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solniwko [45]
3 years ago
10

My number is a multiple of 15 it is also a multiple of 10 it is greater rthan 100 and less than 200

Mathematics
2 answers:
marusya05 [52]3 years ago
7 0

Answer:

150. 15*10=150 and it is inbetween 100 and 200.

Step-by-step explanation:

alexandr402 [8]3 years ago
4 0

150. 15*10 = 150, and its in-between 100 and 200.

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Find an equation of the sphere with center (4, −12, 8) and radius 10. use an equation to describe its intersection with each of
xxMikexx [17]
<span>Sphere: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 Intersection in xy-plane: (x - 4)^2 + (y + 12)^2 = 36 Intersection in xz-plane: DNE Intersection in yz-plane: (y + 12)^2 + (z - 8)^2 = 84 The desired equation is quite simple. Let's first create an equation for the sphere centered at the origin: x^2 + y^2 + z^2 = 10^2 Now let's translate that sphere to the desired center (4, -12, 8). To do that, just subtract the center coordinate from the x, y, and z variables. So (x - 4)^2 + (y - -12)^2 + (z - 8)^2 = 10^2 (x - 4)^2 + (y - -12)^2 + (z - 8)^2 = 100 Might as well deal with that double negative for y, so (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 And we have the desired equation. Now for dealing with the coordinate planes. Basically, for each coordinate plane, simply set the coordinate value to 0 for the axis that's not in the desired plane. So for the xy-plane, set the z value to 0 and simplify. So let's do that for each plane: xy-plane: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 (x - 4)^2 + (y + 12)^2 + (0 - 8)^2 = 100 (x - 4)^2 + (y + 12)^2 + (-8)^2 = 100 (x - 4)^2 + (y + 12)^2 + 64 = 100 (x - 4)^2 + (y + 12)^2 = 36 xz-plane: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 (x - 4)^2 + (0 + 12)^2 + (z - 8)^2 = 100 (x - 4)^2 + 12^2 + (z - 8)^2 = 100 (x - 4)^2 + 144 + (z - 8)^2 = 100 (x - 4)^2 + (z - 8)^2 = -44 And since there's no possible way to ever get a sum of 2 squares to be equal to a negative number, the answer to this intersection is DNE. This shouldn't be a surprise since the center point is 12 units from this plane and the sphere has a radius of only 10 units. yz-plane: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 (0 - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100 (-4)^2 + (y + 12)^2 + (z - 8)^2 = 100 16 + (y + 12)^2 + (z - 8)^2 = 100 (y + 12)^2 + (z - 8)^2 = 84</span>
6 0
3 years ago
A card is drawn from a well-shuffled deck of 52. Find p(drawing a face or a 4)
Musya8 [376]

Answer:

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4 0
3 years ago
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babunello [35]

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3 years ago
Use a double angle or half angle identity to find the exact value of each expression
inna [77]

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aivan3 [116]

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The expression is

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The factored form of given expression after factor out the coefficient of the variable term.

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We have,

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Here, the coefficient of variable n is \dfrac{1}{2}.

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