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2 years ago

586.875 to 2 decimal places

Mathematics

1 answer:

Alex787 [66]2 years ago

7 0

Could you explain the question more in the comment so I can help?

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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

Find the quotient: –10/19÷(−5/7)

Semmy [17]

Answer:

14/19

Step-by-step explanation:

Note that there are two " - " signs here. Thus, the end result will be " + "

We move from left to right, obtaining first 10/19 divided by (5/7):

----- ÷ (5/7)

To divide by (5/7), invert (5/7) and then multiply. We get:

10 7 2(7)

----- * ----- = ------- = 14/19

19 5 19

4 0

2 years ago

Evaluate the expression 14C2

lisabon 2012 [21]

$\bf _nC_r= \cfrac{n!}{r!(n-r)!}\qquad \qquad _{14}C_2=\cfrac{14!}{2!(14-2)!}$

5 0

3 years ago

Assume that we are interested in the average length of 1015 fishes in Square Lake, WI. Also assume that all information for all

zimovet [89]

Answer is given below

Step-by-step explanation:

given data

average length of all 1015 fishes = 98.06 mm

randomly selects 50 fishes average length = 101.04 mm

solution

When we get here, we mean to measure, so here we measure a fish in a square lake.
And the variable means that a fish varies from fish to fish, so the length of the fish in the squares
parameter mean that all individuals in the population so the parameter is average length of all 1015 fish in square lake
statics is selct of individual in sample so statistic is average length of random sected so fish in square lake

8 0

3 years ago

If Shape 1 is a scale copy of shape 2, What side corresponds of side AB?

igor_vitrenko [27]

Answer:

the answer is D. WX

Step-by-step explanation:

just look at the figure

6 0

2 years ago

586.875 to 2 decimal places​

586.875 to 2 decimal places