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4 years ago

15

If the expression (2y^a)^4 is equivalent to 16y^8, what is the value of a

1 answer:

Brrunno [24]4 years ago

5 0

Answer:

A = 2.

Step-by-step explanation:

When raising power to power and there is a base with a exponent and a coefficant, you need to know that the a exponent only belongs to the y. The 2 has a invisible 1 exponent. The new expression is now (2^1 y^a)^4 = 16y^8. Now it is time to solve it. 1x4 = 4 so it is (2^4 y^a) = 16y^8. 2^4 is also 2x2x2x2 which equals 16. Now for the a exponent, 8/4 = ?. 2. The new expression is 16y^2 and a = 2.

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3 years ago

The difference of four times a number and nine is 27. Find the number.

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3 years ago

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3 years ago

Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

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

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

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3 years ago

What is 102.75609756 as a whole number please answer

Komok [63]

Answer:

what? if u mean by rounding, its 103

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4 years ago