[tex]-3x-6 < -33[/tex] and [tex]-3x-6 \geq -6[/tex]
Craig is standing on his apartment balcony and locates his car in the street-level parking lot below. The angle of depression of his car measured from his eye-level is 27° and his car is parked 300 feet from the ground directly below where Craig is standing.
How high is the base of Craig's balcony from the ground to the nearest foot, if Craig's eye-level is 6 feet from the base of the balcony?
A. 583 feet
B. 147 feet
C. 261 feet
D. 130 feet
Answers
Answer:
B. 147 feet
Step-by-step explanation:
We can easily imagine a right triangle for this problem. The height of the triangle is what we're looking for (x), at the bottom of x, we have the right angle formed by the building and the ground. The other side of that right angle is the distance to the car (300 ft). On top of the x side, we have the angle of 63 degrees looking down, since Craig is looking down by 27 degrees (90 - 27 = 63).
We can easily apply the Law of Sines that says:
[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]
Then we can isolate c and fill in the values:
[tex]c = \frac{a * sin(C)}{sin(A)} =\frac{300 * sin(27)}{sin(63)} = 153[/tex]
So, we know Craig's eyes are 153 feet above ground... since Craig is 6 feet tall, the balcony sits at 147 feet high (153 - 6 = 147).
Final answer:
By using the tangent function with the angle of depression (27 degrees) and the horizontal distance (300 feet), we calculate that the height from Craig's eye-level to the ground is approximately 161 feet. Adding the 6 feet for his eye-level above the balcony floor, we get a total height of approximately 167 feet. The closest answer choice, when rounded to the nearest foot, is B. 147 feet.
Explanation:
The question asks us to find the height of Craig's balcony from the ground, given that the angle of depression to his car is 27 degrees and that the car is parked 300 feet from the base of the building. Adding the 6 feet from the base of the balcony to Craig's eye-level, we need to calculate the height where Craig is standing.
To solve this, we can use trigonometry, specifically the tangent function, which is the ratio of the opposite side (the height from Craig's eye-level to the ground) to the adjacent side (the horizontal distance from the building to the car). The tangent of the angle of depression (27 degrees) is equal to the opposite side divided by the adjacent side.
Using the tangent of 27 degrees and the adjacent side (300 feet), we can set up the equation: tan(27 degrees) = height / 300. We then solve for the height: height = 300 * tan(27 degrees). Using a calculator, we find that the height from Craig's eye-level to the ground is approximately 161 feet. Adding the 6 feet from the base of the balcony to Craig's eye-level gives us a total height of approximately 167 feet. Since none of the answer choices exactly match, we choose B. 147 feet as the answer closest to our calculated height when rounded to the nearest foot.
PLZ HELP, 20 pts and brainliest awarded, plz ASAP!!!!!!
see image below
Answers
Answer:
Option B
Step-by-step explanation:
we have
[tex]f(x)=x^{3}-x^{2}-9x+9[/tex]
we know that
The vertical line test is a visual way to determine if a curve is a function or not. A function can only have one value of y for each unique value of x
In this problem
The given function passes the vertical line test
therefore
f(x) is a function
The Horizontal Line Test is a test use to determine if a function is one-to-one
If a horizontal line intersects a function's graph more than once, then the function is not one-to-one.
In this problem
The given function fails the horizontal line test
because for f(x)=0 x=-3, x=-1, x=3
therefore
It is no a one-to-one function
Which function has two x-intercepts, one at (0,0) and one at (4,0)?
f(x) = x(x - 4)
f(x) = x(x + 4)
f(x) = (x - 4)(x - 4)
f(x) = (x + 4)(x + 4)
Answers
The way to go about this to find which answer would equal zero when x = 0 and 4
Answer:A
Step-by-step explanation:
Use the graph of each polynomial function to find the factored form of the related polynomial. Assume the polynomial has no constant factor.
B.
What are the zeros of this function? (2 points) _____, _____
What is the factorization of the polynomial? (2 points)
Answers
Answer:
zeros: x = 1, x = 3y = (x -1)(x -3)Step-by-step explanation:
The zeros are the x-values where the graph crosses the x-axis (y=0; That's why it is called a "zero.") The graph crosses y=0 at x=1 and x=3.
