Answer:
192 cm^3/min
Step-by-step explanation:
Differentiating the volume expression, we get ...
dV/dt = 2xh(dx/dt) +x^2(dh/dt)
We are given that ...
x = 4 cm, dx/dt = 2 cm/min, h = 15 cm, dh/dt = -3 cm/min
Putting these values into the formula for volume rate of change, we get ...
dV/dt = 2(4 cm)(15 cm)(2 cm/min) +(4 cm)^2(-3 cm/min)
= 240 cm^3/min -48 cm^3/min
dV/dt = 192 cm^3/min
Answer:
Step-by-step explanation:
Before we even begin it would be very helpful to draw out a simple layout of the circuit. Then we go ahead and apply kirchoffs second law(sum of voltages around a loop must be zero) on the circuit and we obtain the following differential equation,
where V is the electromotive force applied to the LR series circuit, Ldi/dt is the voltage drop across the inductor and Ri is the voltage drop across the resistor. we can re write the equation as,
Then we first solve for the homogeneous part given by,
we obtain,
This is only the solution to the homogeneous part, The final solution would be given by,
where c is some constant, we added this because the right side of the primary differential equation has a constant term given by V/R. We put this in the main differential equation and obtain the value of c as c=V/R by comparing the constants on both sides.if we put in our initial condition of i(0)=0, we obtain 
, so the overall equation becomes,
where if we just plug in the values given in the question we obtain the answer given below,
Step-by-step explanation:
square of x is x2
Inverse of square of x is 1 / x2
So the equation would be:
y = k / x2
where k is a proportionality constant.
To find the value of k, plug in the known values for x and y: x=3, y=45
45 = k / 32 = k / 9
k=405
Now you have the full equation with proportionality factor.
y = 405 / x2
then, for x=5:
y = 405 / 52 = 405 / 25
y = 16.2
Answer:
Step-by-step explanation:
d i think
Answer:
z = 110
Step-by-step explanation:
The measure of an angle created by the intersection of two secants outside a circle is half the difference of the angles it intercepts. In this it would be:
2x + 15 = 1/2 * (10x + 20 - 80)
We can now solve:
4x + 30 = 10x - 60
30 = 6x - 60
6x = 90
x = 15
This means the values of 10x + 20 is 10(15) + 20, which is 170.
Now, we can add up all the arcs in a circle, which sum to 360 degrees:
360 = z + 170 + 80
360 = z + 250
z = 110
