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3 years ago

Algebra Word Problems

Mathematics

1 answer:

m_a_m_a [10]3 years ago

3 0

Each friend pays $4.25
34 ÷8=4.25

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<img src="https://tex.z-dn.net/?f=%20%28%7B%20%7Bx%7D%5E%7B2%7D%20%20-%204%7D%29%5E%7B5%7D%20%28%20%7B4x%20-%205%7D%29%5E%7B4%7D

Makovka662 [10]

Let $u=x^2-4$ and $v=4x-5$ . By the product rule,

$\dfrac{\mathrm d(u^5v^4)}{\mathrm dx}=\dfrac{\mathrm d(u^5)}{\mathrm dx}v^4+u^5\dfrac{\mathrm d(v^4)}{\mathrm dx}$

By the power rule, we have $(u^5)'=5u^4$ and $(v^4)'=4v^3$ , but $u,v$ are functions of $x$ , so we also need to apply the chain rule:

$\dfrac{\mathrm d(u^5)}{\mathrm dx}=5u^4\dfrac{\mathrm du}{\mathrm dx}$

$\dfrac{\mathrm d(v^4)}{\mathrm dx}=4v^3\dfrac{\mathrm dv}{\mathrm dx}$

and we have

$\dfrac{\mathrm du}{\mathrm dx}=2x$

$\dfrac{\mathrm dv}{\mathrm dx}=4$

So we end up with

$\dfrac{\mathrm d(u^5v^4)}{\mathrm dx}=10xu^4v^4+16u^5v^3$

Replace $u,v$ to get everything in terms of $x$ :

$\dfrac{\mathrm d((x^2-4)^5(4x-5)^4)}{\mathrm dx}=10x(x^2-4)^4(4x-5)^4+16(x^2-4)^5(4x-5)^3$

We can simplify this by factoring:

$10x(x^2-4)^4(4x-5)^4+16(x^2-4)^5(4x-5)^3=2(x^2-4)^4(4x-5)^3\bigg(5x(4x-5)+8(x^2-4)\bigg)$

$=2(x^2-4)^4(4x-5)^3(28x^2-57)$

7 0

3 years ago

Ashley spend half of her weekly allowance playing mini golf .to earn more money her parents let her wash the car for $9. what is

Semmy [17]

Her weekly allowance is $8.

7 0

2 years ago

Is 9.78083 a rational number

Alexus [3.1K]

No it’s not as its not constant and its a fraction

4 0

3 years ago

Read 2 more answers

What is -390 = 26c=52?

Alexandra [31]

Answer:

i think im not sure but try c= -35

Step-by-step explanation:

4 0

3 years ago

A girl's feet are negative 4 over 5 yards from the surface of a pool. A boy's feet are negative 2 over 5 yards from the surface

ANTONII [103]

There are many ways you can do this. To me, the easiest way is cross multiplying, but since the denominators are the same, there is no need to do that. Also, the fractions are negatives, the one closest to 0 is closer to the surface of the pool
-4/5 = -2/5 in this case -2/5 is closer to the surface of the pool.

Answer: the boy's feet are closer to the surface of the pool

6 0

3 years ago

Read 2 more answers