Answer:
17. surface area ≈ 441.84
04π m² or 1387.38 m²
18. Ratio of volumes = 8/27
19. volume of the smaller solid = 339 yards³
Step-by-step explanation:
17 .
To find the surface area of the sphere we have to find the radius of the sphere first.
volume of a sphere = 4/3πr³
volume = 1548π m³
r = ?
volume of a sphere = 4/3πr³
1548π = 4/3 × π × r³
multiply both sides by 3/4
1548π × 3/4 = πr³
4644π/4 = πr³
1161π = πr³
divide both sides by π
r³ = 1161
cube root both sides
r = ∛1161
r = 10.5101942
r ≈ 10. 51
surface area of a sphere = 4πr²
surface area = 4 × π × 10.51²
surface area = 4 × 110.4601 × π
surface area = 441.8404π m²
surface area = 441.8404 × 3.14 = 1387.378856 m² ≈ 1387.38 m²
18
If two figure or solid are similar with scale factor or ratio of x/y then the ratio of their volume is (x/y)³. If the ratio of of two similar prism is 2 : 3 the volume will be (2/3)³ = 8/27 .
19
If two solids are similar then the ratio of their surface area is the squared of the scale factor.
121/361 = (x/y)²
square root both sides
x/y = 11/19
If two solids are similar then the ratio of their volume is the cube of the scale factor.
(11/19)³ = a/1747
1331/6859 = a/1747
cross multiply
6859a = 2325257
divide both sides by 6859
a = 2325257/6859
a = 339.008164455
a ≈ 339 yards³
volume of the smaller solid ≈ 339 yards³
Answer:
It will be in the air until P(x) is zero.
P(x) = -16x2 + 32x = -16x(x - 2)
P(x) = 0 ⇒ x = 0 or x = 2
It starts on the ground at x = 0, so the total time in the air must be x = 2 seconds.
A)
well, we know the elevator's rate is -20 f/s, ok, so every second, is dropping 20 feet, therefore, "y" is "distance from the ground floor", so when y = 0, meaning the distance to the ground floor is 0, so you ARE at the ground floor then.
and "x" is how many seconds you've been in the elevator.
now, she got in the elevator for 6 seconds, so, the elevator went down by 20 * 6, or 120 feet down, reason why the slope is negative, when she stopped, she was 350 feet away from the ground floor still though.
if the elevator went down 120 feet, and she's still 350 feet from the ground floor, that means she boarded the elevator at 120 + 350 feet, or 470 feet.
b)
Answer: 5.3 Hours
Step-by-step explanation: 140 mi there at 56 mi per hour would be 2.5 hours. Then back 140 mi at 50 mi/h would be 2.8. 2.5 plus a 2.8 is 5.3 hours
Answer:
The equation that will determine the cost of two folders is; 3x = 2× $2.91
and the cost of the 2 folders is $1.94
Step-by-step explanation:
To solve this problem, we will follow the steps below;
Using proportion;
Let x be the cost of 2 folders
3 folders = $2.91
2 folders = x
Cross-multiply
3x = 2× $2.91
The equation that will determine the cost of two folders is
3x = 2× $2.91
We can go ahead and solve
3x = $5.82
Divide both-side of the equation by 3
= 
x = $ 1.94
The cost of 2 folders is $1.94