Answer:
1/6
Step-by-step explanation:
Given:
- Length of the trough: 9 ft
=> The volume of the trough: V =
* (b * h) (1)
- An isosceles right triangle with hypotenuse 2 feet
=> the other two sides of the triangle is:
= tan(45 degrees) = h/(b/2)
<=> b = 2h substitute in (1), we have:
V = *(2h *h) = 9
Take derivative of volume with respect to time to find equation for rate of filling the trough
dV/dt = 2 * 9 *h dh/dt = 18h dh/dt
<=> dh/dt = dV/dt /(18h)
As we know that, dV/dt = 2
So, dh/dt = 2 / 18h = 1/9h
<=> V = t * rate = 2 * 2 = 4
But V = 9
<=> 9 = 4
<=> h = 2/3
The rate is the height h feet of the water in the trough changing 2 minutes after the water begins to flow:
dh/dt = 1/(9h) = 1/(9 * 2/3) = 1/6
Answer:
$1806.06 million
Step-by-step explanation:
-This is a question of proportionality.
We are given that 13.2% is equivalent to $238.4 million in chocolate expenses
-To find the total value of chocolate expenditurerealized, we divide $238.4 million by 13.2%:
Hence, the total amount spent on chocolate is $1806.06 million
Answer:
No solution
Step-by-step explanation:
y=x-1 and y-x=-9
1st make sure both equations are in slope intercept form
since the 2nd equation isn't, you change it by adding x to both sides and rewrite it as y=mx+b so
y-x=-9
+× +×
y=×-9
now you have y=x-1 and y=x-9
substitute the y with the other equation
x-1=x-9
subtract x from both sides since you can't have the variable on both sides
now you've got -1 = -9
and since that equation isn't true, it has no solution.
There are 3 in. of snow on the ground when it begins to snow 0.5 in./h.
Initial depth of snow = 3 in.
it begins to snow 0.5 in./h. The constant rate of snow is 0.5. So slope = 0.5
Let x be the number of hours
y be the total depth of the snow
To frame linear equation we use y=mx+b
where m is the slope and b is the y intercept (initial depth of snow)
We know m=0.5 and b=3
Replace it in the equation
y = 0.5x + 3
The linear equation that represents the total depth of the snow(y), in inches, after x hours
is y= 0.5x + 3
Answer:
you would just combine like terms
5x+5y
Step-by-step explanation:
