A reflecting telescope is purchased by a library for a new astronomy program. The telescope has a horizontal parabolic frame and contains two mirrors, 3 inches apart from each other- the first in the base and the second at the focal point. The astronomy teacher would like to attach a digital monitoring system on the edge of the telescope, creating a straight line distance above the focal point. Assuming that the telescope is placed on the edge of the roof in such a way that it is parallel to the ground, the position of the monitoring system, in relationship to the distance between the base and the focal point is modeled by the equation, x = 1/12y2 (x = the distance between the base and the focal point; y= the height of the monitoring system).

Rewrite the model so that the height of the digital monitoring system is a function of the distance between the base and the focal point of the telescope. How high above the focal point is the digital monitoring system attached to the telescope? Include your function and the height, rounded to the nearest tenth of an inch, in your final answer.

Answers

Answer 1
so hmm check the picture below, it looks more or less like so, a parabolic frame with the focus point and on the tip from the stem coming from its center, the digital monitoring system.

[tex]\bf x=\cfrac{1}{12}y^2\implies 12x=y^2\implies \sqrt{12x}=y \\\\\\ \textit{now, what's \underline{y} when x = 3?}\qquad \sqrt{12(3)}=y[/tex]
A Reflecting Telescope Is Purchased By A Library For A New Astronomy Program. The Telescope Has A Horizontal
Answer 2

The digital monitoring system attached at 6 inch from telescope.

What is Parabola?

A curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a stationary point is equal to its distance from a fixed line.

Here, we have a parabolic frame with the focus point and on the tip from the stem coming from its center, the digital monitoring system.

So, the equation that in this situation is

x = y² / 12

12x = y²

y= √12x

So, at x= 3 the y will be

y = √12(3)

y = √36

y = 6

Thus, the digital monitoring system attached at 6 inch from telescope.

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Related Questions

You make $30,000.00 and your spouse makes $35,000.00. using the 20% range, calculate the least and greatest amount you spend on housing

Answers

30,000 x 0.20 = $6,000 least amount

30,000 +35,000 = 65,000

65000 x 0.20 = $13,000 greatest amount

If f(x)=4^x , which statements are true of g(x)? Check all that apply

Answers

It looks like the first two boxes are the exact same thing, if they are check those. It should be g(x) = 4^x - 1

Check the 4th box; the graph is translated down 1 unit because the y goes down by 1.


The true statements about functions f(x) and g(x) are:

b. g(x) = 4^x - 1d.The function f(x) is translated 1 units down to get the function g(x)

How to determine the true statements?

The function f(x) is given as:

f(x) = 4^x

From the table of values, we can see that the function g(x) is 1 less than the function f(x).

This means that:

g(x) = f(x) - 1

This can be rewritten as:

g(x) = 4^x - 1

In transformation, it means that the function f(x) is translated 1 units down to get the function g(x)

Hence, the true statements are: b and d

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Three painters can paint three walls in three minutes. how many painters are needed to paint 27 walls in nine minutes?

Answers

Final answer:

To paint 27 walls in 9 minutes, you would need 9 painters working at the same speed. This is based on the proportional relationship that each painter can paint 1 wall in 3 minutes.

Explanation:

This problem can be solved with a clear understanding of proportions. Given that 3 painters can paint 3 walls in 3 minutes, it implies that each painter can paint 1 wall in 3 minutes.

Thus, in 9 minutes, a single painter can paint 3 walls.

Therefore, to paint 27 walls in 9 minutes, we would need 27/3 equals 9 painters.

It is important to note that this implies all painters are working at the same speed. This is a simple and practical example of proportions in mathematics

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which of the following functions are graphed below

Answers

The correct answer is C, y=[x]-6. All I did was plug in some of the points from the line and see if they worked. Like the point (2,-4) when I plug it in to y=[x]-6 it equals out   

Answer:

The equation of given graph is f(x)=[x]-6

C is correct

Step-by-step explanation:

We are given a graph and to find the equation of graph.

It is a graph of greatest integer function or floor function.

Parent function of greatest integer function:

[tex]f(x)=[x][/tex]

For x = 0 to x= 1 , f(x)=0

For x =1 to x=2 , f(x)=1

We are given a function,

For x = 0 to x= 1 , f(x)=-6

For x = 1 to x= 2, f(x) = -5

If we shift 6 unit down the parent function. We will get original function.

