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3 years ago

9

Complete the statement 10/7 x __= 1

1 answer:

Pavlova-9 [17]3 years ago

3 0

Answer:

7/10

Step-by-step explanation:

as 10/7×7/10 is 70/70 which can also be written as 1

hope it helps , pls mark me as brainliest

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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

Which expression is equivalent to 32

Nadusha1986 [10]

2 times (9+7) is correct.

9 + 7 = 16.
16 multiplied by 2 is 32.

3 0

3 years ago

A man bought a house for 3600 Naira he repairs the house with 150 Naira if he sold the house for 4950 Naira . Find his percentag

kozerog [31]

Step-by-step explanation:

profit%=

$\frac{selling \: price - cost \: price}{cost \: price} \times 100\%$

$\frac{4950 \: naira - 3600 \: naira + 150 \: naira}{3750 \: naira} \times 100\%$

$\frac{4950 - 3750}{3750} \times 100\%$

$\frac{1200}{3750} \times 100\%$

=36%

7 0

3 years ago

Give the explicit and recursive formula for the sequence 0,6,12,18,24

Zigmanuir [339]

<span>Your input 6,12,18,24,30,36,42,48 appears to be an arithmetic sequence</span>

3 0

3 years ago

PLEASE HELP!!!!

grandymaker [24]

10 is 20 degrees

11 is 180-145= 35 degrees

12, so the way you do it is by the fact that one opposite exterior angle is equal to two interior angles, so 40+46= 86 degrees.

8 is 86-35= 51 degrees

9 is 29 plus 62 equals 91 degrees.

Hope this helps! I tried to type this really fast

3 0

3 years ago

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