Slope intercept form is y=mx+b
So the answer is...
y=-1/6x+24
A is the answer because if we want the unit rate we do
2/3÷2/3 and 15 1/5, we can turn 15 1/5 into a improper fraction first so 76/5 and we do 76/5 ÷2/3 which is equal to
76/5×3/2=114/5
114/5 simplifies into 24 4/5.
so Naomi can travel 24 4/5 gal per mile.
Hope this helps!
Check if the equation is exact, which happens for ODEs of the form
if .
We have
so the ODE is not quite exact, but we can find an integrating factor so that
<em>is</em> exact, which would require
Notice that
is independent of <em>x</em>, and dividing this by gives an expression independent of <em>y</em>. If we assume is a function of <em>x</em> alone, then , and the partial differential equation above gives
which is separable and we can solve for easily.
So, multiply the original ODE by <em>x</em> on both sides:
Now
so the modified ODE is exact.
Now we look for a solution of the form , with differential
The solution <em>F</em> satisfies
Integrating both sides of the first equation with respect to <em>x</em> gives
Differentiating both sides with respect to <em>y</em> gives
So the solution to the ODE is
Answer:
The dimensions are 10 2/3 feet by 5 1/3 feet (Ten and two-thirds and five and one third).
Step-by-step explanation:
This is our system of equations:
y=Length
x=Width
y=2x
2x+2y=32
We can substitute the y value in the second equation by plugging in the first equation:
2x+2(2x)=32
2x+4x=32
6x=32
x=16/3 or 5 1/3
We can plug in this x value into the first equation to find the y value:
y=2(16/3)
y=32/3 or 10 2/3
Answer:
Rate of change in height of the water level is 2.91 cm per second.
Step-by-step explanation:
Height of the inverted pyramid = 10 cm
Length of the square base = 7 cm
If water is filled up to the level of h cm then the volume of water up to height h will be
V =
V =
It is given that rate of water is filling with 70 cubic centimeters per second.
From two similar triangles in the figure attached,
By replacing the value of h,
V =
V =
V =
Now we integrate the equation with respect to time 't'
70 =
For h = 7 cm
Therefore, rate of change in height of the water level is 2.91 cm per second.