let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.
[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}[/tex]
now let's check for the asymptotes.
[tex]\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2[/tex]
Which line of music shows a glide reflection
choices are below
The first line of music shows a glide reflection from all the lines.
What is a glide reflection?A glide reflection is one of the types of reflection in 2-dimensional geometry.
It is a symmetry figure that consists of a reflection over a line and then translates along the line.
In this figure, the first option shows the exact symmetry operation and reflection. but the second and third line doesn't represent a glide reflection.
In the second option, the reflection does not take place, the music lines are the same before and after.
In the third option, the music lines are just interchanged which doesn't prove the glid reflection.
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Please help...........
Answer:
x=18
Step-by-step explanation:
The two triangles are similar. The ratio of the sides are the same.
20/20=40/(40+x)
Cross multiply and solve. Hint: the easiest way to solve is to simplify, then solve.
Graph the lines 2x=-y+7 and 2y=-4x+10. What is the solution?
A) (0,5)
B) (5/2, 5)
C) No solution
C) no solution
use desmos.com to help with these problems
Answer: Option C
C) No solution
Step-by-step explanation:
To graph both lines identify the cut points with the axes
For [tex]2x = -y + 7[/tex]
The intersection with the x axis is:
[tex]2x = -(0) +7\\\\x = 3.5[/tex]
The intersection with the y axis is:
[tex]2 (0) = -y +7\\\\y = 7[/tex]
Draw a line that cuts the y-axis in 7 and the x-axis in 3.5
For [tex]2y = -4x + 10[/tex]
The intersection with the x axis is:
[tex]2 (0) = -4x +10\\\\4x = 10\\\\x = 2.5[/tex]
The intersection with the y axis is:
[tex]2y = -4 (0) +10\\\\y = 5[/tex]
Draw a line that cuts the y-axis in 5 and the x-axis in 2.5
The intersection of both lines will be the solution of the system. Observe the attached image
The lines are parallel, so they never intercept. Therefore the system has no solution
which is the value of the expression ((10^4)(5^2)/(10^3)(5^3))^3
Answer:
8
Step-by-step explanation:
Let's set this up to see if we can simplify it a bit:
[tex](\frac{10^4*5^2}{10^3*5^3})^3[/tex]
Notice we have 4 tens on top and 3 on bottom, so we can eliminate the bottom 3 altogether and leave just one on top. And we have 2 fives on the top and 3 on bottom, so we can eliminate the 2 on the top and leave one on the bottom. Now that looks like this:
[tex](\frac{10}{5})^3[/tex]
10 divided by 5 is 2, and 2 cubed is 8
Final answer:
To find the value of the expression ((10⁴)(5²)/(10³)(5³))³, we simplify the powers of 10 and 5 and then raise the result to the power of 3, obtaining the final answer of 8.
Explanation:
To solve the expression ((10⁴)(5²)/(10³)(5³))³, we start by simplifying inside the parentheses. We use the properties of exponents to divide the powers of tens and fives separately:
10⁴ / 10³ = 10⁽⁴⁻³⁾ = 10¹ = 105² / 5³ = 5⁽²⁻³⁾ = 5⁻¹ = 1/5So the inside of the parentheses simplifies to (10 * 1/5) which is 2. Then, we raise 2 to the power of 3 as indicated by the expression:
(2)^3 = 2*2*2 = 8
Therefore, the value of the expression ((10⁴)(5²)/(10³)(5³))³ is 8.
The probability that traffic lights on a certain road will be green is 0.6. When a driver on that road approaches two traffic lights in a row, X is the number of traffic lights that are green. What is P(X=1)? Enter your answer, as a decimal, in the box. P(X=1) =
There are two possible ways for X=1: first light is green and second is red OR first light is red and second is green. The probabilities for these two options are to be summed: 0.6*0.4 + 0.4*0.6 to give the probability of exactly one light being green, namely 0.48.
