All categories

3 years ago

What is the answer to this question

Mathematics

1 answer:

zimovet [89]3 years ago

3 0

Answer:

n^10/(144m^4)

Step-by-step explanation:

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

(a^b)(a^c) = a^(b+c)

(a^b)/(a^c) = a^(b-c)

a^-b = 1/a^b

(ab)^c = (a^c)(b^c)

Using these rules, we can simplify the given expression as follows:

$\left(\dfrac{3m^{-5}n^2}{4m^{-2}n^0}\right)^2\left(\dfrac{mn^4}{9n}\right)^2=\left(\dfrac{3}{4}m^{-5(-(-2))}n^{2-0}\right)^2\left(\dfrac{1}{9}mn^{4-1}\right)^2\\\\=\left(\dfrac{3n^2}{4m^3}\right)^2\left(\dfrac{m^3}{9}\right)^2=\dfrac{3^2n^4}{4^2m^6}\cdot\dfrac{m^2n^6}{9^2}=\boxed{\dfrac{n^{10}}{144m^4}}$

You might be interested in

Kathy is baking cakes each cake requires 1/12 of a teaspoon of vanilla and she has 9/12 of a teaspoon how many cakes can she bak

masya89 [10]

Kathy can make 9 cakes

8 0

3 years ago

Read 2 more answers

1/2x-2/3>3 enter your answer using interval notation

Nata [24]

So basically u keep the x on one side and the rest on the other. Get a common denominator. to get rid of the half u times both sides by 2.
hope this helps

7 0

3 years ago

U th th V 3 D F Geometry

loris [4]

Answer:

interesting can i get brainliest

Step-by-step explanation:

8 0

3 years ago

∫(cosx) / (sin²x) dx

kirza4 [7]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2822772

_______________

Evaluate the indefinite integral:

$\mathsf{\displaystyle\int\! \frac{cos\,x}{sin^2\,x}\,dx}\\\\\\
=\mathsf{\displaystyle\int\! \frac{1}{(sin\,x)^2}\cdot cos\,x\,dx\qquad\quad(i)}$

Make the following substitution:

$\mathsf{sin\,x=u\quad\Rightarrow\quad cos\,x\,dx=du}$

and then, the integral (i) becomes

$=\mathsf{\displaystyle\int\! \frac{1}{u^2}\,du}\\\\\\
=\mathsf{\displaystyle\int\! u^{-2}\,du}$

Integrate it by applying the power rule:

$\mathsf{=\dfrac{u^{-2+1}}{-2+1}+C}\\\\\\
\mathsf{=\dfrac{u^{-1}}{-1}+C}\\\\\\
\mathsf{=-\,\dfrac{1}{u}+C}$

Now, substitute back for u = sin x, so the result is given in terms of x:

$\mathsf{=-\,\dfrac{1}{sin\,x}+C}\\\\\\
\mathsf{=-\,csc\,x+C}$

$\therefore~~\boxed{\begin{array}{c}\mathsf{\displaystyle\int\! \frac{cos\,x}{sin^2\,x}\,dx=-\,csc\,x+C} \end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: indefinite integral substitution trigonometric trig function sine cosine cosecant sin cos csc differential integral calculus

5 0

4 years ago

Order the side lengths AB, BC, and CA from least to greatest.

jarptica [38.1K]

Answer:

BC < AC < AB

Step-by-step explanation:

In triangle smallest has the smallest opposite side and so on

first find ∠A = 180 - 59 - 79

= 42

∠A < ∠B < ∠C

Then ∠A opposite side is BC is less

so BC < AC < AB

3 0

3 years ago