Answer:
The car requires 192 feet to stop from a speed of 48 miles per hour on the same road
Step-by-step explanation:
- Direct proportion means that two quantities increase or decrease in the same ratio
- If y is directly proportional to x (y ∝ x) , then
<em>OR</em> y = k x, where k is the constant of proportionality
∵ The stopping distance d of an automobile is directly
proportional to the square of its speed s
- That means d ∝ s²
∴ ![\frac{d_{1}}{d_{2}}=\frac{(s_{1})^{2}}{(s_{2})^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bd_%7B1%7D%7D%7Bd_%7B2%7D%7D%3D%5Cfrac%7B%28s_%7B1%7D%29%5E%7B2%7D%7D%7B%28s_%7B2%7D%29%5E%7B2%7D%7D)
∵ A car requires 75 feet to stop from a speed of 30 miles per hour
∴ d = 75 feet
∴ s = 30 miles/hour
- Change the mile to feet
∵ 1 mile = 5280 feet
∴ 30 miles/hour = 30 × 5280 = 158400 feet/hour
∵ The car require to stop from a speed of 48 miles per hour
on the same road
- Change the mile to feet
∴ 48 miles/hour = 48 × 5280 = 253440 feet/hour
∵ ![\frac{d_{1}}{d_{2}}=\frac{(s_{1})^{2}}{(s_{2})^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bd_%7B1%7D%7D%7Bd_%7B2%7D%7D%3D%5Cfrac%7B%28s_%7B1%7D%29%5E%7B2%7D%7D%7B%28s_%7B2%7D%29%5E%7B2%7D%7D)
- Substitute the values of
by 75 feet,
by 158400 feet/hour
and
by 253440 feet/hour
∴ ![\frac{75}{d_{2}}=\frac{(158400)^{2}}{(253440)^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B75%7D%7Bd_%7B2%7D%7D%3D%5Cfrac%7B%28158400%29%5E%7B2%7D%7D%7B%28253440%29%5E%7B2%7D%7D)
∴ ![\frac{75}{d_{2}}=\frac{25}{64}](https://tex.z-dn.net/?f=%5Cfrac%7B75%7D%7Bd_%7B2%7D%7D%3D%5Cfrac%7B25%7D%7B64%7D)
- By using cross multiplication
∴ 25 ×
= 75 × 64
- Divide both sides by 25
∴
= 192 feet
The car requires 192 feet to stop from a speed of 48 miles per hour on the same road
Answer: OPTION D.
Step-by-step explanation:
Below are some transformations for a function f(x):
If
, then the function is reflected over the x-axis.
If
, then the function is reflected over the y-axis.
If
and
, then the function is horizontally compressed.
If
and
, then the function is horizontally stretched.
In this case you know that the parent function is:
![y=x^3](https://tex.z-dn.net/?f=y%3Dx%5E3)
According to the information given in the exercise, the parent function IS horizontally stretched by a factor of
and it is also reflected over the y-axis.
Therefore, based on the transformations explained before, you can notice that the transformation is:
Where ![0 < b](https://tex.z-dn.net/?f=0%20%3C%20b%20%3C1)
Therefore, the equation of the transformed function is:
![y=(-\frac{1}{5}x)^ 3](https://tex.z-dn.net/?f=y%3D%28-%5Cfrac%7B1%7D%7B5%7Dx%29%5E%203)
Answer:
at 6:06
Step-by-step explanation:
since it took 13 to be half full just add an extra 13 minutes. 5:53+ 13 minutes= 6:06
Answer:
50 cm^2
Step-by-step explanation:
area of rectangle = base * height
5 * 7 = 35
area of triangle = base * height / 2
5 * 4 = 20/2 = 10
5 * 2 = 10/2 = 5
add them all up
35 + 5 + 10 = 50 cm^2