P(X = 1) = 0.48
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
What is binomial distribution?"It is a probability distribution that gives only two possible results in an experiment, either success or failure. "
The formula of Binomial distribution:[tex]P(x)=n_C_x\times (p)^{x}\times (q)^{n-x}[/tex], here n is the total number of outcomes, 'p' is the probability of success and 'q' is the probability of failure
For given example,
The probability that traffic lights on a certain road will be green is 0.6
This means, the probability of success (p) = 0.6
So, the probability of failure (q) = 1 - p
q = 0.4
When a driver on that road approaches two traffic lights in a row, X is the number of traffic lights that are green.
here, n = 2, p = 0.6, q = 0.4, x = 1
Using the formula of Binomial distribution the required probability is,
[tex]P(x=1)=2_C_1\times (0.6)^{1}\times (0.4)^{2-1}\\\\P(x=1)=\frac{2!}{1!\times (2-1)!}\times 0.6\times 0.4^1\\\\P(x=1)=2\times 0.6\times 0.4\\\\\bold{P(x=1)=0.48}[/tex]
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Find the missing values of the variables. The diagram is not to scale.
X=93 degrees
Y=74 degrees
A right cone has radius 2 ft and slant height 5 ft. The radius and slant height are both multiplied by 1/4. Which of the following correctly describes the effect on the surface area?
The surface area is multiplied by 8.
The surface area is multiplied by 1/16.
The surface area is multiplied by 16.
The surface area is multiplied by 1/8.
k = coefficient of similarity for lengths
k ^ 2 = coefficient of similarity for surfaces
k ^ 3 = coefficient of similarity for volumes
[tex]\displaystyle\bf\\ \text{Coefficient of similarity for lengths}=~k=\frac{1}{4}\\\\\implies~\text{Coefficient of similarity for surfaces}=k^2=\left(\frac{1}{4}\right)^{\b2}=\boxed{\bf\frac{1}{16}}[/tex]
⇒ The surface area is multiplied by 1/16When both the radius and slant height of a right cone are multiplied by 1/4, the effect on the surface area is that it is multiplied by 1/16.
Explanation:In the case of a right cone, the total surface area is given by the formula πr(r + l), where r is the radius and l is the slant height. If both the radius and slant height are multiplied by 1/4, then the new surface area becomes π(1/4r)((1/4r)+(1/4l)) = π(1/16)r(r+l). This tells us our new surface area is 1/16 of the original surface area.
Therefore, the correct effect on the surface area when both the radius and slant height of a right cone are multiplied by 1/4 is that the surface area is multiplied by 1/16.
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y+7=4(x-3) in standard form
If x - 3 is a factor of P(x)=x^3-7x^2+15-9, which of the following represents the complete factorization for P(x)
A.(x-3)(x+3)(x+1)
B.(x-3)(x+4)(x+1)
C.(x-3)(x+3)(x-1)
D.(x-3)(x-3)(x-1)
Answer:
Option D.
Step-by-step explanation:
Given that (x-3) is a factor of P(x)=x^3-7x^2+15x-9. If we divide the P(x) by (x-3) we will get a second grade polynomial, which is easier to factorize.
Dividing x^3-7x^2+15x-9 by (x-3), the answer is: x^2 - 4x + 3 with a remainder of zero.
Now, to factorize x^2-4x+3 we just need to find two numbers that equal -4 when added and 3 when multiplied. These two numbers are -1 and -3.
So the complete factorization of P(x) is: (x-3)(x-1)(x-3)
Which is option D.
Answer: D. (x-3)(x-3)(x-1)
Step-by-step explanation:
At East Side Middle school, 3/4 of the students ride the bus to school. What percent of the students ride the bus?