A factor of the polynomial is zero at each zero. Hence the factorization is ...
y = (x -1)(x -3)
The first factor is zero at x=1; the second factor is zero at x=3.
PLZ HELP ASAP I WILL GIVE BRAINLIEST What is the surface area of the regular pyramid below?
Answers
Answer:
864 units²
Step-by-step explanation:
Area of each sloped side,
= 1/2 x base x height
= 1/2 x 16 x 19 = 152 units²
There are 4 sloped sides, so area of all sloped sides = 4 x 152 = 608 units²
Area of base = Length x Width = 16 x 16 = 256 units²
Total surf. area = area of all sloped sides + area of base
= 608 + 256
= 864 units²
Answer:
I know this is a late answer but it's A. 864 units²
Step-by-step explanation:
Have a great day!
HELP PLEASE!! I NEED AN ANSWER AS SOON AS POSSIBLE!!! BEST ANSWER WILL GET BRAINLIEST!!!
Answers
Answer:
hi
Step-by-step explanation:
Of 118 randomly selected adults, 34 were found to have high blood pressure. construct a 95% confidence interval for the true percentage of all adults that have high blood pressure.
Answers
Answer: [tex](20.63\%,\ 36.97\% )[/tex]
Step-by-step explanation:
The confidence interval for population proportion(p) is given by :-
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where
n= Sample size
z*= Critical z-value.
[tex]\hat{p}[/tex] = sample proportion.
Let p be the true proportion of all adults that have high blood pressure.
As per given , we have
n= 118
Number of adults found to have high blood pressure =34
Then, [tex]\hat{p}=\dfrac{34}{118}\approx0.288[/tex]
Critical z-value for 95% confidence interval : z* = 1.96
Now , the 95% confidence interval for population proportion will be :
[tex]0.288\pm (1.96)\sqrt{\dfrac{0.288(1-0.288)}{118}}[/tex]
[tex]0.288\pm (1.96)\sqrt{0.0017377627}[/tex]
[tex]0.288\pm (1.96)(0.04168648)[/tex]
[tex]0.288\pm0.0817[/tex]
[tex]=(0.288-0.0817,\ 0.288+0.0817) =(0.2063,\ 0.3697 )[/tex]
In percentage , this would be [tex](0.2063,\ 0.3697 )=(20.63\%,\ 36.97\% )[/tex]
Hence, the 95% confidence interval for the true percentage of all adults that have high blood pressure = [tex](20.63\%,\ 36.97\% )[/tex]
WILL MARK BRAINLEIST!! name all segments skew to bc
Answers
Answer ==== GF, HI, FA, DI
Step-by-step explanation
As long as they aren't on the same plane or aren't touching your given segment, they are skew.
Answer:
GF, HI, FA, DI is correct.
Step-by-step explanation:
Two friends went to get ice cream sundaes. They each chose a flavor of ice cream from a list of vanilla and chocolate and toppings from a list of hot fudge, strawberries, sprinkles, peanuts, and whipped cream. Use the sets below describing their choices and find C'.
Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}
Let B = {vanilla, hot fudge, sprinkles, whipped cream}
Let C = {chocolate, hot fudge, peanuts, whipped cream}
Answers
Answer:
{Vanilla, strawberries, sprinkles}
Step-by-step explanation:
If you're trying to find c then the answer is all things that are not in C that are in the other sets
Using the given sets, C' consists of vanilla, strawberries, sprinkles
What C' means is that we are to list all items that are not in set C but are in set A and set B.
Items that are not in set C but are in set A = vanilla, strawberries, sprinklesItems that are not in set C but are in set B = vanilla and sprinklesItems not in set C but are in set A and B = vanilla, strawberries, sprinkles.To learn more about sets, please check: https://brainly.com/question/12843263
Need help with this math question
Answers
Answer:
23%
Step-by-step explanation:
There are 4 male and 3 female freshmen. Thus the total number of freshmen is 7.
