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lorasvet [3.4K]

2 years ago

11

A bus covers a certain distanc in 45 minutes if it runs at a Speed of 60km/hr. What must be the speed of the bus in order to red

uce the time by 20 minutes .

1 answer:

Ket [755]2 years ago

8 0

2.66 is the speed

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Expand the following x(x-6), x(4x-1), 2x(5x+4), 3x(5x-y)

zlopas [31]

Answer:

x^2-6x, 4x^2-1x,10x^2+8x,15x^2-3xy

Just use the distributive property like you have before and you will get these answers, Hope this helped!

4 0

3 years ago

Read 2 more answers

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

Simplify quantity 1 over 36 minus 1 over x squared all over 1 over 6 plus 1 over x.

Ne4ueva [31]

<span>[ (1 / 36) - (1 / x²) ] / [ (1 / 6) + (1 / x) ]

[ (x² - 36) / 36x² ] / [ (x + 6) / 6x ]

</span>remember that<span>:
x² - 36 = (x + 6)(x - 6)

so

[ (x+6)(x-6) / 36x² ] / [ (x + 6) / 6x ]

[ (x+6)(x-6) / 36x² ] * [ 6x / (x + 6) ]

6x / 36x² = 1 / 6x

[ (x+6)(x-6) / 6x ] * [ 1 / (x+6) ] -------------------- > </span>(x - 6) / 6x<span>

The answer is </span>(x - 6) / 6x<span>

</span>

7 0

3 years ago

How do I do this? I really need help

dimulka [17.4K]

If you want to find the diameter of a circle multiply the radius by 2
Dh-2

4 0

3 years ago

Read 2 more answers

Claire makes hot coco with 2 cups of milk with 5 tablespoons of coco. How many tablespoons of coco would he need for 1 cup of mi

postnew [5]

Answer:

2.5

Step-by-step explanation:

5/2=2.5

half of 2 is 1 so for 1 cup of coco has 2.5 tbs of coco.

6 0

3 years ago

Read 2 more answers