Answer:
75%
Step-by-step explanation:
3/4=0.75
Percent: 75%
Your answer would be 75%
A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent. g
Answer:
$ 163.54Explanation:
1) Write the model for the volume and base area of the rectangular sotorage container:
Base area, B = base length × base widthbase width, w = x
base length, l = 2x
B = (2x) (x) = 2x²
Volume, V = base area × height = 10 m³height = h
V = 2x² h = 10 ⇒ h = 10 / (2x²)
2) Total area, A
Base, B = 2x²Side 1, S₁S₁ = (x) . (h) = (x) . 10 / (2x²) = 10 / (2x) = 5 / x
Side 2, S₂S₂ = S₁ = 5 / x
Side 3, S₃S₃ = (2x) . (h) = (2x) . 10 / (2x²) = 10 / x
Side 4, S₄S₄ = S₃ = 10 / x
3) Cost
Material for the base:$ 10 (2x²) = 20x²
Material for the sides$6 (S₁ + S₂ + S₃ + S₄) = 6 (5/x + 5/x + 10/x + 10/x ) = 6 ( 30/x) = 180/x
Total cost = 20x² + 180 / x4) Cheapest container
Minimum cost ⇒ find the minimum of the function 20x² + 180 / x, which formally is done by derivating the function and making the derivative equal to zero.
Derivative: (20x² + 180 / x)' = 40x - 180 / x² = 0Solve to find the value of x that makes the first derivative equal to zero:
40x - 180 / x² = 0Assume x ≠ 0 and multiply by x² : 40x³ - 180 = 0Add 180 to both sides: 40x³ = 180Divide by 40: x³ = 4.5Cubic root: x = 1.65Replace x = 1.65 in the equations of costs to find the minimum cost:
20x² + 180 / x = 20 (1.65)² + 180 / (1.65) = 163.54That is the final answer, already rounded to the nearest cent: $163.54
The question is about the optimization of the costs for constructing a rectangular container with a specific volume of 10 m^3. This is done by creating equations for volume and cost, and then optimizing the cost using calculus.
Explanation:The subject of this question is Optimization in Calculus. Here, we trying to minimize the cost of a rectangular storage container with given constraints. First, we need to setup equations for the volume, V = length x width x height and cost, as given. Since the volume of the box is fixed at 10 m3 and given that the length is twice the width we have:
Volume, V = lwh = 2w^2h = 10 m^3Cost, C = base cost + sides cost = $10(2w^2) + $6(2w(2h)+wh)We solve for h in terms of w from the volume equation and substitute it in the cost, we can then take the derivative of the cost equation and solve it to get the width. Lastly, we plug the width value in the cost equation to get the minimal cost.
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Please help me with this
Answer:
x = 18
Step-by-step explanation:
The parts of the triangles are proportional, so you can write ...
2x/80 = 27/60
Multiply by 120:
3x = 54
Divide by 3:
x = 18
Sketch the graph of y= 2(x-2)^2 +5 and identify the axis of symmetry.
Answer:
x = 2
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
use the Vertex form, Y=a(x-h)^2+k, to determine the values of a, h, and k.
a=2
h=2
k=5
since the values of a are positive the parabola opens up
Find the vertex (h,k)
(2,5)
Find p from the vertex and the focus
1/8
find the focus
(2,41/8)
Find the axis of symmetry by finding the line that passes though the Vertex and the focus
x=2
Or also a line that goes through the middle but that is just my opinion!
The graph shows the distance y, in centimeters, a pendulum moves to the right (positive displacement) and to the left (negative displacement), for a given number of seconds x.
What is the pendulum's maximum displacement?
ANSWER
The pendulum's maximum displacement is 2cm.
EXPLANATION
The maximum value of the graph is the pendulum's maximum displacement.
The graph is a periodic function
The amplitude of the graph is 2.
The range of the graph is -2≤y≤2
The maximum value is 2.
The pendulum's maximum displacement is 2cm
The correct choice is B.
Please help?????!!!!!
10√2
and this simplifies to a = -----------
2Answer:
Step-by-step explanation:
The cosine function links the angle (45°), the side a and the hypotenuse (10):
a
cos 45° = ------------
10
1
and so a = 10 cos 45° = 10(------) = 10√2 / 2 = a
√2
Maria drives to school in 20 minutes. She drives home in 24 minutes. What was her average driving speed in terms of d, the distance from her home to school?
