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olga55 [171]
4 years ago
11

celia donates 10.2 inches of her hair to a company that makes wings.danielle donates 2.4 fewer inches of her hair than celia.how

many total inches of hair do the two girls donate combined
Mathematics
1 answer:
Mashcka [7]4 years ago
7 0

mathematically the answer to that is 18 because 10.2 minus 2.4 is equal to the difference of 7.8 and 7.8 plus 10.2 is equal to the sum of exactly and positively 18

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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}

\boxed{ \tt   \red{C}arry  \: \red{ O}n \:  \red{L}earning}  \:  \underline{\tt{5/13/22}}

4 0
2 years ago
What is 2/4 as a decimal and percent
galben [10]
.5 as a decimal and 50% as a percent
3 0
3 years ago
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Please help question in the picture
tigry1 [53]
There really isn’t a possible answer since there is not enough information given. Not from what I have learned so far at least, but using common sense, and the process of elimination I would say 30
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Simplify with distributive property: 3(4 - 8x)
Lana71 [14]

Answer:

12-24x

Step-by-step explanation:

4 0
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SOMEONE PLEASE HELP ME!!! I REALLY NEED SOME HELP!!!
Lostsunrise [7]

Answer:

A. (1, -2)

Step-by-step explanation:

We can substitute the variables of x and y into the inequality of y < -|x|.

Let's start with A, -2 being y and 1 being x.

-2 < - |1|

The absolute value of 1 is 1, and negating that gets us -1.

-2 < -1

Indeed, -2 is less than -1! So A is a solution to the inequality.

Let's test the rest of them, just in case.

For B:

-1 < -|1|

Absolute value of 1 is 1, negating it is -1.

-1

-1 is EQUAL to -1, not less than it, so is not a solution to the inequality.

Let's try C.

0 < -|1|

Absolute value of 1 is 1, negating it is -1.

0 < -1

0 is GREATER than -1, so that is not a solution to the inequality.

Hope this helped!

4 0
3 years ago
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