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3 years ago

How long can a go-kart travel on 6 gallons of gas

Mathematics

1 answer:

PilotLPTM [1.2K]3 years ago

6 0

Answer:

It depends in the go kart. But my guess is about 8 miles?

Step-by-step explanation:

I dont know.

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Geometry Homework Question

mash [69]

Answer:

Distance is 8.485

Midpoint is (3,4)

Step-by-step explanation:

Use the points (-1,7) and (5,1)

Insert them into the equation and solve for D

$D=\sqrt{x} ((5-(-1))^2 + (1-7)^2)\\D=\sqrt{x} ((6)^2 + (-6)^2)\\D=\sqrt{x} (36+36)\\D=\sqrt{x} (72)\\D=8.485$

Insert points into second equation to find midpoint

$(\frac{_1+5}{2} , \frac{7+1}{2}) \\(\frac{6}{2} ,\frac{8}{2} )\\(3,4)$

7 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

Anyone? will mark you as brainlist

scoray [572]

Answer:

true

Step-by-step explanation:

5 0

3 years ago

Ratio is 4:7, smaller volume is 1, 331, find larger volume

viva [34]

If the smaller volume ratio is 4 to 1331, divide 1331 by 4 to get the multiplying factor.
1331/4 = 332.75
Now we multiply 332.75 by 7 to get our larger volume.
332.75 x 7 = 2329.25
2,329 is our larger volume.
I hope this helps!

3 0

2 years ago

Write an integer that is located on a number line between the given integers.

Anna11 [10]

Creo que es la 15 porque si fuera otra pues no lo sé sería 12/56 y ya luego 4/5

4 0

2 years ago

Read 2 more answers