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3 years ago

Factorise:

Mathematics

1 answer:

Sliva [168]3 years ago

6 0

Answer:

a)(5m+3n)^3 b)(4a-3b)^3

Step-by-step explanation:

a)125m^3+27n^3+225m^2 n+135mn^2

Use the binomial cube formula, a^3+3a^2

b+3ab^2+b^3=(a+b)^3, where a=5m and b=3n.

(5m+3n)^3

b)64a^3-144a^2 b+108ab^2-27b^3

Use the binomial cube formula, p^3-3p^2q+3pq^2-q^3=(p-q)^3, where p=4a and q=3b.

(4a-3b)^3

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

3 years ago

Can someone tell me the answer for this please?

Tom [10]

4x+1+57=90
4x+58=90
4x=32
X=8

4 0

3 years ago

Please help meeeeeeeee

nata0808 [166]

Answer Q3:

A) 2/6

This decimal would be written as 0.33333333 and on.

I don't get number 4 but I'm pretty sure its A because 12 times 12 is 144 and and you have to add the 18.

4 0

3 years ago

Read 2 more answers

Andrea spent a total of $43.87 on new clothes at a clothing store. She bought 1 pair of sandals for $8, 2 t-shirts for $9.49 eac

Misha Larkins [42]

43.87 - 8 = 35.87 (sandals)
9.49 + 9.49 = 18.98 ( for two t-shirts)
35.87 - 18.98 = 16.89 (t-shirts)
16.89 - 2.87 = 14.02 (taxes)
Andrea payed $14.02 for a pair of jeans
Hopes this helps you!

6 0

3 years ago

What is 3467+5895? Btw thanks

Akimi4 [234]

9,362 is the answer.

hope this helps!

4 0

3 years ago

Read 2 more answers