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3 years ago

Is is true that when two probabilities are multiplied the probability represents a simple event

Mathematics

2 answers:

irakobra [83]3 years ago

7 0

Yes that is a true statement.

Dvinal [7]3 years ago

3 0

This is actually an entirely false statement

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The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When

atroni [7]

Answer:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

Step-by-step explanation:

The area for a rectangle is given by the formula:

$A=w\ell$

Where w is the width and l is the length.

We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.

First, differentiate the equation with respect to t, where w and l are both functions of t:

$\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]$

By the Product Rule:

$\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w$

Since we know that dl/dt = 6 and that dw/dt = 5:

$\displaystyle \frac{dA}{dt}=5\ell + 6w$

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

$\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}$

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

8 0

3 years ago

Integral of 17/(x^3-125)

daser333 [38]

Answer:

17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

Step-by-step explanation:

∫ 17 / (x³ − 125) dx

= 17 ∫ 1 / (x³ − 125) dx

= 17 ∫ 1 / ((x − 5) (x² + 5x + 25)) dx

Use partial fraction decomposition:

= 17 ∫ [ A / (x − 5) + (Bx + C) / (x² + 5x + 25) ] dx

Use common denominator to find the missing coefficients.

A (x² + 5x + 25) + (Bx + C) (x − 5) = 1

Ax² + 5Ax + 25A + Bx² − 5Bx + Cx − 5C = 1

(A + B) x² + (5A − 5B + C) x + 25A − 5C = 1

Match the coefficients and solve the system of equations.

A + B = 0

5A − 5B + C = 0

25A − 5C = 1

A = 1/75

B = -1/75

C = -2/15

So the integral is:

= 17 ∫ [ 1/75 / (x − 5) + (-1/75 x − 2/15) / (x² + 5x + 25) ] dx

Simplify:

= 17/75 ∫ [ 1 / (x − 5) − (x + 10) / (x² + 5x + 25) ] dx

Factor ½ from the numerator of the second fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 20) / (x² + 5x + 25) ] dx

Split the fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − ½ (15) / (x² + 5x + 25) ] dx

Multiply the last fraction by 4/4:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 30 / (4x² + 20x + 100) ] dx

Complete the square:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 15 / ((2x + 5)² + 75) ] dx

Split the integral:

= 17/75 ∫ 1 / (x − 5) dx − 17/150 ∫ (2x + 5) / (x² + 5x + 25) dx − 17/5 ∫ 1 / ((2x + 5)² + 75) dx

The first integral is:

∫ 1 / (x − 5) dx = ln│x − 5│

The second integral is:

∫ (2x + 5) / (x² + 5x + 25) dx = ln(x² + 5x + 25)

The third integral is:

∫ 1 / ((2x + 5)² + 75) dx = 1/√75 tan⁻¹((2x + 5) / √75)

Plug in:

= 17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

4 0

3 years ago

4. Find the area of this figure.

mihalych1998 [28]

Answer:

I believe it is 100 ft

Step-by-step explanation:

3 0

3 years ago

Which value represents the horizontal translation from the graph of the parent function f(x) = x^2 to the graph of the function

Vsevolod [243]

Translation by h (right) and k (up)
g(x)=f(x-h)+k
=f(x-4)^2+2
so h=4, k=2
horizontal translation (to the right) is h=+4, but is shown as -4 for the translation value.

7 0

3 years ago

HELP ME PLZ PLZ PLZ!

Triss [41]

Answer:

I don't know the value of either, could you add more information?

Step-by-step explanation:

I'd be glad to help.

6 0

3 years ago