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3 years ago

How could you find which weighs more, one tone of pillows or one ton of bowling balls?

Mathematics

2 answers:

yuradex [85]3 years ago

8 0

By measuring them both

In-s [12.5K]3 years ago

3 0

Neither! As you said ''a ton'' for both of them. Also IF it refers to mass then they are obviously the same. My answer is: Neither.

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Find the measure of each angle in the figure. Enter your answers as numbers.

lyudmila [28]

Angle 6 - 30
Angle 5 - 73
Angle 1 - 37
Angle 2 - 52
Angle 4 - 63
Angle 3 - 128

4 0

4 years ago

A line has a slope of 5 and passes through the point (-1,2).

Andreyy89

Answer:

Step-by-step explanation:

slope=m= 5

points=(-1,2)

<u>By point-slope form:</u>

$y$ - $y_{1}$ =m( $x-x_{1}$ )

<u>Substitute the values in formula:</u>

<u>y-2=5(x+1)</u> (It is the point slope form)

Now,

<u>Slope intercept form:</u>

y-2=5x+5

y=5x+5+2

<u>y=5x+7</u>

<u />

<h3><u>If you need to ask any questions, please let me know.</u></h3>

5 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

3 years ago

What does this graph show<br> inverse <br>direct<br> neither

grin007 [14]

Answer:

i think the given graph is inverse

3 0

2 years ago

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y + 1 = 0?

Bezzdna [24]

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

4x + y + 1 = 0

y = - 4x - 1

Comparing with the above formula

Slope / m = - 4

Since the lines are parallel their slope are also the same

That's

Slope of the parallel line is also - 4

Equation of the line using point ( 1 , 2) is

y - 2 = -4(x - 1)

y - 2 = - 4x + 4

4x + y - 2 - 4

We have the final answer as

Hope this helps you

7 0

3 years ago