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2 years ago

Find two numbers whose difference is 154 and whose product is a minimum.

1 answer:

7 0

Y - x = 154
let z = xy = x(154 + x) = x^2 + 154x

we need to find the minimum value of z

z' = 2x + 154 which = zero for minm or maxm value

x = -77 and y = 154 -77 = 77

so the 2 numbers are -77 and 77

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The diameter of the base of the cone measures 8 units.

weeeeeb [17]

Answer: $32\pi$ cubic units.

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

$V_{cone}=\frac{1}{3}\pi r^2h$

Where "r" is the radius and "h" is the height.

You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:

$r=\frac{8units}{2}\\\\r=4units$

Since you already know that height and the radius, you can substitute them into the formula. Then, the volume of this cone is:

$V_{cone}=\frac{1}{3}\pi (4units)^2(6units)$

$V_{cone}=32\pi \ units^3$

3 0

2 years ago

Read 2 more answers

Sarah has a collection of nickels, dimes, and quarters worth $28.75. She has 10 more dimes than nickels and twice as many quarte

Ymorist [56]

Answer:

Step-by-step explanation:

Write an equation for each statement:

"Sarah has a collection of nickels, dimes, and quarters worth $15.75."

.05n + .1d + .25q = 15.75

"She has 10 more dimes than nickels"

d = n + 10

"twice as many quarters as dimes."

q = 2d

How many coins of each kind does she have?

Take the 2nd equation and arrange it so n is in terms of d also

n + 10 = d

n = (d - 10)

In the 1st equation substitute (d-10) for n and 2d for q:

.05n + .1d + .25q = 15.75

.05(d-10) + .1d + .25(2d) = 15.75

.05d - .5 + .1d + .5d = 15.75

.65d - .5 = 15.75

.65d = 15.75 + .5

.65d = 16.25

d = 16.25/.65

d = 25 dimes

Remember the statement "twice as many quarters as dimes."

q = 2(25)

q = 50 quarters

The statement "She has 10 more dimes than nickels"

n = 25 - 10

n - 15 nickels

Check our solutions

.05(15) + .1(25) + .25(50) =

.75 + 2.50 + 12.50 = 15.75 proves our solutions

8 0

1 year ago

I don’t how to solve this problem

Illusion [34]

If you divide the larger lake's size by the smaller lake's size, you'll get the answer.
890/80=11.125
Rounds off to 11.13
Answer C
***
example, 10/2=5. 10 is 5 times larger than 2.

6 0

2 years ago

Read 2 more answers

Yana plans to run 1 mile she has run 7/10 of a mile what fraction of a mile does she have left to run

Andre45 [30]

Answer:

3/10

Step-by-step explanation:

7+3= 10 so 7+3=10/10 which is one mile

8 0

2 years ago

NEED ANSWER NOW PLEASE!

Len [333]

For this case, the first thing you should do is the following sum:
income = Annual Salary + benefits
Substituting values we have:
income = (48500) + (2500 + 5000)
income = 56000
Answer:
She can expect a total amount of income with benefits from:income = 56000
(option 4)

7 0

2 years ago