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3 years ago

What is the value of x?

Mathematics

1 answer:

Marysya12 [62]3 years ago

4 0

A triangle always adds up to 180 degrees:

Therefore, 48 + 6x + 9x-3 = 180

Solve for x:

180 - 45 = 15x
135 = 15x

x = 9 degrees

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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

Can someone help me with this please?

Pepsi [2]

The 5x5 square grid has 6 , 2 x 2 subgrids and the least value of n for which you can be certain that it will have a 2 x 2 subgrid of grey squares is 12.

<h3>What is a Square ?</h3>

A square is a polygon with four sides and all the sides are equal and parallel and all the angle value is 90 degree.

(a) The 5x5 square grid has 6 , 2 x 2 subgrids.

(b) the least value of n for which you can be certain that it will have a 2 x 2 subgrid of grey squares is 12

as it can be understood from the figure 2 that only the last square doesn't have a pair and the rest all does

more than that will be extra but 12 will be enough to make all the grey squares of 2 x 2 subgrid .

To know more about Square

brainly.com/question/14198272

#SPJ1

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2 years ago

What is the constant of proportionality in the equation y=25X?

Ad libitum [116K]

Answer:

Step-by-step explanation:

y = kx

If y = 25x , then k = 25

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3 years ago

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svp [43]

The answer is <span>0.10619469026.

It takes about 9lbs of seed to plant 1-acre, so to find the answer divide 12/113 and you get how many acres 1lb of seed could cover.

Hope this helps :-)

</span>

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