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MrRissso [65]
3 years ago
9

Complete the statement 10/7 x __= 1

Mathematics
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
Read 2 more answers
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