Speed is distance/time so
[(d/20)+(d/24)]/2= 24d+20d/24•20•2=44d/20•24•2=22d/20•24=11d/240
Find the diagonal of the rectangular solid with the given measures. l = 18, w = 10, h = 2
[tex]\boxed{d=2\sqrt{107}}[/tex]
Step-by-step explanation:For a rectangular prism whose side lengths are [tex]a,\:b\:and\:c[/tex] the internal diagonal can be calculated as:
[tex]d=\sqrt{a^{2}+b^{2}+c^{2}}[/tex]
So here, we know that:
[tex]a=l=18 \\ \\ b=w=10 \\ \\ c=h=2[/tex]
So:
[tex]d=\sqrt{l^{2}+w^{2}+h^{2}} \\ \\ d=\sqrt{18^{2}+10^{2}+2^{2}} \\ \\ d=\sqrt{324+100+4} \\ \\ d=\sqrt{428} \\ \\ \boxed{d=2\sqrt{107}}[/tex]
Answer : The value of diagonal of the rectangular solid is, 20.69 unit.
Step-by-step explanation :
First we have to calculate the side AC.
Using Pythagoras theorem in ΔABC :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
Given:
Side AB = l = 18
Side BC = w = 10
Now put all the values in the above expression, we get the value of side AC.
[tex](AC)^2=(18)^2+(10)^2[/tex]
[tex]AC=\sqrt{(18)^2+(10)^2}[/tex]
[tex]AC=\sqrt{324+100}[/tex]
[tex]AC=\sqrt{424}[/tex]
Now we have to calculate the side AD (diagonal).
Using Pythagoras theorem in ΔACD :
[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
[tex](AD)^2=(AC)^2+(CD)^2[/tex]
Given:
Side AC = [tex]\sqrt{424}[/tex]
Side CD = h = 2
Now put all the values in the above expression, we get the value of side AD.
[tex](AD)^2=(\sqrt{424})^2+(2)^2[/tex]
[tex]AD=\sqrt{(\sqrt{424})^2+(2)^2}[/tex]
[tex]AD=\sqrt{424+4}[/tex]
[tex]AD=\sqrt{428}[/tex]
[tex]AD=20.69[/tex]
Thus, the value of diagonal of the rectangular solid is, 20.69 unit.
Since it's Wednesday, Buy for Less gives a 10% discount for purchases. The items in Rhonda's cart total $85.00. She needs to know the cost of the items with the discount. So, she multiplies 10% times $85.00 and subtracts the amount from $85.00 Which expression would give Rhonda the same result in one step?
A) .08(85.00) B) .90(85.00) C) 1.1(85.00) D) 85.00 - .01(85.00)
Answer: D.
Step-by-step explanation:
Find the volume of the cone shown:
A. 1176 units^3
B. 1176pie units^3
C. 392pie units^3
D. 392 units^3
Answer:
C
Step-by-step explanation:
The volume of the cone can be calculated using formula
[tex]V=\dfrac{1}{3}\cdot \pi r^2 h,[/tex]
where h is the height of the cone, r is the base radius.
In your case, h=24 un., r=7 un. So
[tex]V=\dfrac{1}{3}\cdot \pi \cdot 7^2\cdot 24=49\cdot 8\pi=392\pi \ un^3.[/tex]
ANSWER
C.
[tex] 392\pi \: {units}^{3} [/tex]
EXPLANATION
The volume of a cone is calculated using the formula:
[tex]V= \frac{1}{3} \pi {r}^{2} h[/tex]
The radius of the cylinder is
r=7 units.
The height is 24 units.
We substitute these values into the formula to obtain:
[tex]V= \frac{1}{3} \times \pi \times {(7)}^{2} \times 24[/tex]
[tex]V = 392\pi \: {units}^{3} [/tex]
How does the graph of [tex]f(x) = \frac{1}{2} (3)^{x+2}-1[/tex] related to its parent function?
(Possibly multiple answers)
A. The parent function has been compressed.
B. The parent function has been translated to the left.
C. The parent function has been stretched.
D. The parent function has been translated down.
Answer:
Answer one: the parent function has been translated to the left
Answer tw: the parent function has been translated down
Answer three: the parent function has been compressed
Mike is putting up a snow fence on the west side of his property. He needs a post at each end to hold the fence up and would like to put a post in every 8 ft. If he uses 25 post for his fence, his wide is the west side of his property ?