[tex]f(x)=[x]-6[/tex]

Hence, The equation of given graph is f(x)=[x]-6

Solve for x.
3:12 = x:16
2 1/4
4
64

Answers

Hi!

We can set up a proportion to solve this

[tex] \frac{3}{12} \frac{x}{16} [/tex]

Cross multiply

3 x 16 = 48
48/12 = 4

The answer is 4

Hope this helps! :)

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

we have

[tex]\frac{3}{12}=\frac{x}{16}[/tex]

solve for x

Cross multiply

[tex]12*x=3*16\\x=3*16/12\\x=48/12\\x=4[/tex]

Please Help ASAP!
Will award brainliest!

Answers

ratio of AB to DE = 30/6 = 5

do 24/6 = 4

x = 4

Which of the sums below can be expressed as 8(2 + 7) 2+56......10+15.....16+7......16+56

Answers

use the Distributive law:-

8(2 + 7) = 8*2 + 8*7 = 16 + 56

Answer:

The correct answer is D) 16+56

Step-by-step explanation:

The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 40 + 0.008p^3 and that its demand function is D(p) = 200 - 0.16p^2, where p is the price. Determine the price for which the supply equals the demand.

Answers

In this item, we are to determine the price to which there would be a breakeven between the supply and demand. This can be done by equating the equations given for each as shown below.
       S(p) = D(p)
     40 + 0.008p³ = 200 - 0.16p²

We transpose all the terms to left side of the equation. 
     0.008p³ + 0.16p² - 160 = 0
Then, we factor out the given function. This can either be done through long division or synthetic division. Divide the equation by 0.008.
        p³ + 20p² - 20000 = 0

One of the roots of the equation is 21.86. This is the only real root of the equation and the rest are imaginary. 

Hence, the price should be approximately $21.86 before the demand and supply is breakeven. 

Jonathan sets a camera on a tripod to film birds in a nest. The camera is 1.8 m off the ground and 16.4 m away from the tree. The angle of elevation from the camera to the bird’s nest is 29°. How far above the ground is the bird’s nest? Round your answer to the nearest tenth of a meter. 7.3 m 9.1 m 10.9 m 14.3 m

Answers

tan29°=(n-1.8)/16.4

n=16.4tan29°+1.8

n≈10.9 meters  (to nearest tenth of a meter)

draw a diagram

we need to find the area of the other leg

alright

we have one leg is 16.4
the other one is ?
tan(29°)=?/16.4
16.4tan(29°)=?
and the height of the nest is ?+height of camera=?+1.8

so
16.4tan(29°)+1.8≈10.8907
so about 10.9m

Maximal use of bezels, gradients, and drop shadows make an interface highly user friendly True False

Answers

Bezels, gradients, and drop shadows can make an interface user-friendly if used wisely and minimally. If too much, the interface can be distracting. The problem used the term "maximal." This means that the bezels, gradients, and drop shadows are excessively used in an interface. So, the answer to this question is 
FALSE
Using too much image effects can make an interface not user-friendly.

A wooden plank of length x is cut into 8 sections such that each section is at most 2 1/2 meters long. What is the length of the entire plank in meters?
a x ≤ 3.2 meters
b x ≤ 20 meters
c x ≥ 10.5 meters
d x ≥ 20 meters

Answers

[tex]\bf 2\frac{1}{2}\implies \cfrac{2\cdot 2+1}{2}\implies \cfrac{5}{2} \\\\\\ \textit{now, 8 sections that long?}\qquad 8\cdot \cfrac{5}{2}\implies 20 \\\\\\ x\le 20[/tex]

Answer:

b

Step-by-step explanation:

Hiram raises earthworms. In a square of compost 4 ft by 4 ft, he can have 1000 earthworms. How many earthworms can he have if his square of compost has a side length that is 8 times longer?
A. 8000
B. 64,000
C. 256,000
D. 32,000

Answers

Hiram can have 8,000 earthworms.
hmm, find the area

area=length times widtha
rea=4 times 4=16 square feet

so every 16 square feet is 1000 earthworms
so ratio of worms to area is 1000:16


if each side length is 8 then
8 times 8=64 area
but how many worms?

