Hi there!
Let's solve this equation step by step!
First add 7 to both sides.
Next we need to take a look at the meaning of the stripes between our variable. Those stripes mean we are dealing with an absolute value function. The absolute value stripes make everything between the stripes positive; also when we plug in a number. In this particular question we can plug in both -13 and 13 at the position of n, because when -13 is made positive, it fulfils the equation.
Hence,
or
~ Hope this helps you!
Answer:
Step-by-step explanation:
Let the speed of the car be "X". From 3 am until 1 pm (10 hours), the car will travel 10*X miles.
The speed of the airplane is (X +200). From 11 am until 1 pm (2 hours), the plane will travel 2*(X+200).
The distance travelled is the same, so:
10*X = 2*(x+200)= 2x+400
Subtract 2*X from both sides:
8*X = 400
X = 400/8 = 50 mph.
<h3>Given</h3>
- a cone of height 0.4 m and diameter 0.3 m
- filling at the rate 0.004 m³/s
- fill height of 0.2 m at the time of interest
<h3>Find</h3>
- the rate of change of fill height at the time of interest
<h3>Solution</h3>
The cone is filled to half its depth at the time of interest, so the surface area of the filled portion will be (1/2)² times the surface area of the top of the cone. The filled portion has an area of
... A = (1/4)(π/4)d² = (π/16)(0.3 m)² = 0.09π/16 m²
This area multiplied by the rate of change of fill height (dh/dt) will give the rate of change of volume.
... (0.09π/16 m²)×dh/dt = dV/dt = 0.004 m³/s
Dividing by the coefficient of dh/dt, we get
... dh/dt = 0.004·16/(0.09π) m/s
... dh/dt = 32/(45π) m/s ≈ 0.22635 m/s
_____
You can also write an equation for the filled volume in terms of the filled height, then differentiate and solve for dh/dt. When you do, you find the relation between rates of change of height and area are as described above. We have taken a "shortcut" based on the knowledge gained from solving it this way. (No arithmetic operations are saved. We only avoid the process of taking the derivative.)
Note that the cone dimensions mean the radius is 3/8 of the height.
V = (1/3)πr²h = (1/3)π(3/8·h)²·h = 3π/64·h³
dV/dt = 9π/64·h²·dh/dt
.004 = 9π/64·0.2²·dh/dt . . . substitute the given values
dh/dt = .004·64/(.04·9·π) = 32/(45π)
