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zmey [24]
3 years ago
15

Establish for which constants c the following function is a density.

Mathematics
1 answer:
Valentin [98]3 years ago
7 0
By "density" I assume you mean "probability density function". For this to be the case for f(x), we require

\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=1

Since

f(x)=\begin{cases}cx^{1/2}&\text{for }0

you have

\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=\int_0^2cx^{1/2}\,\mathrm dx=\dfrac{2c}3x^{3/2}\bigg|_{x=0}^{x=2}=\dfrac{2^{5/2}c}3=1

which means

c=\dfrac3{2^{5/2}}=\dfrac3{4\sqrt2}
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Find the equation is standard form, of the line passing through he points (2,-3) and (4,2)
Simora [160]

The point slope formula:

y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

(2,\ -3)\to x_1=2,\ y_1=-3\\(4,\ 2)\to x_2=4,\ y_2=2

Substitute:

m=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}=2.5\\\\y-(-3)=2.5(x-2)\\\\y+3=2.5x-5\ \ \ \ |+5\\\\y+8=2.5x\ \ \ \ \ \ |-y\\\\2.5x-y=8\ \ \ \ \ |\cdot2\\\\\boxed{5x-2y=16}

5 0
3 years ago
Which expression represents the volume of the composite figure? (2)(4.4)(5) (2)(4.4)(3.9) (2)(4.4)(5) – (2)(4.4)(3.9) one-half(2
larisa86 [58]

The expression that represents the volume of the composite figure is (8*6*4)+ 1/3 * (8*6*6).

<h3>What will be the volume of the composite figure?</h3>

The volume of the composite figure will be the sum of the volume of the cube and the volume of the pyramid.

Volume of the cube = length*breadth*height

So, the volume of the cube = 8*6*4

The volume of the pyramid = 1/3 *(area of the base) * (height of the pyramid)

Area of the base of the pyramid = 8*6

Height of the pyramid = total height - height of the cube

Height of the pyramid = 10-4 =6

So, the volume of the pyramid = 1/3 * 8*6*6

So, total volume = (8*6*4)+ 1/3 * (8*6*6)

Hence, the expression that represents the volume of the composite figure is (8*6*4)+ 1/3 * (8*6*6).

To get more about prism visit:

brainly.com/question/23963432

6 0
2 years ago
Read 2 more answers
PLZZ HELP ME I NEED ANSWERRS ASAP the number of words x that tina can type per minute is at least 50. write and graph an inequal
swat32
I think it is C hope that helped 
8 0
3 years ago
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PLEASE HELP!!!!!! The length of a rectangle is three times its width. If the perimeter of the rectangle is 56 cm, find its area.
Alexus [3.1K]

Step-by-step explanation:

l = length

w = width

l = 3w

perimeter p = 2l + 2w = 56

using the identity of the first equation

p = 2(3w) + 2w = 56

6w + 2w = 56

8w = 56

w = 7 cm

l = 3w = 3×7 = 21 cm

so, the area is

l×w = 21×7 = 147 cm²

8 0
2 years ago
A collection of dimes is arranged in a triangular array with 17 coins in the base row, 16 in the next, 15 in the next, and so fo
Alona [7]

Good evening ,

Answer:

<h2>153 dimes.</h2>

Step-by-step explanation:

1+2+3+...+17 =  (17×18)/2 = (17×18)÷2 = 153 dimes.

it’s the sum of 17 terms of a geometric series.

:)

8 0
3 years ago
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