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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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the population of a city increased from 24500 to 41600 between 2003 and 2012 . find the change of population per year if we assu
AURORKA [14]
The change of population per year is 1,900

We'll start by subtracting; 41,600-24,500= 17,100
Then we'll divide 17,100 by 9 because there is a 9 year difference between 2003 and 2012.
17,100/<span>9=1,900</span>
5 0
3 years ago
Solve the following system of equations using substitution.<br><br> 4x + 2y = 12<br> x = y + 3
BigorU [14]

Answer:

x = 3

y = 0

Step-by-step explanation:

The method of substitution is when one solves an equation for one of the variables, and then substitutes the expression into the other equation. After doing so, one will solve the other equation for the remaining variable and then backsolve for the first variable.

4x + 2y = 12

x = y + 3

The second equation is already sovled for parameter (x), subttiute this into the other equation,

4(y + 3) + 2y = 12

Distribute,

4y + 12 + 2y = 12

Simplify,

6y + 12 = 12

Inverse operations,

6y + 12 = 12

-12

6y = 0

/6

y = 0

Backsolve for (x), substitute the value of (y) into the equation for (x) and solve,

x = y + 3

x = 0 + 3

x = 3

4 0
3 years ago
Read 2 more answers
A) 1.0 mile <br>b) 5.0 mile <br>c) 5.8 mile <br>d) 0.8 mile ​
nordsb [41]

Answer:

d) 0.8 mile

Step-by-step explanation:

Coordinate of object B = (6, 6)

Coordinate of object C = (1, 4)

Coordinate of the archaeologist = (6, 1)

✍️Distance between Object B (6, 6) and the archaeologist (6, 1):

Distance = |6 - 1| = 5 units = 5 miles

✍️Distance between Object C (1, 4) and the archaeologist (6, 1):

Using the distance formula, d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, we would have:

d = \sqrt{(6 - 1)^2 + (1 - 4)^2}

d = \sqrt{(5)^2 + (-3)^2}

d = \sqrt{25 + 9}

d = \sqrt{34} = 5.8 units = 5.8 miles (nearest tenth)

Comparing how far each object is from the archaeologist, object C is 0.8 mile (5.8 - 5 = 0.8) farther than object B.

3 0
3 years ago
the actual length of a Corvette is 15 feet. Using the scale factor 1:3, determine the length of the model Corvette in inches
vlada-n [284]
The length of the model will be 5”.

15/3=5
8 0
3 years ago
What is two filths plus one eighth
pantera1 [17]

Answer: 21/40

Step-by-step explanation:

25+18=?The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(2/5, 1/8) = 40

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(25×88)+(18×55)=?

Complete the multiplication and the equation becomes

1640+540=?

The two fractions now have like denominators so you can add the numerators.

Then:

16+540=2140

This fraction cannot be reduced.

Therefore:

25+18=2140

4 0
3 years ago
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