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allochka39001 [22]
3 years ago
7

A rental truck cost $48 plus $0.40 per mile.

Mathematics
1 answer:
Natalija [7]3 years ago
3 0
(a) If we let x be the number of miles and y be the total cost, the equation for relating the number of miles and the total cost would be,
                                y = 0.4x + 48

(b) If the rental cost is 60,
                               60 = 0.4x + 48
The value of x from the equation is 30.

(c) You may prepare the table of values by allowing x be any number and then solve for y until we arrive with an answer for y being equal to 60. 
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Consider the following equation. f(x, y) = y3/x, P(1, 2), u = 1 3 2i + 5 j (a) Find the gradient of f. ∇f(x, y) = Correct: Your
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f(x,y)=\dfrac{y^3}x

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\boxed{\nabla f(x,y)=-\dfrac{y^3}{x^2}\,\vec\imath+\dfrac{3y^2}x\,\vec\jmath}

b. The gradient at point P(1, 2) is

\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}

c. The derivative of f at P in the direction of \vec u is

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It looks like

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so that

\|\vec u\|=\sqrt{\left(\dfrac{13}2\right)^2+5^2}=\dfrac{\sqrt{269}}2

Then

D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}

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Which number is greater . 60 or 7.5
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60 is greater than 7.5.

step by step

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