Since they are congruent, cpctc,
just set the congruent parts equal to each other.
so 2x-20=30
and
15=3y-9
Answer:
a. 12 feet b. 12 feet 0.5 inches c. 8.33 %
Step-by-step explanation:
a. How far out horizontally on the ground will it protrude from the building?
Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.
So, by ratios rise/run = 1/12 = 12/x
1/12 = 12/x
x = 12 × 12
x = 144 inches
Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet
b. How long should the ramp be?
The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.
So, L = √(12² + 144²)
= √[12² + (12² × 12²)]
= 12√(1 + 144)
= 12√145
= 12 × 12.042
= 144.5 inches
Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches
c. What percent grade is the ramp?
The percentage grade of the ramp = rise/run × 100 %
= 12 inches/144 inches × 100 %
= 1/12 × 100 %
= 0.0833 × 100 %
= 8.33 %
Answer:
The rate of change was 3.5 degrees / h.
Step-by-step explanation:
In order to calculate the rate of change we need to divide the variation of temperature by the variation of time. Since the time is given to us in a 12 h format (am/pm), we first need to convert it to 24 h. To do that we sum the time that is "pm" by 12, we have:
time2 = 3 + 12 = 15
Therefore the rate of change in temperature is:
rate = variation of temp / variation of time
rate = (temp final - temp init) / (time final - time init)
rate = (82 - 54) / (15 - 7) = 28 / 8 = 3.5 degrees / h
The rate of change was 3.5 degrees / h.
