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4 years ago

HELP WITH QUESTION! IT IS BELOW! COUSIN NEED SHLEP

Mathematics

1 answer:

Contact [7]4 years ago

6 0

Answer:

The answer is

Step-by-step explanation:

To find an equation of a line given a slope and a point we use the formula

$y - y_1 = m(x - x_1)$

where

m is the gradient

( x1 , y1) is the point

From the question

Gradient = 2

The point is ( 1 , 4)

The equation is

$y - 4 = 2(x - 1) \\ y - 4 = 2x - 2 \\ y = 2x - 2 + 4 \: \:$

We have the final answer as

$y = 2x + 2$

Hope this helps you

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4 years ago

Integrate the following

enot [183]

I suppose you mean to have the entire numerator under the square root?

$\displaystyle\int_2^4\frac{\sqrt{x^2-4}}{x^2}\,\mathrm dx$

We can use a trigonometric substitution to start:

$x=2\sec t\implies\mathrm dx=2\sec t\tan t\,\mathrm dt$

Then for $x=2$ , $t=\sec^{-1}1=0$ ; for $x=4$ , $t=\sec^{-1}2=\frac\pi3$ . So the integral is equivalent to

$\displaystyle\int_0^{\pi/3}\frac{\sqrt{(2\sec t)^2-4}}{(2\sec t)^2}(2\sec t\tan t)\,\mathrm dt=\int_0^{\pi/3}\frac{\tan^2t}{\sec t}\,\mathrm dt$

We can write

$\dfrac{\tan^2t}{\sec t}=\dfrac{\frac{\sin^2t}{\cos^2t}}{\frac1{\cos t}}=\dfrac{\sin^2t}{\cos t}=\dfrac{1-\cos^2t}{\cos t}=\sec t-\cos t$

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3 years ago

What is a equation in slope intercept form for a line that passes through (5,4) and has a slope of -5

liubo4ka [24]

Answer:

Step-by-step explanation:

The easiest way to complete this is too use this data and put it into point-slope form. This is written as, y-y1=m(x-x1)

In this equation y1 is the y- coordinate of your point and x1 is the x-coordinate. M in this case would also be known as the slope.

Now we can submit our data-----

y-4=-5(x-5) -------- simplify

y-4=-5x+25 --------

y=-5x+28

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4 years ago