This question is a piece-o-cake if you know the formulas for the area and volume of a sphere, and impossible of you don't.
Area of a sphere = 4 π R² (just happens to be the area of 4 great circles)
Volume of a sphere = (4/3) π R³
We know the area of this sphere's great circle, so we can use the
first formula to find the sphere's radius. Then, once we know the
radius, we can use the second formula to find its volume.
Area of 4 great circles = 4 π R²
Area of ONE great circle = π R²
225 π cm² = π R²
R² = 225 cm²
R = √225cm² = 15 cm .
Now we have a number for R, so off we go to the formula for volume.
Volume = (4/3) π R³
= (4/3) π (15 cm)³
= (4/3) π (3,375 cm³)
= 14,137.17 cm³ (rounded)
This answer feels very good UNTIL you look at the choices.
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I've gone around several loops and twists trying to find out what gives here,
but have come up dry.
The only thing I found is the possibility of a misprint in the question:
If the area of a great circle is 225π cm², then the sphere's AREA is 900π cm².
I'm sure this is not the discrepancy. I'll leave my solution here, and hope
someone else can find why I'm so mismatched with the choices.
Answer:
x = 20
y = 100
Step-by-step explanation:
To figure out x do this.
3x + 2x = 7x - 40 (collect like terms)
5x = 7x -40 (subtract 7x on both sides)
-2x = -40 (divide by -2 on both sides)
x = 20
Plug in to get y
Since 7x - 40 and y are vertical they equal the same amount
7(20) - 40 = y (multiply 7 by 20)
140 - 40 = y (collect like terms)
100 = y
Hope this helps ya! Keep smiling!
<h3>
Answer: 10 metal bats</h3>
"Ratio of wooden bats to metal bats is 2 to 1" basically means "there are twice as many wooden bats (compared to metal ones)". So if we had 3 metal bats, then we'd have 2*3 = 6 wooden bats. If we had 7 metal bats, then we have 14 wooden ones (because 2*7 = 14). And so on. The basic rule is to multiply the amount of metal bats by 2 to get the amount of wooden ones.
We can go in reverse to divide the amount of wooden bats to get the amount of metal ones. So 20/2 = 10 is the amount of metal bats.
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A more formal approach is to use the proportion below to solve for x
20/x = 2/1
20*1 = x*2
20 = 2x
2x = 20
2x/2 = 20/2
x = 10
and we get the same answer.
A number pattern would be something that just gets repeated over and over
so for this example 120+120+120=360
so the least common multiple is 120 because adding 120, three times will get you to 360
Answer:
tan(a) = -4/3
sec(a) = 5/3
Step-by-step explanation:
sine is opposite over hypotenuse. so no we have a triangle with a hypotenuse of 5 and an opposite side relative to some angle a of -4. the hypotenuse is never negative.
so draw a right triangle, mark one of the non right angles as a then the side opposite to that is -4 and the hypotenuse is 5. use the pythagorean theorem to find the remaining angle. The result could be positive or negative, but the questions specifically tells us we want the positive version.
b^2 + -4^2 = 5^2
b = 3
tangent is opposite over adjacent. for a we know the opposite is 3now so tan(a) = -4/3
Now, secant is 1/cos, so lets find cos(a)
cos is adjacent over hypotenuse, and we jsut found the adjacent is 3. so cos(a) = 3/5
Now 1/cos(a) = hypotenuse over adjacent so 5/3
