Answer:

Step-by-step explanation:
Surface area of cylinder = 2πr(h + r)
Volume of cylinder = πr²h
Given that S.A = Volume of the cylinder, therefore, we have:
2πr(h + r) = πr²h
Radius (r) is given as 2.5 cm
height (h) = x cm
Input the values and solve for x
2πr(h + r) = πr²h
2πr(h + r) = πr(rh)
2(h + r) = rh (πr cancels πr)


Subtract 2x from both sides


Divide both sides by 0.5



Answer: 7000
Step-by-step explanation:
Let the amount invested in 8% account be P1 and the amount invested in 6% account be P2
. If the total amount invested is $20,000 then:
P1+P2=20,000. (Eq. 1)
The interest earned in one year from the 8% account is:
I1=0.08P1
and the interest earned in one year from the 6% account is:
I2=0.06P2
If the total interest earned is $1460, then:
I1+I2=1460
0.08P1+0.06P2=1460
(Eq. 2) From Eq. 1 :
P1=20000−P2
Substituting this into Eq. 2:
0.08 (20000−P2) + 0.06P2 = 1460
1600 − 0.08P2 + 0.06P2 = 1460
0.02P2 = 140
P2 = 140 / 0.02
P2 = 7000
Hence, he invested $7000 at the rate of 6%.
Answer:
First we need to put all the given information in a table, that way we'll express it better into inequalities.
Cost Production Max.
Console screen (x) $600 450
Wide-screen (y) $900 200
$360,000
We have:

Because they can't spend more than $360,000 in production.

Because the number of television is restricted.
The profit function is
(this is the function we need to maximize).
First, we need to draw each inequality. The image attached shows the region of solution, which has vertices (0,200), (300,200), (450, 100) and (450,0).
Now, we test each point in the profit function to see which one gives the highest profit.
For (300,200):

300 console screen and 200 wide screen give a profit of $77,500.
For (450,100):

450 console screen and 100 wide screen give a profit of $76,250.
<h3>
Therefore, to reach the maximum profits, TeeVee Electronic, Inc., must produce 300 console screen televisions and 200 wide-screen televisions to profit $77,500,</h3>