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TEA [102]
3 years ago
5

What are the zeros for the function f(x)=x^3-4x

Mathematics
1 answer:
Harman [31]3 years ago
4 0

Answer:

x = 0

x = 2

x = -2

Step-by-step explanation:

f(x) = x^{3} - 4x

Factor

f(x) = x ( x^{2} - 4)

f(x) = x ( ( x - 2 ) ( x + 2 ) )

zeros;

x = 0

x = 2

x = -2

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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
What system of equations is shown on the graph?
lakkis [162]
Blue: y = 1/2x - 2
Orange: y = -2x - 4

Answer:
B) x - 2y = 4 and 2x + y = -4
8 0
3 years ago
Please help asap! Correct answers only!
SOVA2 [1]

Answer:

$98100

Step-by-step explanation:

Using the given formula :

I = P × R × T

I = 90000 × 3/100 × 3

I = $8100

He saves = 8100 + 90000 = $98100

5 0
3 years ago
If a sample size is less than​ ________, the sample size must come from a population having a normal distribution in order to fo
salantis [7]
My guess is 30 for the sample size.
8 0
3 years ago
Read 2 more answers
How can you tell by looking at a graph if there is a proportional relationship?
IgorLugansk [536]
If there is a porpotional relationship then it there will be a pattern like, 7, 14, 21 etc. You can tell because the line will go straight in a perfect line and won't go at a different andle from the rest of the line.
3 0
3 years ago
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