What is the total perimeter of the pitch and seating area

The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasin

hoa [83]

Answer:

$\frac{dI}{dt}=-0.00016 A/s$

Step-by-step explanation:

We are given that

By ohm's law

$V=IR$

R=389 ohm

I=0.03 A

$\frac{dV}{dt}=-0.06V/s$

$\frac{dR}{dt}=0.07ohm/s$

We have to find rate of change of current I means $\frac{dI}{dt}$

Differentiate the equation w.r.t t

$\frac{dV}{dt}=\frac{dI}{dt}R+I\frac{dR}{dt}$

Substitute the values then we get

$-0.06=\frac{dI}{dt}\times 389+0.03\times 0.07$

$-0.06=389\frac{dI}{dt}+0.0021$

$-0.06-0.0021=389\frac{dI}{dt}$

$-0.0621=389\frac{dI}{dt}$

$\frac{dI}{dt}=\frac{-0.0621}{389}=-0.000160 A/s$

Hence, the current I is changing at the rate=-0.00016A/s

4 0

4 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

Jen is making a receipt for pancakes.A receipe calls for 4/10 kilogram flour and 12/100 sugar. if Jen measures corre

lorasvet [3.4K]

If you take the numerator and the denominator from flour and multiply both by 10, you'll get 40/100. then, add 40/100 to 12/100. your answer should be 52/100. if not, look back through your math. hope that helped.

6 0

3 years ago

Easy algebra question below first correct answer gets brainliest

Alexxx [7]

Answer:

3

Step-by-step explanation:

Easy pythagorean theorum question.

The law states that "A squared plus B squared, equals C squared."

A and B are the two sides that border the 90 degree mark.

C is the hypotenuse or the longest side/diagonal.

Since we know C and A (I chose to use A because why not) we can fill in the equation with what we know

2^2 + ?^2 = $\sqrt{13^{2} }$

So

4 + ?^2 = $\sqrt{13^{2} }$

Since the 13 is already squared in side of a root, it stays as 13

4 + x^2 = 13

4 - 4 + x^2 = 13 - 4

x^2 = 9

x^2 root = root of 9

x = 3

The missing side is 3.

Or you could use an online calculator xD

7 0

3 years ago

Question 15 of 24

deff fn [24]

Answer: B. m=-23 and -23=m. *The answer should be the negative sign.*

Step-by-step explanation:

addition property of equality is adding the same number to both sides of an equation does not change the equation.

a+c=b+c

add by 10 both sides of equation.

m-10+10=-33+10

simplify.

33-10=23

23+10=33

33-23=10

m=-23

It changes positive to negative.

Hope this helps!

Thanks!

Have a great day!

8 0

3 years ago