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RUDIKE [14]
4 years ago
13

If f(x) = -x + 4 and g(x) = x^2 - 5, then g(f(3)) = ? A) -8 B) -4 C) -3 D) 0

Mathematics
1 answer:
kenny6666 [7]4 years ago
4 0

Answer:

B) -4

Step-by-step explanation:

To solve g(f(3)), we first have to solve f(3):

Since f(x) = -x +4 , f(3) = -3 + 4 = 1

Now we have to solve g(1) , since that is what f(3) left us;

Since g(x) = x^2 - 5 , g(1) = 1^2 - 5 = 1 - 5 = -4

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Any help with this greatly appreciated.
Anestetic [448]

Put the equation in standard linear form.

x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}

Find the integrating factor.

\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5

Multiply both sides by \mu.

(t+5) x'(t) + x(t) = 5(t+5)e^{5t}

Now the left side the derivative of a product,

\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}

Integrate both sides.

(t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt

On the right side, integrate by parts.

(t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C

Solve for x(t).

\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}

3 0
2 years ago
Please help me worth a bunch of points 26 points
Romashka [77]
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3 years ago
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Steve Rogers invested $2400 in an account tht pays 4% compounded continuously and how has $3500. How long did it take Steve's mo
Sedbober [7]

Answer:20years

Step-by-step explanation:

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3 years ago
anyone know how to do this?
Ugo [173]

Answer: A reasonable estimate of the minimum is 20.

8 0
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Find the volume of each figure. PLZZZ I NEED HELP ASAP!!!!!! :/
ella [17]
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