Answer:
A)
62/3 = 20.67 hours
B)
60.00 hours
C)
2074.29 miles
Step-by-step explanation:
If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.
A)
In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;
(24/360) = (x/310)
solving for x;
x = (24/360) * 310 = 62/3 = 20.67 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;
(24/2π radians) = (x/5π radians)
Solving for x;
x = (24/2π radians)*5π radians = 60 hours
C)
If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;
circumference = 2*π*R = π*D
= 7920π miles
Therefore, the speed of the earth is approximately;
(7920π miles)/(24 hours) = 330π miles/hr
The distance covered by a point in 2 hours will thus be;
330π * 2 = 660π miles = 2074.29 miles
This problem can be solved by calculating the area of the figure before removing the triangles, then subtracting the combined area of the triangles.
First, we have to find the area of the original composite figure. It appears that the figure consists of a 16 ft by 16 ft square with an 8 ft by 8 ft square cut out:
SA = (16*16) - (8*8)
SA = 256 - 64
SA = 192
The ORIGINAL area of this composite figure is 192 ft². Now we have to find the area of the removed triangles. Triangle area is found using half base times height. The base and height of each triangle appears to be 8, so we can plug in :
The area of each triangle is 32 ft
². Finally, we should subtract the 3 triangles' area from the composite figure's area:
SA - 3(TA)
192 - 3(32)
192 - 96
96
The shaded region's area is 96 ft².
11/2 is greater than 4/8
11/2=5.5
4/8=1/2=0.5
Answer:
7+9(3-1)=25
Step-by-step explanation:
Determine the volume
The mayonnaise is sold per unit of volume (in³). Therefore we need to find the volume of the jar to determine the cost. The volume of the jar is equal to the volume of a cylinder.
v = π × r² × h
Input the numbers
v = 3.14 × (1.5)² × 7
v = 3.14 × 2.25 × 7
v = 49.445
The volume of the jar is 49.445 in³
Determine the cost
cost = volume in in³ × the cost per in³
cost = 49.445 × 0.08
cost = 3.9564
to the nearest hundredth
cost = 3.96
The cost of the jar of mayonnaise is $3.96