Answer:
Step-by-step explanation:
From the given information:

Given that the solution is pumped at a slower rate of 4gal/min
Then:


The differential equation can be expressed as:

Integrating the linear differential equation; we have::


multiplying above integrating factor fields; we have:

![\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdt%7D%5Cbigg%20%5B%20%2850%20%2Bt%29%5E2%20A%20%5Cbigg%20%5D%20%3D%203%20%2850%20%2Bt%29%5E2)

A = (50 + t) + c(50 + t)²
Using the given conditions:
A(0) = 20
⇒ 20 = 50 + c (50)⁻²
-30 = c(50) ⁻²
c = -30 × 2500
c = -75000
A = (50+t) - 75000(50 + t)⁻²
The no. of pounds of salt in the tank after 35 minutes is:
A(35) = (50 + 35) - 75000(50 + 35)⁻²
A(35) = 85 - 
A(35) =69.6193 pounds
A(35)
70 pounds
Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.
It is a 2 out of three chance of getting a composite number because that means that it is not odd. There are 10 odd numbers between 1 and 30 (2,3,5,7,11,13,17,19,23,29) and that means that there is a 20 out of 30, or 2 out of 3 chance taht the number will be composite.
Answer:
Option D
Step-by-step explanation:
Vertices of the polygon are A(1, 3), B(7, 3), C(7, 7), D(4, 7)
Measure of AB = 7 - 1 = 6 units
Measure of BC = 7 - 3 = 4 units
Measure of CD = 7 - 4 = 3 units
From the figure attached,
Area of the trapezoid =
[Here, AB and CD are the parallel bases and BC is the height of the trapezoid]
= 
= 18 square units
Therefore, Option D will be the correct option.
First we need to find out the volume of one cylinder. We already know the volume of the block of gold is 360cm3
V = Pie * radius squared* height.
Pie is 3.142
radius is 6.18/2 = 3.09 cm
height is 6cm
V = 3.142 * 3.09 * 3.09 * 6
V = 180cm3
Now we divide the volume of this cylinder with the volume of block of gold.
360/180 = 2
So it will take 2 cylinders to mold one block of gold.