Answer:
Difference in speed = 10.28 miles/hour
Step-by-step explanation:
Whovenile Delinquents takes 32 minutes to hike up a mountain and 3 minutes to hike down a mountain.
Distance hiked = 3000 feet
We have to find the speed difference of climbing in both the journeys in miles/hour.
Conversions :
therefore 3000 feet = 0.57 miles
32 minutes = 0.53 hours
3 minutes = 0.05 hours
Speed = 
Speed uphill = 
Speed uphill = 1.08 miles/hour
Speed downhill = 
Speed downhill = 11.36 miles/hour
Difference in speed = 10.28 miles/hour
(Please check the attachment for the diagram which will support the answer)
The regular pentagon is made up of five triangles as shown in the diagram. Let us now take the case of the bottom triangle ODC. We know from basic geometry that the area of any triangle is half times base times height. So, the area of the triangle will be half times DC (which is the base) times OP (which is the height).
Now, if we take into account all the triangles that make the pentagon we will get similar areas. The height of all such triangles will remain the same as OP because this is a regular pentagon.
Adding all these areas will give us the area of the pentagon which will come out to be:
Area of Pentagon=Area of Triangle OCD + Area of Triangle OBC +Area of Triangle OAB + Area of Triangle OAE + Area of Triangle OED
(Please see attachments for complete solution)
As we can see from the last attachment, the sum in the parenthesis is the perimeter of the pentagon and thus we get the area of the pentagon as
1/2 times apothem times Perimeter
Answer:
(sqrt(7))/3 or decimal 0.8819171036881968635005385845464201419034197276941500601227781530...
Step-by-step explanation:
Simplify the following:
(sqrt(14))/(sqrt(18))
Hint: | Simplify radicals.
sqrt(18) = sqrt(2×3^2) = 3 sqrt(2):
(sqrt(14))/(3 sqrt(2))
Hint: | Multiply numerator and denominator of (sqrt(14))/(3 sqrt(2)) by sqrt(2).
Rationalize the denominator. (sqrt(14))/(3 sqrt(2)) = (sqrt(14))/(3 sqrt(2))×(sqrt(2))/(sqrt(2)) = (sqrt(14) sqrt(2))/(3×2):
(sqrt(14) sqrt(2))/(3×2)
Hint: | Multiply 3 and 2 together.
3×2 = 6:
(sqrt(14) sqrt(2))/6
Hint: | For a>=0, sqrt(a) sqrt(b) = sqrt(a b). Apply this to sqrt(14) sqrt(2).
sqrt(14) sqrt(2) = sqrt(14×2):
(sqrt(14×2))/6
Hint: | Multiply 14 and 2 together.
14×2 = 28:
(sqrt(28))/6
Hint: | Simplify radicals.
sqrt(28) = sqrt(2^2×7) = 2 sqrt(7):
(2 sqrt(7))/6
Hint: | In (2 sqrt(7))/6, divide 6 in the denominator by 2 in the numerator.
2/6 = 2/(2×3) = 1/3:
Answer: (sqrt(7))/3
Answer:
.0039
Step-by-step explanation:
