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bearhunter [10]
2 years ago
7

My question is asking me..."A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 centimeter

s cubed, what is the volume of the sphere"...I'm not entirely sure how to work this out pls help...i only have like 35 minutes left to do my test T-T
Mathematics
1 answer:
sattari [20]2 years ago
3 0

Answer:

12 cm^{3}

Step-by-step explanation:

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Find the equation of the circle with center (4,5) which passes through the y-intercept of the line 5x-2y+6=0​
Elena-2011 [213]

Answer:

(x-4)^2 + (y-5)^2 = 20

Step-by-step explanation:

Rearrange the line equation of 5x - 2y + 6 = 0

So y = 5/2x +3

The y-intercept of the line equation is 3 as when x=0, y=3.

We know the Circle has the formula (x-4)^2 + (y-5)^2 = ?^2 from the question but with the intercept, we can find the entire equation as the y-intercept is (0,3) so we can substitute it into the equation to find the full equations so:

(0-4)^2 + (3-5)^2 = ?^2

This simplifies to:

(-4)^2 +(-2)^2 = ?^2

16 + 4 = 20 = ?^2

The answer is 20 so the equation of the circle is (x-4)^2 + (y-5)^2 = 20

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2 years ago
(PLEASE IM DESPERATE) 3. A toy catapult launched a ball. The height of the ball could be modelled by
Elena-2011 [213]

Answer:

I think it could be modelled by the function I'm  not 100 percent sure but i hope it helps

Step-by-step explanation:

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3 years ago
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Find the distance between P1(4,16degrees) and P2(-2,177degrees) on the polar plane.
bazaltina [42]
Polar coordinates give the distance from the origin and the angle from the positive x axis. Cartesian coordinates give the distance from the x and y axes.

You can draw a right triangle with these values. (see attached)
If you know the r value and theta of that triangle below, you can use trig to find x and y.

Let's convert (4, 16°) to Cartesian coordinates.

Note that since our angle is acute, (in Quadrant I) our sine and cosine will both be positive, as you should be able to derive from the unit circle, where cosine is represented as an x value and sine is represented as a y value.

cosine = adjacent / hypotenuse
cosθ = x/r
cos(16°) = x/4
4cos(16°) = x ≈ 3.84504678375

sine = oppsite / hypotenuse
sinθ = y/r
sin(16°) = y/4
4sin(16°) = y ≈ 1.10254942327<span>

So (4, 16°) </span>⇒ (3.84504678375, 1.10254942327).

Let's convert (-2, 177°)  to Cartesian coordinates.
Whenever you have a negative radius, that means to put the point opposite where it would have been if it had a positive radius. (see attached)

In that case, we can essentially add 180° to our current 177° to the same effect. That means that (-2, 177°) = (2, 357°).

Note that since our angle is in Quadrant IV, our cosine will be positive, but our sine will be negative. (as derived from the unit circle) We don't have to worry about this since our calculator figures this for us, but you should pay attention to it if you are converting from Cartesian to polar.

cosine = adjacent / hypotenuse
cosθ = x/r
cos(357°) = x/2
2cos(357°) = x ≈ 1.99725906951

sine = opposite / hypotenuse
sinθ = y/r
sin(357°) = y/2
2sin(357°) = y ≈ -0.10467191248

So (-2, 177°) ⇒ (1.99725906951, -0.10467191248).

Now we must use the distance formula with our two points.
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
d\approx\sqrt{(1.99725906951-3.84504678375)^2+(-0.10467191248-1.10254942327)^2}
d\approx\sqrt{-1.84778771^2+-1.20722134^2}
d\approx\sqrt{3.41431942+1.45738336}
d\approx\sqrt{4.87170278}
\boxed{d\approx2.20719342}

7 0
3 years ago
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