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3 years ago

Write (7x - 4)(3x - 1) in standard form

Mathematics

1 answer:

liraira [26]3 years ago

5 0

Answer:

21x² - 19x + 4

Step-by-step explanation:

Step 1: Write factors

(7x - 4)(3x - 1)

Step 2: FOIL (First Outside Inside Last)

21x² - 7x - 12x + 4

Step 3: Combine like terms

21x² - 19x + 4

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A closed box with a square base is to have a volume of 171 comma 500 cm cubed. The material for the top and bottom of the box co

Zepler [3.9K]

Answer:

$C(x)=\dfrac{20x^3+1715000}{x}\\$Minimum cost, C(35)=\$29,400$

The dimensions that will lead to minimum cost of the box are a base length of 35 cm and a height of 140 cm.

Step-by-step explanation:

Volume of the Square-Based box=171,500 cubic cm

Let the length of a side of the base=x cm

Volume $=x^2h$

$x^2h=171,500\\h=\dfrac{171500}{x^2}$

The material for the top and bottom of the box costs $10.00 per square centimeter.

Surface Area of the Top and Bottom $=2x^2$

Therefore, Cost of the Top and Bottom $=\$10X2x^2=20x^2$

The material for the sides costs $2.50 per square centimeter.

Surface Area of the Sides=4xh

Cost of the sides=$2.50 X 4xh =10xh

$\text{Substitute h}$=\dfrac{171500}{x^2} $into 10xh\\Cost of the sides=10x(\dfrac{171500}{x^2})=\dfrac{1715000}{x}$

Therefore, total Cost of the box

$= 20x^2+\dfrac{1715000}{x}\\C(x)=\dfrac{20x^3+1715000}{x}$

To find the minimum total cost, we solve for the critical points of C(x). This is obtained by equating its derivative to zero and solving for x.

$C'(x)=\dfrac{40x^3-1715000}{x^2}\\\dfrac{40x^3-1715000}{x^2}=0\\40x^3-1715000=0\\40x^3=1715000\\x^3=1715000\div 40\\x^3=42875\\x=\sqrt[3]{42875}=35$

Recall that:

$h=\dfrac{171500}{x^2}\\Therefore:\\h=\dfrac{171500}{35^2}=140cm$

The dimensions that will lead to minimum costs are base length of 35cm and height of 140cm.

Therefore, the minimum total cost, at x=35cm

$C(35)=\dfrac{20(35)^3+1715000}{35}=\$29,400$

8 0

3 years ago

Use a computer algebra system to draw a direction field for the differential equation y' = 3y^3 − 12y. Get a printout and sketch

Diano4ka-milaya [45]

Answer: simplest reason is that Infinity is not a number, it is an idea.

So 1∞ is a bit like saying 1beauty or 1tall.

Maybe we could say that 1∞= 0, ... but that is a problem too, because if we divide 1 into infinite pieces and they end up 0 each, what happened to the 1?

In fact 1∞ is known to be undefined.

But We Can Approach It!

So instead of trying to work it out for infinity (because we can't get a sensible answer), let's try larger and larger values of x:

graph 1/x

x 1x

1 1.00000

2 0.50000

4 0.25000

10 0.10000

100 0.01000

1,000 0.00100

10,000 0.00010

Now we can see that as x gets larger, 1x tends towards 0

We are now faced with an interesting situation:

Step-by-step explanation:

8 0

3 years ago

If angle 5 measures 150 degrees, what is the measure of angle 6?

sesenic [268]

Answer:

A. 30 degrees

Step-by-step explanation:

side by side angles on a flat line have to equal 180 degrees. if angle 5 = 150 degrees, 180 - 150 = 30 degrees.

5 0

3 years ago

Read 2 more answers

How to solve for 4d-7=25/4

RideAnS [48]

4d-7=25/4

Add 7 to both sides

4d-7+7=25/4 +7

4d=53/4

Divide both sides by 4

4d/4= 53/4/4

d= 53/16

I hope that's help:0

7 0

3 years ago

What is the solution to this system?

Rudik [331]

Answer:

x= -8, y= -6/5, z= -6

Step-by-step explanation:

that is the answer

6 0

4 years ago