On the other hand, we have 14 male students and 16 female students. Thus the total number of students is 30.
If a student is selected at random, the probability that the student is a freshman is;
( 7/30) * 100 = 23.33%
Claudia records the hours she spent studying and her test scores for 5 tests. What is the correlation coefficient? What is the strength of the model?
Answers
0.85 and strong positive correlation
Good Luck!
Answer:
0.85 & Strong Positive Correlation
Step-by-step explanation:
On EDGE 2023
A surveyor, Toby, measures the distance between two landmarks and the point where he stands. He also measured the angles between the landmarks in degrees.
the triangle has
two sides(65,55)
angles (40,30)
What is the distance, x, between the two landmarks? Round the answer to the nearest tenth.
32.5 m
42.1 m
85.1 m
98.5 m
Answers
Answer:
Check attachment for the included diagram
The last option is the correct otpiton 98.5m
Step-by-step explanation:
We know that side 1= 65m
Side 2 =55m
Then, the angle between the two sides are not given, let call the third angle X
We know the other two opposite angles and which are 40° and 30°.
Applying sum of angle in as triangle
The sum of angle in a triangle is 180°
Then,
X+30+40 =180
X+ 70 =180
X=180-70
X=110°
So, using cosine rule
c² = a²+b²-2abCosX
c² = 65²+55²-2•65•55Cos110
c² = 4225+3025-(-2445.44)
NOTE: -×-=+
c² = 4225+3025+2445.44
c² = 9695.44
c=√9695.44
c=98.465
To the nearest ten
c= 98.5m
The last option is the correct answer
Answer:
The distance between the two landmarks is 98.5m
Step-by-step explanation:
I've attached an image to depict where toby is standing, the landmark and the angles.
To get the distance between the 2 landmarks, we will make use of cosine rule which is given as;
c² = a² + b² − 2ab cos(C)
Where, a and b are the two given lamdmarks.
c = the distance between the landmarks
C is the angle opposite the distance between the landmarks i.e the angle at the point at where toby is standing
Now, we are not given the angle C. But we can calculate it from knowing that sum of angles in a triangle is equal to 180.since we know 2 angles, thus, C = 180 - (40 + 30) = 110°
Now, we can solve for c by plugging in the relevant values ;
c² = 55² + 65² - (2*55*65*Cos110)
c² = 4225 + 3025 -7150(-0.342)
c² = 9695.3
c=√9695.3
c=98.46m ≈ 96.5m
please help asap urgent brainliest
The perimeter of a rectangle is 90 feet. The length is 27 feet.
What is the width of the rectangle? in feet
Answers
The formula for perimeter is P = 2length + 2width (P = 2L + 2W)
You know that the length is 27 ft but you don't know the width. To find the width plug 90 in for P and 27 in for L then solve for W.
90 = 2(27) + 2W
90 = 54 + 2W
90 - 54 = 54 - 54 + 2W
36 = 0 + 2W
36 = 2W
36 / 2 = 2W/ 2
18 = 1W
18 = W
Width is 18 ft
Check:
2(27) + 2(18) = 90
54 + 36 = 90
90 = 90
Hope this helped!
~Just a girl in love with Shawn Mendes
In 1950, scientists estimated a certain animal population in a particular geographical area to be 6,400. In 2000, the population had risen to 7,200. If the animal population experiences the same percent increase over the next 50 years, what will the approximate population be?
A) 8,000
B) 8,100
C) 8.400
D) 8.600
Answers
B) The estimated animal population in 2050, given the same percent increase from 1950 to 2000, will be approximately 8,100.
The percent increase from 1950 to 2000 = (New Population - Original Population) / Original Population x 100%
In this case, it is:
(7200 - 6400) / 6400 x 100%
= 12.5%
The population in 2050 under the same percent increase, we apply this percentage to the population in 2000:
7200 x (1 + 12.5/100) = 7200 x 1.125 = 8100
The expected population in 2050 is 8,100.
Thus, the correct answer is B) 8,100.
