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3 years ago

‼️Someone Please help Me the graph is in the picture ‼️ Will make brainliest

Mathematics

1 answer:

baherus [9]3 years ago

6 0

Answer:

Step-by-step explanation:

The equation $V=-32t+256$ and the graph below describe the velocity V in feet per second of a ball <em>t</em> seconds after it is shot into the air.

To find the balls velocity after seven seconds, substitute t = 7 into the function expression:

$V(7)=-32\cdot 7+256\\ \\=-224+256\\ \\=32\ ft/sec$

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

(b) $y=-0.25x+0.75$

Step-by-step explanation:

The given function is

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

According to the first principle of the derivative,

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

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

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

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

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

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

Cancel out common factors.

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

By applying limit, we get

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

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

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

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

$y-y_1=m(x-x_1)$

$y-0.25=-0.25(x-2)$

$y-0.25=-0.25x+0.5$

$y=-0.25x+0.5+0.25$

$y=-0.25x+0.75$

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

5 0

3 years ago

A number is multiplied by 6 and the result is 48. Find the number.

eduard

Answer:

the answer is 8

Step-by-step explanation:

8x6=48

7 0

3 years ago

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An exterior angle of a triangle measures 110°. One of the interior opposite angle measures 50°. Then the other interior opposite

saw5 [17]

Answer:

60°

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the 2 interior opposite angles.

let the other interior angle be x, the

x + 50 = 110 ( subtract 50 from both sides )

x = 60

Thus the other interior opposite angle is 60°

5 0

3 years ago

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H.C.F of 4,5 and 10 in Division method

Tasya [4]

Answer:

Step-by-step explanation:

yan po sagot ko Hindi ko po alam kung tama o Hindi basta yan po sagot ko...

4 0

3 years ago

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Need help due tonight

Degger [83]

Answer:

an=7n-19

(the last one)

Step-by-step explanation:

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3 years ago