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ElenaW [278]
4 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]4 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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Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f.
Alex17521 [72]

The function that is a  tangent to the graph of f is f(x) = (5/4)x^4+60

<h3>What is the concept of integral?</h3>

The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.

Knowing that :

  • 40x + y = 0 is tangent of f(x)
  • slope of the line = -40

therefore, f'(x)|x=a = -40, so only look for a we have:

5a^3 = -40\\a^3 = -8\\a = -2

if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:

f'(x) = 5x^3\\f(x) = (5/4)x^4 + c\\80 = (5/4)(-2)^4 + c\\c = 60

Therefore,

f(x) = (5/4)x^4+60

See more about tangent at brainly.com/question/401236

#SPJ1

4 0
2 years ago
Como se daca el area de un triangulo​
Ivahew [28]
Area= base x altura dividido entre 2
7 0
3 years ago
If y varies directly with x and
SashulF [63]
So this is direct proportional question
so y=(k)x
sub y=48 and x=6
48=6k
k=8
now you got a constant k
now sub x=3
y=(8)(3)
=24
8 0
2 years ago
The product of two consecutive even integers is 224. Find their sum.
lawyer [7]
X(x+2)=224x2+2x-224=0(x+16)(x-14) =0x= 16 or 14
the answer is 16 and 14
7 0
4 years ago
JPJ Corp has sales of $1.34 million, accounts receivable of $52,000, total assets of $4.99million(of which $2.79 million are fix
Alex Ar [27]

Answer:

Account Receivable Days : 14.16 days

Fixed Asset Turnover : 0.48 times

Total Asset Turnover : 0.27 times

Inventory Turnover : 3.98 times

Step-by-step explanation:

1) Account Receivable days is calculated as : (Account Receivable/Revenue) * Number of days in a year. Hence the answer is calculated as = (52000/134

0000) * 365 = 14.16.

2) Fixed Assets Turnover is calculated as : Net Sales/Fixed Assets. Hence the answer is calculated as 1340000/2790000 = 0.48.

3) Total Asset turnover is calculated as : Nets Sales/Total Assets. Hence the answer is = 1340000/4990000 = 0.28.

4) Inventory Turnover is calculated as : COGS/Average Inventory. Hence the answer is = 601000/151000 = 3.98.

5 0
3 years ago
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