Answer:
k.lkkkkkkkkkkkkk
Step-by-step explanationkkkkkkkkkkkkkkkkkkkkkkmm:hhhhhhhhhhhhhhmjj200 ft because 8x25 is 200
A sphere has a volume of approximately 14,137 cubic inches. What is the length of the radius of the sphere, rounded to the nearest whole inch?
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=14137 \end{cases}\implies 14137=\cfrac{4\pi r^3}{3}\implies 42411=4\pi r^3 \\\\\\ \cfrac{42411}{4\pi }=r^3\implies \sqrt[3]{\cfrac{42411}{4\pi }}=r\implies 14.99994\approx r\implies \stackrel{\textit{rounded up}}{15=r}[/tex]
Identify the volume of the composite figure rounded to the nearest tenth. HELP PLEASE ASAP!!
Answer:
A is the closest one
Step-by-step explanation:
Remark
The general formula is
V = V_2 cones + V_cylinder.
Formula
That turns out to be
V = 2*(1/3)*pi*r^2*h1 + pi*r^2*h
Givens
r = 7 feet
h = 22 feet
h1 = 12 feet
pi = 3.14
Solution
V = 2*(1/3)*3.14 * 7^2*12 + 3.14* 7^2 * 22
V = 1231.5 ft^3 + 3384.92
V = 4616.42
Answer:
4618.1 ft3
Step-by-step explanation:
That's the exact correct answer :)
Please help me with this
2:6 so simplify it 1:3. This means the scale ratio is 1:3 for the figures. To find w, sub in the 3 from the smaller figure to the ratio so 3×3=9, 3:9 w=9
Answer:
w = 9
Step-by-step explanation:
Since the 2 polygons are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{2}{6}[/tex] = [tex]\frac{3}{w}[/tex] ( cross- multiply )
2w = 18 ( divide both sides by 2 )
w = 9
can someone please help me with this geometry question???
Answer:
x = 6BC = 10AC = 12Step-by-step explanation:
The length of EA is the difference between AD (6) and ED (5), so is ...
6 - 5 = 1
That is, the distance ED is 5 times the distance EA.
The two triangles are similar, so the distance BC will be 5 times the distance BA:
BC = 5·AB
BC = 5·2 = 10 . . . . . substitute for length AB
x +4 = 10 . . . . . . . . . substitute for length BC
x = 10 -4 = 6 . . . . . . subtract 4
We already know BC = 10. Of course AC = AB + BC = 2+10 = 12.
The lengths of interest are x=6, BC=10, AC=12.
California is hit every year by approximately 500 earthquakes that are large enough to be felt. However, those of destructive magnitude occur, on the average, once a year. Find the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs.
A destructive earthquake happens once per year.
The exponential equation would be f(x) = 1-e^-x
The probability of going 3 months out of a year would be
P(X≥3/12) ( divide 3 months by 12 months per year).
Now x equals 3/12
Now you have
P = 1-(1-e^-3/12)
= e^-1/4
= 0.7788
The probability that at least 3 months elapse would be 0.7788
(Round answer as needed).
The probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is; 0.7788
What is the probability of occurence?We are told that a destructive earthquake happens once per year.
Thus, the exponential equation in this scenario is;
f(x) = 1 - e⁻ˣ
Thus, the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs is given as;
P(X ≥ ³/₁₂) since 12 months make a year
This will be;
P(X ≥ ³/₁₂) = 1 - (1 - e^(⁻³/₁₂))
P(X ≥ ³/₁₂) = e^-1/4
P(X ≥ ³/₁₂)= 0.7788
In conclusion, the probability that at least 3 months elapse would be 0.7788
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A total of 150 students have taken an Algebra 2 final exam. The scores are normally distributed with a mean of 71% and standard deviation of 6%. How many students would you expect have scored between 65% and 77%?
Answer:
102 students
Step-by-step explanation:
Note that 65% and 71% are both 1 standard deviation from the mean (71%). According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.
68% of 150 students would be 0.68(150 students) = 102 students
68% of 150 students would be 0.68 (150 students) is, 102 students.