1000:16=?:64
1000/16=?/64
times both sides by 64
64000/16=?
4000=?
wat, not listed? why


if we assume it's a cube then
voluem is 4^3 or 64
1000:64 is the ratio

if 8ft then 8^3=512
so
1000:64=?:512
1000/64=?/512
512000/64=?
8000=?

I guess it was a cube then
A would be the answer

Eliza Savage received a statement from her bank showing a checking account balance of $324.18 as of January 18. Her own checkbook shows a balance of $487.38 as of January 29. The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28. How much did Eliza deposit in her account between January 18 and January 29?

Answers

3 checks total : 15.00 + 77.49 + 124.28 = 216.77

 that amount will still need to be deducted from the bank

so 324.18- 216.77=107.41

her checkbook has a total of 487.38

487.38-107.41 = 379.97 is the amount she deposited into her account

Answer:

The amount she deposited in her account between January 18 and January 29 is $379.97

Step-by-step explanation:

Given :

Eliza showing a checking account balance of $324.18 as of January 18.

Her own checkbook shows a balance of $487.38 as of January 29.

The bank returned all of the cancelled checks but three. The amounts of these three checks are $15.00, $77.49, and $124.28.

To Find : Eliza deposit in her account between January 18 and January 29.

Solution :

Eliza showing a checking account balance of $324.18 as of January 18.

Total amount of three checks =  $15.00 + $77.49+ $124.28 =$216.77

The account balance after the deduction of three checks amount

=  $324.18 -$216.77 = $107.41

So, the new balance is $107.41.

Her own checkbook shows a balance of $487.38 as of January 29.

So, the amount she deposited  between January 18 and January 29

= $487.38-$107.41 = $379.97

Hence , The amount she deposited in her account between January 18 and January 29 is $379.97

Saving account has a principal of 1,800.00 it earns 6 percent interest compounded semiannually. How much is the compound interest after 1 year

Answers

First find the future value
A=p (1+r/k)^kt
A future value?
P principle 1800
R interest rate 0.06
K compounded semiannual 2
T time 1 year
A=1,800×(1+0.06÷2)^(2×1)
A=1,909.62

Now find the compound interest
I=A-p
I=1,909.62−1,800
I=109.62

Help^^^^^^^^^^^^^^^^^

Answers

Answer: choice D

----------------------------------------------

Work Shown:

I'm assuming the problem is -4*(1-x) <= -12+2x where the first term is -4 and not 4

-4*(1-x) <= -12+2x
-4*(1-x) <= -12+2x
-4+4x <= -12+2x
-4+4x-2x <= -12+2x-2x
-4+2x <= -12
-4+2x+4 <= -12+4
2x <= -8
2x/2 <= -8/2
x <= -4

To graph x <= -4, you plot a closed circle at -4. Then you shade to the left of the closed circle. This matches with choice D

Use the graph below to answer the question that follows:

graph of curve that passes through the following points, 0, 5; pi over 2, 2; pi, negative 1; 3 pi over 2, 2; 2 pi, 5.

What is the rate of change between the interval x = π and x = three pi over two?

Answers

Final answer:

The rate of change between x = π and x = three pi over two is 6/π.

Explanation:

The rate of change between the interval x = π and x = three pi over two can be found by calculating the slope of the line connecting these two points on the graph. In this case, we can calculate the slope by finding the difference in y-values and dividing it by the difference in x-values:

Slope = (y₂ - y₁) / (x₂ - x₁) = (2 - (-1)) / (π - 3π/2) = (2 + 1) / (3π/2 - π) = 3 / (π/2) = 6 / π

Therefore, the rate of change between the interval x = π and x = three pi over two is 6/π.

Final answer:

The rate of change between x = π and x = three pi over two is 6/pi.

Explanation:

The rate of change between the interval x = π and x = three pi over two can be found by determining the slope of the line connecting the two points on the graph corresponding to these x-values.

Using the coordinates (pi, -1) and (3 pi over 2, 2), we can calculate the slope as follows:

Slope = (change in y)/(change in x) = (2 - (-1))/(3 pi over 2 - pi) = 3/(pi/2) = 6/pi

So, the rate of change between x = π and x = three pi over two is 6/pi.

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Find the radius of a circle with an x-intercept of -2 if the circle’s center is (2,3) on a coordinate plane.

