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3 years ago

What is bigger one yard or one meter

Mathematics

1 answer:

Rus_ich [418]3 years ago

5 0

One meter is greater than 1 yards because we know 1 meter = 1.093 yards

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-1/5(x-4)=-2 how do you solve this equation

m_a_m_a [10]

Multiple both sides by 5/1 and get

-1/1 • (x-4) = -10/1

divide the numbers and get

-1 • (x-4) = -10

remove the parentheses

- x-4 = 10

move the constant to the right

-x = -10-4

calculate

-x = -14

change the signs

x= 14

8 0

3 years ago

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

4 years ago

100 points!!! Which graph represents an exponential function?

drek231 [11]

Answer:

its 50 points but still answer is a

5 0

3 years ago

Read 2 more answers

Write a recursive formula for an, the nth term of the sequence 3, -4, -11

yKpoI14uk [10]

Answer:

, 12, 48, 192...

a. Write a recursive formula for the nth term of the sequence

Ans: a(n+1) = 4*a(n)

------------------------------

b. Write a general formula for the nth term of the sequence

a(n) = 3*4^(n-1)

--------------

c. Calculate S10 for this sequence

Geometric sequence with a(1) = 3 and r = 4

----?

Step-by-step explanation:

8 0

3 years ago

Simple geometry problem

vova2212 [387]

Answer:

Step-by-step explanation:

I gather that you need to find the area of the sector and then subtract from it the area of the segment to get the area of the triangle (although there are other ways in which to find the area of the triangle).

The area of a sector is:

$A=\frac{\theta}{360}\pi r^2$ where our angle is given as 34, pi is 3.1415, and the radius is 5:

$A=\frac{34}{360}(3.1415)(25)$ and if you multiply and divide that all out you get that the area of the sector is:

A = 7.417

Now subtract from it the area of the segment, 2.209. to get the area of the triangle:

7.417 - 2.209 = 5.208

7 0

3 years ago

Read 2 more answers