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3 years ago

How do you find the volume of compound shapes

1 answer:

3 0

First, you need to find the volume of each figure that you see in compound shapes. Finally, add all of them together. Hope it helped!

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F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2) I need to factor and find the zeros.

Ratling [72]

Answer:

$\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)$

$\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1$

Step-by-step explanation:

Given function:

$f(x)=3x^3-2x^2-11x+10$

If (x + 2) is a factor then:

$\implies f(x)=(x+2)(ax^2+bx+c)$

Expand:

$\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c$

$\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c$

$\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c$

To find a, compare the coefficients of x³:

$\implies a=3$

To find b, substitute the found value of a into the coefficient for x² and compare:

$\implies 2a+b=-2$

$\implies 2(3)+b=-2$

$\implies b=-8$

To find c, compare the constants:

$\implies 2c=10$

$\implies c=5$

Therefore:

$\implies f(x)=(x+2)(3x^2-8x+5)$

Now factor (3x²-8x+5):

$\implies 3x^2-3x-5x+5$

$\implies 3x(x-1)-5(x-1)$

$\implies (3x-5)(x-1)$

Therefore the factored function is:

$\implies f(x)=(x+2)(3x-5)(x-1)$

Zero Product Property

$\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}$

To find the zeros, set each factor equal to zero and solve for x:

$\implies x+2=0 \implies x=-2$

$\implies 3x-5=0 \implies x=\dfrac{5}{3}$

$\implies x-1=0 \implies x=1$

Therefore, the zeros of the function are:

$x=-2, \quad x=\dfrac{5}{3},\quad x=1$

3 0

1 year ago

Evaluate the following expression. 6 squared -1

natita [175]

Answer:

Step-by-step explanation:

$6^2 - 1\\36-1\\35$

4 0

3 years ago

Read 2 more answers

Choose what the expressions below best represent within the context of the word problem.

Nimfa-mama [501]

The number is 10x + y

4 0

3 years ago

According to a survery 52% of the residents of a city oppose a downtown casino. Of these 52% about 5 out of 10 strongly oppose t

nignag [31]

I need to satert by stating the questions clearly. Question A: What is the probability that a radomly selected resident opposes the casino and strongly opposes the casino? This is the joint probability of being opposed and being strongly opposes which is calculated as the product of both: 52/100 * 5/10 = 26/100 = 0.26. Question B. What tis the probability that a radomly selected resident opposes the casino and does not strongly oppose the casino. Again it is a joint probability, the product of being opposed and not being strongly opposed: 52/100 * 5/10 = 26/100 = 0.26. The are the same because the the half of the 52% oppose strongly and the other half does not.

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3 years ago

Not a math question but they dont have a PE subject (math nerd who dont know sports needs help)

eduard

Answer:

i think its cancellation the others don't make sense.

Step-by-step explanation:

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2 years ago