5
25
16
9

Answers

hello : 
 let : A(2;3) and : P(-2; 0)
the radius of a circle is : AP = √((2+2)² +(3-0)²)=√25 = 5

Radius of the circle is option (1) 5 units

What is radius?

A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.

What is circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center

Center of the circle is (2,3) on a coordinate plane,

Radius of the circle with an x intercept of -2

There for the point is (-2,0)

Distance between the (2,3) and (-2,0) = Radius of the circle

Distance between (2,3) and (-2,0)

D= [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Substitute the values

[tex]D=\sqrt{(-2-2)^{2}+(0-3)^{2} }\\D=\sqrt{16+9} \\D=\sqrt{25}\\ D=5[/tex]

Hence, the radius of the circle is option (1) 5 units

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ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss. (I needed to fill up this space somehow).

Answers

[tex]-4 \ \textless \ 3 \\ f(-4) = (-4) ^{2} - 5 \\ f(-4) = 16 -5 = 11[/tex]

Determine the growth factor corresponding to 25% increase.

a.
1.75
c.
25
b.
1.25
d.
0.25




 

Answers

25% = 0.25

growth factor is 1 + 0.25 = 1.25

Answer:

Step-by-step explanation:

Alright, lets get started.

The given increase is 25 %.

Which means in terms : [tex]25*\frac{1}{100}[/tex]

That will be equal to : [tex]0.25[/tex]

So, the growth of 0.25 means the complete term will be :

[tex]1+0.25=1.25[/tex]

Hence the growth factor of 25 % will be equal to 1.25    :    Answer

Hope it will help :)

Find the circumference of a circle that has an area of 452.16 square meters. (Use 3.1416 as the value of π.)


Answers

Final answer:

The circumference of a circle with a given area is 75.40 meters

Explanation:

To find the circumference of a circle, we can use the formula C = 2πr, where C is the circumference and r is the radius. First, we need to find the radius from the given area.

The formula for the area of a circle is [tex]A = \pi r^2[/tex]

Rearranging the formula, we get [tex]r = \sqrt{(A/\pi \p).[/tex]

Now, substitute the given area (452.16 square meters) into the formula and solve for r:

[tex]r = \sqrt{(452.16/3.1416)[/tex]

=  12.00 meters

Finally, plug the value of r into the circumference formula:

[tex]C = 2\pi (12.00)[/tex]

= 75.40 meters

Solve the equation by extracting the square roots. when a solution is irrational, list both the exact solution and its approximation rounded to two decimal places.

Answers

The polynomial that is given here in which the goal is to find out the roots of the equation is x2 = 196  where x is the root of the equation. we transform the given equation into its standard form that is x^2 - 196 = y in which y should be equal to 0 in order to get x. 
In this case, 

x^2 - 196 = 0 
x^2 = 196
we take the square root of both sides in order to extract x
square root x^2 = square root 196
x = +- 14
there are two roots in this function which are positive and negative numbers.
square of a positive number leads to a positive number while the square of a negative number also yields to a positive number. 

Find the terminal point p(x y) on the unit circle determined by the given value of t. t = -3 pi / 2

Answers

-3pi/2 is the same thing as pi/2

the terminal point on the unit circle for pi/2 is (0,1)

so that means the terminal point for -3pi/2 is also (0,1).


Answer:

It is B, just got it on a p e x

Step-by-step explanation:

A (-1,0)

B (0,-1)

C (1,0)

D (0,1)

The graph shows the distance, y, that a car traveled in x hours:

A graph is shown with x axis title as Time in hours. The title on the y axis is Distance Traveled in miles. The values on the x axis are from 0 to 5 in increments of 1 for each grid line. The values on the y axis are from 0 to175 in increments of 35 for each grid line. A line is shown connecting ordered pairs 1, 35 and 2, 70 and 3, 105 and 4, 140. The title of the graph is Rate of Travel.

What is the rate of change for the relationship represented in the graph?
fraction 1 over 35
fraction 1 over 34
34
35

Answers

Answer: 35

Step-by-step explanation:

The rate of change of a graph is given by :-

[tex]k=\dfrac{\text{Change in y avlues}}{\text{Change in x values}}[/tex]

For points : (1, 35) and (2, 70)

The rate of change for the relationship in the graph is given by :-

[tex]k=\dfrac{70-35}{2-1}=35[/tex]

Hence, the rate of change for the relationship represented in the graph = 35.

