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2 years ago

How do you estimate 12.062g to the nearest tens of a gram

Mathematics

1 answer:

gtnhenbr [62]2 years ago

6 0

12.602 = 10g
or if you meant tenTHs it will be 13g

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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

Eleven oz of ground coffee is 2 cups. How many cups is 12 oz?

SVETLANKA909090 [29]

Answer:

66 oz

Step-by-step explanation:

Every 2 cups have 11 ounces of ground coffee. Two times six is 12, so 11 times 6 is 66.

Another explanation is-

2/12 = 11/x

12 times 11 is 132. Then divide that by two to get 66

4 0

3 years ago

Randys garden has 3 rows of carrot with 3 plants in each row. next year he plans to plant 4 times the number of rows of 3 plants

Gnesinka [82]

He will have 36 plants next year.
hope that helped! :)

5 0

3 years ago

How much would you need to deposit in an account now in order to have $3000 in the account in 15 years? Assume the account earns

Rzqust [24]

Answer:

Principal = Total ÷ (1 + Rate)^years

That formula is found here: http://www.1728.org/compint2.htm

Principal = 3.000 / (1.03) ^ 15

Principal = 3.000 / 1.5579674166

Principal = $1,925.59

Step-by-step explanation:

7 0

2 years ago

PLEASE HELP WILL MARK BRAINLIEST<br><br>Find the area of the right triangle.

sweet-ann [11.9K]

Answer:

Step-by-step explanation:

This right triangle is on a grid.

The area is the height * base/2

The base is on a line segment parallel to the x axis which is 6 squares.

The height is on a line segment parallel to the y axis which is 2 squares

The area is the height * base /2

Area = 6 * 2 /2 = 12/2 = 6 square units.

4 0

3 years ago