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ElenaW [278]
3 years ago
12

A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x^2=4y around

its axis of symmetry (assume that x and y are in units of inches). In order to have the brightest, most concentrated light beam, how far from the vertex should the bulb be placed? Express your answer as a fraction or a decimal rounded to two decimal places.
Mathematics
1 answer:
Nadya [2.5K]3 years ago
7 0

Answer:

  1.00 inches

Step-by-step explanation:

The distance from vertex to focus is "p" in the quadratic equation ...

  x^2 = 4py

In the given equation, p=1. Since units are inches, ...

the bulb should be placed 1.00 inches from the vertex.

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Eleanor and Max used two rectangular pieces of plywood, placed end-to-end, to make a long rectangular stage for the school play.
Flauer [41]

Answer:the width of plywood = 6.25 feet wide or  6 1/4 feet wide

Step-by-step explanation:

Step 1

Area of  a rectangular plywood = length x width

Area of Ist Plywood= 7 x w

Area of 2nd  Plywood= 61/2 x w=6.5 xw

But Total Arae of trhe two Plywoods are = 84 3/8 square feet.

Therefore Our equation to solve the problem becomes

Area of Ist Plywood + Area of 2nd  Plywood =84 3/8 square feet.

7w + 6.5w =  84 3/8

13.5w= 84 3/8

w =  84 3/8/13.5

675/8  / 13.5

w=6.25

Therefore the width of plywood = 6.25 feet wide or 6 1/4 feet.

3 0
3 years ago
Daisy has a marble collection in her room the ratio of blue marbles to red marbles are 4 : 7 if she has 24 blue marbles how many
Masteriza [31]

Answer:

The answer is 24:42

Step-by-step explanation:

All you have to do is multiply 7 by 6 because for every red marbles there are 6 marbles.

Hopes this helps!!

4 0
2 years ago
Read 2 more answers
Solve the system of equations: <br> X+y+z=5<br> -3x-4y+4z=15<br> 2x-y-4z=-8
atroni [7]

Answer:

  (x, y, z) = (3, -2, 4)

Step-by-step explanation:

The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...

  z = 5 -(3 +(-2)) = 4

The solution is (x, y, z) = (3, -2, 4).

__

Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:

  \left[\begin{array}{ccc|c}1&1&1&5\\-3&-4&4&15\\2&-1&-4&-8\end{array}\right]

__

If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:

  -3x -4y +4(5 -x -y) = 15   ⇒   -7x -8y = -5

  (-3x -4y +4z) +(2x -y -4z) = (15) +(-8)   ⇒   -x -5y = 7

This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...

  -7(-5y -7) -8y = -5   ⇒   27y = -54   ⇒   y = -2

  x = -5(-2) -7 = 3

  z = 5 -(3) -(-2) = 4

_____

<em>Additional comment</em>

If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.

6 0
2 years ago
What is 2/3 times 4/5 as a decimal!
Nitella [24]
Hey there,

Your correct answer to \frac{2}{3}×\frac{4}{5} as a decimal would be 0.53

Your correct answer would be \boxed{0.53}

Hope this helps

~Jurgen
5 0
3 years ago
Read 2 more answers
Express in the form 1:n<br> Give n as a fully simplified fraction.<br><br> 12:2
statuscvo [17]

Answer:

divide 12

12/12 : 2/12

1 : 2/12

1 : 1/6

n=1/6

7 0
3 years ago
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