The rate of change of the relationship shown in the graph is 35 miles per hour.

Linear equation

Linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept.

Let y represent the elevator height after x seconds.

From the graph using points (0, 0) and (4, 140):

m = (140 - 0)/(4 - 0) = 35

The rate of change of the relationship shown in the graph is 35 miles per hour.

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How much would $120 invested at 86% interest compounded monthly to be worth after 21 years round to the nearest cent

Answers

The formula is
A=p (1+r/k)^kt
A future value?
P present value 120
R interest rate 0.86
K compounded monthly 12
T time 21 year
A=120×(1+0.86÷12)^(12×21)
A=4,510,568,953.1372

Which of the following is quantitative data?
eye colors of a group of people

hair colors of a group of people

heights of a group of people

genders of a group of people

Answers

Heights of a group of people. Quantitative data is data with numbers and of all your choices, height is the only data with numbers.

The table below shows 10 data values:


88

92

94

80

85

90

72

83

93

91



What is the five-number summary for these data?
Minimum = 72, Q1 = 83, median = 89, Q3 = 92, maximum = 94
Minimum = 80, Q1 = 85, median = 89, Q3 = 91, maximum = 93
Minimum = 80, Q1 = 83, median = 90, Q3 = 92, maximum = 93
Minimum = 72, Q1 = 85, median = 90, Q3 = 91, maximum = 94

Answers

The first step to do is to arrange the data set from least to greatest.

72  80  83  85  88 90  91 92  93  94

From the arrangement, we can see that the minimum is 72 and the maximum is 94. Next, the median is the middle number of the data. Since there are 10 data points, we take the average of the middle 2 numbers. The median is (88+90)/2 = 89. 

When you talk about the quartiles, you draw divisions in your set. Q₁ is the middle data between the smallest and the median; Q₂ is the median; and Q₃ is the middle data between the largest and the median.


72  80  83  85  88 | 89 | 90  91 92  93  94

Q₁ is 83
Q₂ is 89
Q₃ is 92

Therefore, in summary, the answer is: Minimum = 72, Q1 = 83, median = 89, Q3 = 92, maximum = 94

(02.02 LC)

Figure ABCD is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure A′B′C′D′:
Which statement best compares the lengths of the sides of the two figures?

Length of AB = Length of C′D′
Length of CD = Length of A′B
′ Length of CD = Length of B′C′
Length of AB = Length of A′B′

Answers

Length of AB=Length of A'B' because they are corresponding sides.
The figure was simply rotated, the relative side lengths have not changed.

Length AB=Length A'B'

The points in a coordinate plane are reflected in the y-axis. In general, every point (x, y) is mapped onto what point? (___,___)

Answers

since it's over y axis that means all the y value will stay the same (-x,y)
Final answer:

In a Cartesian coordinate system, a point (x, y) reflected over the y-axis is mapped to the point (-x, y), as the x-component changes direction in the reflection while the y-component remains the same.

Explanation:

When a point is reflected across the y-axis in a Cartesian xy-coordinate system, which has orthogonal directions defined by the unit vectors i and j for the x and y axis respectively, the coordinates of the point change in a specific way. For every point whose coordinates are initially (x, y), after being reflected over the y-axis, the resultant point will have coordinates (-x, y).

This happens because the reflection over the y-axis effectively reverses the direction of the x-component of the point's position vector, changing its sign from positive to negative or vice-versa, while leaving the y-component unaffected. Therefore, after reflection, a point (x, y) is mapped onto the point (-x, y).

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A pet store has k tanks of fish. Each tank has 30 fish. Using k, write an expression for the total number of fish in the store.

Answers

This is the concept of algebra, given that the total number of tanks in a pet store is k tanks and the total number of fish in each tank is 30 fish. An expression form the total number of fish in the pet store will be:'
Total number of fish=[number of tanks]*[number of fish in each tank]
f(k)=k*30
f(k)=30k
the answer is f(k)=30k

Find the midpoint of A and D. Simplify completely.

option 5 is none of these.

Answers

ill say answer D is the one it seems like it fits in the middle between them.

A = (1,3)

D= (5,0)


 midpoint = (x1+x2)/2 , (y1+y2)/2

5+1=6/2 =3

3+0=3/2 = 3/2

(3,3/2)

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