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defon
3 years ago
13

ed has $36 to buy paint and brushes for school project. Jars of paint cost $4 each. The paint brushes are $2 each write an equat

ion to determine the combination of brushes and paint he can buy if he bought 3 jars of paint how many brushes can he buy
Mathematics
1 answer:
Sauron [17]3 years ago
8 0
Ok so basically it will be 4 x 3 = 12 which leaves $24 ok then you divide 24 by 2 and you get 12 so the amount of brushes that can be purchased is 12.
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Answer:

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Step-by-step explanation:

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Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2
Verdich [7]

Answer:

(a) f'(x)=-\frac{2}{x^3}

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Step-by-step explanation:

The given function is

f(x)=\frac{1}{x^2}                  .... (1)

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Cancel out common factors.

f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}

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f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}

f'(x)=\frac{-2x)}{x^4}

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Therefore f'(x)=-\frac{2}{x^3}.

(b)

Put x=2, to find the y-coordinate of point of tangency.

f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}

Substitute x=2 in equation 2.

f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

y-y_1=m(x-x_1)

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y-0.25=-0.25x+0.5

y=-0.25x+0.5+0.25

y=-0.25x+0.75

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

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