Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
Answer:
the answer is 67.5
Step-by-step explanation:
look at the photo
Answer:
5 people
Step-by-step explanation:
For each people Ms Hernandez bring to the zoo, she will pay $15.50, so if she go alone, 1×15.50, if she go with one person, 2×15.50, with three 3×15.50, and keep growing this way. The price each person pay is constant and equal to 15.50, and what will determine the final price is the number of people. Also remember that she always will have to pay $ 10 on parking, so you can write an equation with this:
15.50x +10 = y, as x being the number of people and y being the final price.
She have $100, so this is the max she can spend. Two know the number of people she can bring to the zoo, put 100 in place of y and find the value of x:
15.50x + 10 = 100
15.50x = 100 - 10
15.50x = 90
x = 90/15.50
x = 5.8
But there's no way to bring 0.8 person, so the max she can bring are 5 people, including her
Answer:
(-6, 6)
Step-by-step explanation:
The coordinates of B to start with is
(-2, 2)
To dilate this by a factor of 3....
-2 * 3 = -6
2 * 3 = 6
The new coordinates of B' would be
(-6, 6)
A few things to know:
- The number 3 is called a "<u>scale factor</u>"
- Dilation means we are multiplying all the (X, Y)'s by the scale factor
- If the scale factor is <u>greater than 1</u>, the size of the shape overall increases
- If the scale factor is <u>less than 1</u>, the size of the shape overall decreases
- If the scale factor is <u>negative</u>, the shape size stays the same. The shape just rotates 180 degrees and moves to the opposite quadrant.