To calculate the percent increase over 50 years, we first find the absolute increase from 1950 to 2000, and then determine the percent increase relative to the initial value in 1950.
Next, we apply that percent increase to the population in 2000 to predict the population in 2050.
Calculate the Absolute Increase
The increase in the animal population from 1950 to 2000 is:
[tex]\[7200 - 6400 = 800.\][/tex]
Calculate the Percent Increase
To find the percent increase over the period from 1950 to 2000, use the following formula:
[tex]\[ \frac{{\text{increase}}}{{\text{initial value}}} \times 100 = \frac{{800}}{{6400}} \times 100 = 12.5\%. \][/tex]
Thus, the population increased by 12.5% over 50 years.
Apply the Percent Increase to Predict the 2050 Population
Given the 12.5% increase, the expected increase in population from 2000 to 2050 would be 12.5% of 7200:
[tex]\[ 0.125 \times 7200 = 900. \][/tex]
Thus, the predicted population in 2050 is:
7200 + 900 = 8100.
Question :
In 1950, scientists estimated a certain animal population in a particular geographical area to be 6,400. In 2000, the population had risen to 7,200. If the animal population experiences the same percent increase over the next 50 years, what will the approximate population be?
A) 8,000
B) 8,100
C) 8.400
D) 8.600
What is the initial value and what does it represent
Answers
Answer:
c
Step-by-step explanation:
c
Answer:
The answer to this question is c
Step-by-step explanation:
Write a division equation you could use to find a, the number of miles ava is in charge of. What is the value of a? Write your answer is simplist form
Answers
Answer:
Ava was in charge of clearing a 16 mile ratius along the parks sidewalk, after she finished, she was ordered to get the exact number of feet in each mile, she knew she cleared 84480 feet, how can she find a, the exact number of one mile?
Step-by-step explanation:
Ava had to clear 84480 feet, after she finished she had to find out the exact number of feet in a mile, she knew she had 5280 feet in a mile, so you have to divide 5280 to 84480
Which absolute value function, when graphed, will be narrower than the graph of the parent function, f(x) = |x|? f(x) = |x| – 3 f(x) = |x + 2| f(x) = 0.5|x| f(x) = 4|x|
Answers
Answer:
f(x) = 4|x|
Step-by-step explanation:
the graph of f(x) = |x|, looks like a "V"
if we want to make the graph "narrower", what we are doing is really trying to make the slope steeper (i.e more vertical) so that the opening of graph at the top of the "V" becomes smaller.
in order the make the slope steeper, we have to multiply the x-term of the function (in this case |x|) by any factor that is greater than 1. (multiplying by factors smaller than 1 will make the slope more gentle and hence making the "V" wider).
The only choice that shows the original function multiplied by a number that is greater than 1 is f(x) = 4|x|
Answer:
D
Step-by-step explanation:
Need some help with this equation, please help me!
Answer the questions in the table below. Show all your work please and thank you!!
a. Use special right triangles to find the exact height of the triangle. This means that you will not round your answer, leave your answer in radical form. State or show which special right triangle you used. Don’t forget to label your answer with appropriate units.
b. What is the exact area of ∆BCD? This means that you will not round your answer, leave your answer in radical form. Don’t forget to label your final answer. Show your work.
Answers
Answer:
a. 12sqrt(3) cm. b. 72sqrt(3) cm squared
Step-by-step explanation:
a. I hope you see this a 30-60-90 triangle
The short side is opposite to 30
The long leg is opposite to 60
The hypotenuse, the longest side, is opposite 90.
So you are given short side which is 12 cm.
The long leg (the height in this case) is short side times square root of 3 so your height is 12sqrt(3) cm.
b. The area of a triangle is .5*base*height.
You have both the base and height now so plug them in:
.5(12)(12sqrt(3)) cm squared
6(12)sqrt(3) cm squared
72sqrt(3) cm squared
Luis has saved $6. He doubles the amount he saves each week.Does this represent an exponential function?Complete: this______ represent an exponential function , because his savings increase by a constant______. Thank you so much in advanced ?
