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2 years ago

15

When you are trying to find the endpoint when given the midpoint and one point, what would the new formula be? Manipulate the fo

rmula using skills for solving literal equations. How would you find LaTeX: x_2\:\:\:or\:\:\:y_2x 2 o r y 2? Use LaTeX: x_m\:\:and\:\:\:\:y_mx m a n d y mto notate the midpoints. Remember the original midpoint formula is LaTeX: \left(\frac{x_1+\:x_2}{2},\:\:\frac{y_{1\:}+y_2}{2}\right)\:=\:\left(x_m,\:y_m\right)

1 answer:

MariettaO [177]2 years ago

7 0

Answer:

$(x_2,y_2) = (2x_m - x_1 ,2y_m - y_1 )$

Step-by-step explanation:

Given

$\left(\frac{x_1+\:x_2}{2},\:\:\frac{y_{1\:}+y_2}{2}\right)\:=\:\left(x_m,\:y_m\right)$

Required

Determine x2, y2

Start by splitting the expression

$x_m = \left(\frac{x_1+\:x_2}{2})$ and $y_m = (\frac{y_{1\:}+y_2}{2})$

Solving for x2 in $x_m = \left(\frac{x_1+\:x_2}{2})$

Multiply through by 2

$2 * x_m = \frac{x_1 + x_2}{2} * 2$

$2x_m = x_1 + x_2$

Make x2 the subject;

$x_2 = 2x_m - x_1$

Similarly:

$y_m = (\frac{y_{1\:}+y_2}{2})$

Multiply through by 2

$2 * y_m = \frac{y_1 + y_2}{2} * 2$

$2y_m = y_1 + y_2$

Make y2 the subject;

$y_2 = 2y_m - y_1$

Hence:

$(x_2,y_2) = (2x_m - x_1 ,2y_m - y_1 )$

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Suppose integral [4th root(1/cos^2x - 1)]/sin(2x) dx = A<br>What is the value of the A^2?<br><br>

Alla [95]

$\large \mathbb{PROBLEM:}$

$\begin{array}{l} \textsf{Suppose }\displaystyle \sf \int \dfrac{\sqrt[4]{\frac{1}{\cos^2 x} - 1}}{\sin 2x}\ dx = A \\ \\ \textsf{What is the value of }\sf A^2? \end{array}$

$\large \mathbb{SOLUTION:}$

$\!\!\small \begin{array}{l} \displaystyle \sf A = \int \dfrac{\sqrt[4]{\frac{1}{\cos^2 x} - 1}}{\sin 2x}\ dx \\ \\ \textsf{Simplifying} \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt[4]{\sec^2 x - 1}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt[4]{\tan^2 x}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt{\tan x}}{\sin 2x}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sqrt{\tan x}}{\sin 2x}\cdot \dfrac{\sqrt{\tan x}}{\sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\tan x}{\sin 2x\ \sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\dfrac{\sin x}{\cos x}}{2\sin x \cos x \sqrt{\tan x}}\ dx\:\:\because {\scriptsize \begin{cases}\:\sf \tan x = \frac{\sin x}{\cos x} \\ \: \sf \sin 2x = 2\sin x \cos x \end{cases}} \\ \\ \displaystyle \sf A = \int \dfrac{\dfrac{1}{\cos^2 x}}{2\sqrt{\tan x}}\ dx \\ \\ \displaystyle \sf A = \int \dfrac{\sec^2 x}{2\sqrt{\tan x}}\ dx, \quad\begin{aligned}\sf let\ u &=\sf \tan x \\ \sf du &=\sf \sec^2 x\ dx \end{aligned} \\ \\ \textsf{The integral becomes} \\ \\ \displaystyle \sf A = \dfrac{1}{2}\int \dfrac{du}{\sqrt{u}} \\ \\ \sf A= \dfrac{1}{2}\cdot \dfrac{u^{-\frac{1}{2} + 1}}{-\frac{1}{2} + 1} + C = \sqrt{u} + C \\ \\ \sf A = \sqrt{\tan x} + C\ or\ \sqrt{|\tan x|} + C\textsf{ for restricted} \\ \qquad\qquad\qquad\qquad\qquad\qquad\quad \textsf{values of x} \\ \\ \therefore \boxed{\sf A^2 = (\sqrt{|\tan x|} + c)^2} \end{array}$

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4 0

1 year ago

Which of the following is equal to 5 4/9? The answers are:

madam [21]

Answer:

5.4

Step-by-step explanation:

First work out 4/9 this is the same thing as 4 ÷ 9 which equals 0.44444

and then add the whole number 5 so,

5 + 0.44444 = 5.44444

3 0

3 years ago

A trampoline has a rectangular jumping surface that is 10.3 feet long and 9.3 feet wide . What is the area of the jumping surfac

Andrei [34K]

Area is equals length times (*) breath
L*b
10.3*9.3
=95.79l

4 0

2 years ago

2,826 rounded to the nearest tenth

jasenka [17]

Answer:

2,826

Step-by-step explanation:

A tenth is the first place value after the decimal point

In this case, 2,826.<u>0</u>0

To round a number to the tenths place, we look at the hundredths place

If the number is 5 or more, we add 1 to the tenths place, and leave the numbers to the right 0's

If the number is 4 or less, we keep the number as it is in the tenths place, and leave the numbers to the right 0's

In this case, the hundredths place is a 0, which is less than 4, so we keep the 0 in the tenths place, and leave the to the right 0's.

Thus, our final answer is 2,826.

8 0

2 years ago

How do you solve this step by step? “ I’m thinking of a number. If you multiply it by 6 and then add 7, you will get 55. What is

lozanna [386]

Answer:

8

Step-by-step explanation:

55 -7 = 48

48/6= 8

Check answer:

8x6= 48

48+7= 55

5 0

3 years ago

Read 2 more answers