What it means to be normally distributed?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.What does it mean if your data is not normally distributed?Collected data might not be normally distributed if it represents simply a subset of the total output a process produced. This can happen if data is collected and analyzed after sorting.What are the 4 characteristics of a normal distribution?Here, we see the four characteristics of a normal distribution. Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal. A normal distribution is perfectly symmetrical around its center.According to the question:
65% and 71% are both 1 standard deviation from the mean (71%).
According to the empirical rule, 68% of scores lie within 1 std. dev. of the mean.
68% of 150 students would be 0.68(150 students) = 102 students.
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Cooper and Drew are standing on the seashore 10 miles apart. The coastline is a straight line between them. Both can see the same ship in the water. The angle between the coastline and Cooper's view of the ship is 45 degrees. The angle between the coastline and Drew's view of the ship is 35 degrees. How far is the ship from Cooper?
A) 5.8 miles
B) 7.2 miles
C) 8.6 miles
D) 10 miles
Answer:
Option A. 5.8 miles
Step-by-step explanation:
It is given in the question that angle SCD = 45° and ∠ SAD = 35°
Distance between Cooper and Drew = 10 miles
Let distance between Ship and Cooper is = x miles
Now we apply Sine rule in the Δ SCD
[tex]\frac{sin100}{10}=\frac{sin35}{x}[/tex]
[tex]\frac{0.9848}{10}=\frac{0.5736}{x}[/tex]
By cross multiplication
(0.9848)x = 10(0.5736)
[tex]x=\frac{5.736}{0.9848}=5.82[/tex] miles
Option A. 5.8 miles is the correct option.
Which equation represents a parabola that has a focus of (0 0) and a directrix of y = 2
1. x^2 = - (y-1)
2. x^2 = -4y
3. x^2 = -y
4. x^2 = -4 (y-1)
ANSWER
[tex]x ^{2} = - 4(y - 1).[/tex]
EXPLANATION
Since the parabola has the (0, 0) and the directrix at y=2.
The equation is of the form
[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]
where (h,k) is the vertex.
The vertex is half way between the directrix and the focus.
The vertex will be at (0,1)
and is the distance from the vertex to the focus which is 1.
[tex]{(x - 0)}^{2} = - 4(1)(y - 1)[/tex]
[tex]x ^{2} = - 4(y - 1)[/tex]
The logistic equation below can be used to model population growth. In the equation, P is population, t is time, and e = 2.72.
Given this information, which is a correct description of the logistic function?
A. a constant function divided by a polynomial function
B. a constant function divided by an exponential function
C. a constant function divided by the sum of a constant function and a polynomial function
D. a constant function divided by the sum of a constant function and an exponential function
Answer:
D. a constant function divided by the sum of a constant function and an exponential function
Step-by-step explanation:
It's all about the meaning of the math symbols used to create the function. The exponential function is called that because the variable (t) is in the exponent of the expression.
The "numerator" is the part of the expression above the "divided by" line. The "denominator" is the part below that line. When describing a fraction like this, we say, "<the numerator> divided by <the denominator>."
The numerator is a number with no math symbols or variables: it is a constant. The same is true of the left term of the denominator.
The plus sign between the denominator terms indicate these terms are added together. The result of that addition is called a "sum." The terms either side of the plus symbol are those that the symbol is indicating the sum of.
So, we can describe the expression as ...
a constant function divided by the sum of a constant function and an exponential function
The logistic equation is a model of population growth, correctly described as a constant function divided by the sum of a constant function and an exponential function. This matches option D from the choices provided.
Explanation:The logistic equation is a model of population growth where the growth rate decreases as the population approaches its carrying capacity. The equation structure is generally given as a constant function divided by the sum of a constant function and an exponential function. Thus, the correct description from the options provided would be D. A constant function divided by the sum of a constant function and an exponential function.
As an example, the basic form of a logistic function is P(t) = c / (1 + ae-bt). Here c is the constant function representing the maximum achievable population and ae-bt is an exponential function that models the population growth over time 't'.
Learn more about Logistic Equation here:https://brainly.com/question/33469987
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