Answer:
One- half
Step-by-step explanation:
Since the density is uniform
Mass of the sphere = [(4/3) π r^3] d
where d is the uniform density.
Mass of the sphere = [(4/3) π d] r^3 = k r^3
where k = [(4/3) π d] is a constant
Weight = mg = G m M / r^2 = G m [k r^3] /r^2 = G m k r
Using Gauss’ law for gravitation,
Half way to the center of a planet the weight is only due to the inner sphere and the outer sphere does not contribute to his weight,
Inside his weight is mg’ = (G m k r) /2 = mg/2
Answer is one-half.
Answer:
I. Length, L = 9.552 meters
II. Width, W = 7.96 meters
Step-by-step explanation:
Let the length = L
Let the width = W
Given the following data;
Perimeter = 35 m
Translating the word problem into an algebraic equation, we have;
Length = 1.2W
To find the dimension of the room;
The perimeter of a rectangle is given by the formula;
P = 2(L + W)
Substituting into the formula, we have;
35 = 2(1.2W + W)
35 = 2(2.2W)
35 = 4.4W
Width, W = 7.96 meters
Next, we would find the length of the rectangle;
L = 1.2*W
L = 1.2 * 7.96
Length, L = 9.552 meters
Let the first number be = x
Then the second number = 2x
The third number = 2x - 5
Their sum = 55
This can be written in an equation as =
x + 2x + 2x - 5 = 55
= x + 2x + 2x = 55 + 5 ( transposing -5 from LHS to RHS changes -5 to +5 )
= x + 2x + 2x = 60
= 5x = 60
= x = 60 ÷ 5 ( transposing ×5 from LHS to RHS changes ×5 to ÷5 )
= x = 12
The first number = x = 12
The second number = 2x = 2 × 20 = 24
The third number = 2x - 5 = 24 - 5 = 19
Therefore , the three numbers are 12 , 24 and 19 .
Answer:
The circumference formula for a circle is C=πd where C is the circumference, d is the diameter of the circle and π is a constant. If you plug in 6 for C and solve the equation for d like:
6= πd and then divide both sides of the equation by π you get that d = 1.90
To find the central angle of an arc you would use the equation S = rθ where S is the length of the arc, r is the radius of the circle, and θ is the measure of the angle which in this case is unknown. So with S = 1 and r = d/2 = 1.90/2 = 0.9549 you would have an equation that looks like this:
1 = 0.9549θ.
If you divide both sides of the equation by 0.9549 you get θ = 1.047197 radians.
The question asked for the angle measure in degrees so you would need to convert the angle measure to degrees by multiplying the degree measurement by 180/π
1.047197 x 180/π = 60°
