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3 years ago

Which expression is equivalent to 15x^-3z^5/3x^7z^-5 please answer spr fast

Mathematics

2 answers:

ratelena [41]3 years ago

6 0

Answer:

Step-by-step explanation:

Answer:

5^4

Law Incorporation [45]3 years ago

3 0

Answer:

$5x^{-10}z^{10$

Step-by-step explanation:

Given

$\frac{15x^{-3}z^5}{3x^7z^{-5}}$

Required

Evaluate

$\frac{15x^{-3}z^5}{3x^7z^{-5}}$

Start by dividing 15 by 3

$\frac{5x^{-3}z^5}{x^7z^{-5}}$

Apply the following law of indices on indices x and z

$\frac{a^m}{a^n} = a^{m-n$

So, the expression becomes:

$5x^{-3-7}z^{5-(-5)$

$5x^{-3-7}z^{5+5$

$5x^{-10}z^{10$

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

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

In this diagram, BAC~EDF. If the area of BAC=15 in2, what is the area of EDF? 4, 5.

lesya692 [45]

Answer:

9.6 square inches.

Step-by-step explanation:

We are given that ΔBAC is similar to ΔEDF, and that the area of ΔBAC is 15 inches. And we want to determine the area of ΔDEF.

First, find the scale factor k from ΔBAC to ΔDEF:

$\displaystyle 5 k = 4$

Solve for the scale factor k:

$\displaystyle k = \frac{4}{5}$

Recall that to scale areas, we square the scale factor.

In other words, since the scale factor for sides from ΔBAC to ΔDEF is 4/5, the scale factor for its area will be (4/5)² or 16/25.

Hence, the area of ΔEDF is:

$\displaystyle \Delta EDF = \frac{16}{25}\left(15\right) = 9.6\text{ in}^2$

In conclusion, the area of ΔEDF is 9.6 square inches.

5 0

3 years ago

3 gallons of paint cover 900 square feet. How many gallons will cover 300 square feet?

SVEN [57.7K]

Answer:

1 gallon

Step-by-step explanation:

Since the relationship is direct, meaning as the number of square feet decreases, the number of gallons also decreases.

3:900 = x:300

solution:

3(300) = 900x

900=900x

x=1

4 0

3 years ago

Read 2 more answers

Does Emiliano need more than 1 stick of butter or less than 1 stick of butter for the corn bread and the apple muffins?

Nookie1986 [14]

Answer:

Emilio needs less than 1 stick of butter

Step-by-step explanation:

Emilio needs 1/2 stick of butter to make cornbread . He also needs 1/4 stick of butter to make apple muffins . Does Emilio need more than I stick of butter to make both recepes or less than 1 stick of butter ? How do you know?

Cornbread = 1/2 stick of butter

Apple muffins = 1/4 stick of butter

Total sticks of butter = cornbread + apple muffins

= 1/2 + 1/4

= (2+1) / 4

= 3/4 stick of butter

= 0.75 stick of butter

0.75 stick of butter is less than 1 stick of butter

Therefore,

Emilio needs less than 1 stick of butter

4 0

3 years ago

1. Michael buys a chocolate bar which has 50% extra free. The chocolate bar usually weighs 200g. (a) How much extra chocolate do

KiRa [710]

Answer:

1/2 more chocalte or 50% more or 100g more

300g is the new weight

Step-by-step explanation:

200/2=100(50%)

100+200=300g

5 0

3 years ago