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3 years ago

If f(x) = 5x - 3 and g(x) = 2x + 9, determine f(g(4)

Mathematics

1 answer:

Over [174]3 years ago

5 0

Answer:

Step-by-step explanation:

f(x) = 5x - 3

g(x) = 2x + 9

f(g(x)) = 5 (2x + 9) - 3 ..... replace x with g(x)

f(g(4)) = 5 * (2 * 4 + 9) -3 = 85 - 3 = 82

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The perimeter of a rectangle deck is 175 feet.The length of the deck,L, is 6 feet longer than 2 times the width, w. Determine th

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$x-\ length\\y-\ width\\\\
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175=2x+2y\\
x=2y+6\\\\
175=2(2y+6)+2y\\
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3 years ago

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3 years ago

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3 years ago

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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 $\mu$ .

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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 $x(t)$ .

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

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2 years ago