F(x)= x² - 2x + 4, +(a-1)=?

A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $5 per ft2 for the

kramer

Answer:

$18.73ft^3$

Step-by-step explanation:

Let

Side of square base=x

Height of rectangular box=y

Area of square base=Area of top= $(side)^2=x^2$

Area of one side face= $l\times b=xy$

Cost of bottom=$9 per square ft

Cost of top=$5 square ft

Cost of sides=$4 per square ft

Total cost=$204

Volume of rectangular box= $V=lbh=x^2y$

Total cost= $9(x^2)+5x^2+4(4xy)=14x^2+16xy$

$204=14x^2+16xy$

$204-14x^2=16xy$

$y=\frac{204-14x^2}{16x}=\frac{102-7x^2}{8x}$

Substitute the values of y

$V(x)=x^2\times \frac{102-7x^2}{8x}=\frac{1}{8}(102x-7x^3)$

Differentiate w.r.t x

$V'(x)=\frac{1}{8}(102-21x^2)=0$

$V'(x)=0$

$\frac{1}{8}(102-21x^2)=0$

$102-21x^2=0$

$102=21x^2$

$x^2=\frac{102}{21}=4.85$

$x=\sqrt{4.85}=2.2$

It takes positive because side length cannot be negative.

Again differentiate w.r. t x

$V''(x)=\frac{1}{8}(-42x)$

Substitute the value

$V''(2.2)=-\frac{42}{8}(2.2)=-11.55$

Hence, the volume of box is maximum at x=2.2 ft

Substitute the value of x

$y=\frac{102-7(2.2)^2}{8(2.2)}=3.87 ft$

Greatest volume of box= $x^2y=(2.2)^2\times 3.87=18.73 ft^3$

5 0

4 years ago

A class must have fewer than 18 students due to the number of desks that can be placed in the classroom. Write an inequality tha

forsale [732]

Answer:

n < 18
n ≥ 15

Step-by-step explanation:

The wording "fewer than" is translated to the math symbol "less than". The variable n represents the number of students.

the number of students is fewer than 18

translates to ...

n < 18

__

The wording "at least" translates to the math symbol "greater than or equal to."

the number of students is at least 15

translates to ...

n ≥ 15

8 0

3 years ago

Amia went to a flower farm and picked f flowers. When she got home, she put the flowers in 4 vases, with 22 flowers in each vase

Whitepunk [10]

One equation that represents this situation is f/4 = 22.

This shows the total number of flowers (f) being broken into 4 groups (4 vases) with the result being 22 flowers in each vase.

7 0

4 years ago

Read 2 more answers

The sales tax on a 15,000 car is 540. at this rate what is the tax on a 32,000 car

maria [59]

Note : Since unit of currency is not defined, I'll be using units.

Sales tax on a 15000 units car = 540 units
540 = 15000 × tax% / 100
=> 540 = 15000 × tax% / 100
=> 540/15000 = tax% / 100
=> tax% = (540/15000) × 100
=> tax% = 540/140
=> tax% = 3.6

now,
sales tax on a 32000 units car = 32000 × tax%/100
= 32000 × 3.6/100
= 320 × 3.6
= 1152 units
therefore sales tax on a 32000 units car = 1152 units

4 0

3 years ago

Can somebody please help me !!

melisa1 [442]

Answer:

She'll have to pay 4.8USD to get the bike

4 0

3 years ago

F(x)= x² - 2x + 4, +(a-1)=?​

F(x)= x² - 2x + 4, +(a-1)=?