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3 years ago

alexander spins a spinner with four equally-sized regions and flips a coin. how many outcomes are possible?

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

8 0

8 outcomes the other guy is wrong . The coin multiplies it by 2

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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 $b=\frac{40}{13}$ .

5 0

2 years ago

PLEASE HELP!

eduard

Answer:

B) 2828.427g

Step-by-step explanation:

Hope this helps!

7 0

2 years ago

Read 2 more answers

Multiple all the coordinates by 1/5.

Andrew [12]

Answer:

(-1,2) , (2,-1), (2,-1) , (-2,1)

Step-by-step explanation:

-5 x 0.2=-1

5 x 0.2=1

10 x 0.2= 2

-10x 0.2=-2

6 0

2 years ago

I need help ASAP please

Solnce55 [7]

Answer:

x = 6

Step-by-step explanation:

The area of a triangle is equal to the base times the height divided by two. In this case, the base is 6 (or x, it doesn't really matter) and the height is x (or 6, it doesn't matter). That means that the area of this triangle is equal to 6 * x divided by 2, which is also equal to 18. we can say that 6x/2 = 18, meaning that 6x = 36, so x = 6.

6 0

2 years ago

One pound of red grapes cost $2.42 Ella buys worth 0.5 pound how much does she spend on red grapes

Bess [88]

Answer:

1.21

Step-by-step explanation:

The cost of the grapes is the price per pound times the number of pounds

cost = 2.42 * .5

cost = 1.21

7 0

3 years ago