You did not include the figure, but according to the statement the viewing room of the planetarium is in the shape of a hemisphere.
A hemisphere is half a sphere.
So, the volume of a hemisphere is the half of the volume of the complete sphere.
The formula for the volume of a sphere is:
V = (4/3) π (radius)^3
Using π = 3.14 and radius = diameter / 2 = 50 feet / 2 = 25 feet.
You get:
V = (4/3) (3.14) (25 feet)^3 = 65,416.7 feet^3
Answer: 65,416.7 cu. ft.
Answer:
(2x-1)(2x+1)(x^2+2) = 0
Step-by-step explanation:
Here's a trick: Use a temporary substitution for x^2. Let p = x^2. Then 4x^4+7x^2-2=0 becomes 4p^2 + 7p - 2 = 0.
Find p using the quadratic formula: a = 4, b = 7 and c = -2. Then the discriminant is b^2-4ac, or (7)^2-4(4)(-2), or 49+32, or 81.
Then the roots are:
-7 plus or minus √81
p= --------------------------------
8
p = 2/8 = 1/4 and p = -16/8 = -2.
Recalling that p = x^2, we let p = x^2 = 1/4, finding that x = plus or minus 1/2. We cannot do quite the same thing with the factor p= -2 because the roots would be complex.
If x = 1/2 is a root, then 2x - 1 is a factor. If x = -1/2 is a root, then 2x+1 is a factor.
Let's multiply these two factors, (2x-1) and (2x+1), together, obtaining 4x^2 - 1. Let's divide this 4x^2 - 1 into 4x^4+7x^2-2=0. We get x^2+2 as quotient.
Then, 4x^4+7x^2-2=0 in factored form, is (2x-1)(2x+1)(x^2+2) = 0.
Answer:
5x-4=11
Step-by-step explanation:
so you multiply 5 times x (a number) and subtract 4 and it equals to 11
Answer:
No, but you could give her a disease. You should get tested before any type of sexual interaction
Step-by-step explanation:
Answer:
-⅗ = x
Step-by-step explanation:
Here is what you get when you distribute the -2 on the left side of the equivalence symbol and combine like-terms on the right side of the equivalence symbol:
-2x - 4 = 3x - 1
Here is the solution:
-2x - 4 = 3x - 1
-3x -3x
----------------
-5x - 4 = -1
4 +4
----------------
-5x = 3
----- -----
-5 -5
x = -⅗
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