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dmitriy555 [2]
3 years ago
10

Simpify fully 12(x-2)^2/6(x-2)(x+5)

Mathematics
1 answer:
Vika [28.1K]3 years ago
7 0

Answer:

Step-by-step explanation:

to do this you just need to work through the maths, Eg simplify 12/6 to 2 and cancel the (x-2) this will give you an answer of 2(x-2) / X=5

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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
The ratio 25:45 in simplest form is
stepladder [879]
25/45=(5∗5)/(5∗9)=5/9

5/9 is the answer.
5 0
3 years ago
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On the equation 3 +4|v+6|=55 how would you get rid of the numbers outside of the absolute value bars
Aleonysh [2.5K]
What is the sign of 3?
5 0
3 years ago
The three shoppers spent 204$ in all . How much did each girl spend?
aleksley [76]
We would divide $204 by 3 to find out how much did each shopper spent. $204/3 is $68. So, each shopper spent $68. Hope this helped!
4 0
3 years ago
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each sale
Rom4ik [11]

Answer:

12 sales

Step-by-step explanation:

Let x represent the number of sales each man had.

For Salesman A, he earns $65 per sale; this is 65x.

For Salesman B, he earns $40 per sale; this is 40x.  We also add to this his weekly salary of $300; this gives us 40x+300.

Since their pay was equal, set the two expressions equal:

65x = 40x+300

Subtract 40x from each side:

65x-40x = 40x+300-40x

25x = 300

Divide both sides by 25:

25x/25 = 300/25

x = 12

5 0
3 years ago
Read 2 more answers
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