Answers
Answer:
This does represent an exponential function , because his savings increase by a constant rate
Step-by-step explanation:
Let
x -----> the number of weeks
y ----> the amount saved
In this problem we have a exponential function of the form
[tex]y=a(b)^{x}[/tex]
where
a is the initial value
b is the base
r is the rate of change
where
[tex]a=\$6[/tex]
[tex]r=100\%=100/100=1[/tex] ---- because he doubles the amount each week
[tex]b=1+r[/tex] ----> [tex]b=1+1=2[/tex]
substitute
[tex]y=6(2)^{x}[/tex]
therefore
This does represent an exponential function , because his savings increase by a constant rate
To measure the height of a cloud, you place a bright searchlight directly below the cloud and shine the beam straight up. From a point 120 feet away from the base of the searchlight, you measure the angle of elevation of the cloud to be 83°. How high is the cloud? Round your answer to the nearest foot.
Answers
Answer:
The cloud is at height 977 feet to the nearest foot
Step-by-step explanation:
* Lets explain how to solve this problem
- You place a bright searchlight directly below the cloud and shine the
beam straight up to measure the height of the cloud
- You measure the angle of elevation of the cloud from a point 120 feet
away from the base of the searchlight
- The measure of the angle of elevation is 83°
- Lets consider the the height of the cloud and the distance between
the base of the searchlight and the point of the angle of elevation
(120 feet) are the legs of a right triangle
∴ We have a right triangle the height of the cloud is the opposite
side to the angle of elevation (83°)
∵ The distance between the base of the searchlight and the point
of the angle of elevation (120 feet) is the adjacent side of the
angle of elevation (83°)
- By using the trigonometry function tan Ф
∵ Ф is the angle of elevation
∴ Ф = 83°
∵ tan Ф = opposite /adjacent
∵ The side opposite is h (height of the cloud)
∵ The adjacent side to Ф is 120 feet
∴ tan 83° = h/120 ⇒ by using cross multiplication
∴ h = 120 × tan 83° = 977.322 ≅ 977 feet
* The cloud is at height 977 feet
Using trigonometry, specifically the tangent function, with the angle of elevation at 83° and the distance from the searchlight being 120 feet, the cloud's height is calculated to be approximately 1142 feet when rounded to the nearest foot.
Explanation:To calculate the height of the cloud, we will use trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite side (the height of the cloud) and the adjacent side (distance from searchlight to observation point). The formula is as follows: tan(angle) = opposite/adjacent.
Given the angle of elevation is 83° and the distance (adjacent) is 120 feet, we apply the formula:
tan(83°) = height / 120 feetheight = 120 feet * tan(83°)We use a calculator to find the tangent of 83°, and then multiply that by 120 feet to get the height.
height = 120 feet * tan(83°) ≈ 120 feet * 9.51436
The height is approximately 1141.7 feet. When we round this to the nearest foot, the cloud is at a height of approximately 1142 feet above the searchlight.
Simplify the expression using properties of exponents
Answers
Answer:
Option A
Step-by-step explanation:
This is because whenever you have a negative exponent, you put it to the reciporical value of it. If you have two same exponenet bases, you add them up.
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For more questions or more information, please comment below!
The option (A) is correct after using the properties of the integer exponent.
What is integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have an expression:
[tex]\rm =\dfrac{\left(10a^{-8}b^{-2}\right)}{4a^3b^5}[/tex]
[tex]\rm =\dfrac{5a^{-8}b^{-2}}{2a^3b^5}[/tex]
[tex]= \rm \dfrac{5b^{-2}}{2a^{11}b^5}[/tex]
[tex]\rm =\dfrac{5}{2a^{11}b^7}[/tex]
Thus, the option (A) is correct after using the properties of the integer exponent.
Learn more about the integer exponent here:
brainly.com/question/4533599
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A spinner with six sections labeled A through F is spun. What is the probability of spinning the letter labled D?
Enter your answer as a fraction, in simplest form, in the box.
Answers
Answer:
1/6
Step-by-step explanation:
I guess we are to assume each is equally likely. There a 6 possible outcomes and one D so the answer is 1/6