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3 years ago

Joshua rented a movie for $4.49 from Cinema Rentals. If the movie is not returned on the due date, Cinema Rentals charges an

Mathematics

1 answer:

amm18123 years ago

5 0

Answer:

R(x) = 2.25x + 4.49

Step-by-step explanation:

Equation form: R(x) = mx + b

m: represents the additional amount Joshua is charged for every day until he returns the movie, which in this case is $2.25. So, the value of m is 2.25.

b: represents the initial cost of renting the movie. Joshua rented the movie for $4.49, so b is 4.49.

Since we know the value of m and b, we can write the equation:

R(x) = 2.25x + 4.49

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Find the derivative of the following functions: a. f(x) = (x^3 + 5)^1/4 - 15e^x^3 b. f(x) = (x - 3)^2 (x - 5)/(x - 4)^2(x^2 + 3)

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Step-by-step explanation:

Given function is

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$F^{'}\left ( x\right )$ = $0.25\left ( x^{3}+5\right )^{-0.75}\frac{\mathrm{d} x^{3}}{\mathrm{d} x}-15e^{x^{3}}\frac{\mathrm{d} x^{3}}{\mathrm{d} x}$

$F^{'}\left ( x\right )=0.25\left ( x^{3}+5\right )^{-0.75}\times 3x^{2}-15e^{x^{3}}\times \left ( 3x^{2}\right )$

(b)F(x)= $\frac{\left ( x-3\right )^2\left ( x-5\right )}{\left ( x-4\right )^2\left ( x^{2}+3\right )^5}$

$F^{'}\left ( x\right )$ = $\frac{\left [ 2\left ( x-3\right )\right \left ( x-5\right )+\left ( x-3\right )^2]\left [ \left ( x-4\right )^2\left ( x^2+3\right )^5\right ]-\left [ 2\left ( x-4\right )^{3}\left ( x^2+3\right )^5+5\left ( x^2+3\right )^4\left ( 2x\right )\left ( x-4\right )^2\right ]\left [ \left ( x-3\right )^2\left ( x-5\right )\right ]}{\left [\left ( x-4\right )^2\left ( x^2+3\right )^5\right ]^2}$

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