Answer:
31.5 in
Step-by-step explanation:
- Volume of a hemisphere = (2/3)r³
(where r is the radius)
- Volume of a cylinder = r²h
(where r is the radius and h is the height)
- radius r = (1/2) diameter
First, find the volume of the scoop using the volume of a hemisphere formula with r = 21:
Volume = (2/3) x 21³ = 6174 in³
Now equate the found volume of the scoop to the equation of the volume of a cylinder with r = 14, and solve for h:
14²h = 6174
196h = 6174
Divide both sides by : 196h = 6174
Divide both sides by 196: h = 31.5
Therefore, the height of the molten steel in the storage tank is 31.5 in
Answer:
tan(x) = 1
Step-by-step explanation:
I find the least tedious way to answer questions like this is to use a graphing calculator to graph a function that is zero for the desired x. We can write that function by subtracting csc(x) from both sides of the equation:
0 = sin(x)tan(x) +cos(x) -csc(x)
The graph shows a solution to be x=π/4, corresponding to 45°. The values of the trig functions for this angle are ...
- sin(π/4) = (√2)/2
- cos(π/4) = (√2)/2
- tan(π/4) = 1
- csc(π/4) = √2
_____
An algebraic solution might go like this.
1/sin(x) = sin(x)·tan(x) +cos(x)
Multiplying by sin(x), we get ...
1 = tan(x)·sin(x)^2 + sin(x)cos(x)
Substituting for sin(x)^2, this is
1 = tan(x)(1 -cos(x)^2) +sin(x)cos(x)
1 = tan(x) - (sin(x)/cos(x))·cos(x)^2 +sin(x)cos(x) . . . using tan(x) = sin(x)/cos(x)
1 = tan(x)
Answer: $24.38
Step-by-step explanation:
So since the cost of a movie ticket is $20 and the cost is predicted to increase by 2% each year over the next 10 years. to find the cost after 10 years you want to solve for x.
so x=20(1.02)^10
20 is the initial cost and 0.02 is the rate of growth. expressed as a decimal number, the base is b=1+0.02=1.02 and the exponent 10 is the number of years
Answer:
13
Step-by-step explanation:
So the concept is that co-interior angles add up to 180 in parallel line. This means:
3x + 9 + 9x + 15 = 180
So we solve for x.
12x + 24 = 180 ( What I did was simplifying the equation).
12x + 24 - 24 = 180 - 24
12x / 12= 156 / 12
x = 13
HOPE THIS HELPED
Answer:
Step-by-step explanation: