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3 years ago

Which number is NOT in the solution set of the inequality x < −10?

Mathematics

1 answer:

Novay_Z [31]3 years ago

7 0

answer is option A

becoz solution set is x < -10 where -5 > -10 so -5 is not in solution set

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A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs

LenKa [72]

Answer:

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

Step-by-step explanation:

Volume of the Cylinder=400 cm³

Volume of a Cylinder=πr²h

Therefore: πr²h=400

$h=\frac{400}{\pi r^2}$

Total Surface Area of a Cylinder=2πr²+2πrh

Cost of the materials for the Top and Bottom=0.06 cents per square centimeter

Cost of the materials for the sides=0.03 cents per square centimeter

Cost of the Cylinder=0.06(2πr²)+0.03(2πrh)

C=0.12πr²+0.06πrh

Recall: $h=\frac{400}{\pi r^2}$

Therefore:

$C(r)=0.12\pi r^2+0.06 \pi r(\frac{400}{\pi r^2})$

$C(r)=0.12\pi r^2+\frac{24}{r}$

$C(r)=\frac{0.12\pi r^3+24}{r}$

The minimum cost occurs when the derivative of the Cost =0.

$C^{'}(r)=\frac{6\pi r^3-600}{25r^2}$

$6\pi r^3-600=0$

$6\pi r^3=600$

$\pi r^3=100$

$r^3=\frac{100}{\pi}$

$r^3=31.83$

r=3.17 cm

Recall that:

$h=\frac{400}{\pi r^2}$

$h=\frac{400}{\pi *3.17^2}$

h=12.67cm

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

3 0

3 years ago

A washer and a dryer cost $847 combined. The washer costs $53 less than the dryer. What is the cost of the dryer?

Natalija [7]

--------------------------------------------------------------
Define x :
--------------------------------------------------------------
Let the dryer be x.
Dryer = x
Washer = x -53

--------------------------------------------------------------
Construct Equation :
--------------------------------------------------------------
The washer and the dryer cost $847
⇒ x + x - 53 = 847

--------------------------------------------------------------
Solve x :
--------------------------------------------------------------
x + x - 53 = 847
2x - 53 = 847
2x = 847 + 53
2x = 900
x = 450

--------------------------------------------------------------
Find cost of dryer and washer :
--------------------------------------------------------------
Dryer = x = $450
Washer = x = 450 - 53 = 397

--------------------------------------------------------------
Answer: Dryer = $450
--------------------------------------------------------------

3 0

3 years ago

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GIVING BRAINLIEST!! TIME SENSITIVE ANSWER ASAP PLEASE!

ollegr [7]

Answer:so fresh and so clean

Step-by-step explanation:

its cheaper starting price and lower increase

6 0

3 years ago

A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10%

erastovalidia [21]