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3 years ago

Simplify 2x2a^2 x2a^2

Mathematics

1 answer:

horrorfan [7]3 years ago

6 0

Step-by-step explanation:

> 2×2a²×2a²

8a⁴

> 36a³×1/4a²

9a³×1/a²

> 2⁶

> 5²m²

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A box of volume 180 m3 with square bottom and no top is constructed out of two different materials. The cost of the bottom is $4

zysi [14]

Answer:

Side of square bottom=6.46 m

Height of box=4.31 m

Step-by-step explanation:

Let s be the side bottom

Height of box=h

Volume of box= $180m^3$

Volume of box= $lbh=s^2h$

$s^2h=180$

$h=\frac{180}{s^2}$

Cost of bottom=$40 per square m

Cost of sides =$30 per square m

Total cost= $C=40s^2+30(4sh)$

$C=40s^2+120s\times \frac{180}{s^2}$

$C(s)=40s^2+\frac{21600}{s}$

Differentiate w.r.t s

$C'(s)=80s-\frac{21600}{s^2}$

$C'(s)=0$

$80s-\frac{21600}{s^2}=0$

$80s=\frac{21600}{s^2}$

$s^3=\frac{21600}{80}=270$

$s=(270)^{\frac{1}{3}}=6.46$

Again,differentiate w.r.t s

$C''(s)=80+\frac{43200}{s^3}$

Substitute s=6.46

$C''(6.46)=80+\frac{43200}{(6.46)^3}=240.2>0$

Hence, the cost is minimum at s=6.46

$h=\frac{180}{s^2}=\frac{180}{(6.46)^2}=4.31$

Side of square bottom=6.46 m

Height of box=4.31 m

5 0

3 years ago

A grandfather clock’s pendulum has a period of 4.5 seconds. What is its frequency? Round to the nearest hundredth.

Brilliant_brown [7]

Answer: 0.22hz

Step-by-step explanation:

Hi to answer this question we have to analyze the information given:

Period (T) = 4.5 Seconds

So, to calculate the frequency of the pendulum we have to apply the formula;

Frequency (f)= 1 / period

Replacing with the value given:

f = 1/ 4.5 sec = 0.22 hz

Feel free to ask for more if needed or if you did not understand something.

7 0

3 years ago

Write the point slope form of the equation of the line that passes through the points (-3,2) and (-5,3).

DaniilM [7]

Answer:

The answer would be B i think .

7 0

3 years ago

The quotient of a number x and −1.5 is 21

Andru [333]

Answer:

x = -31.5

Explanation:

We are given that the quotient of x and -1.5 is 21

This means that:

$\frac{x}{-1.5} =21$

To get the value of x, we will multiply both sides of the equation by -1.5

This means that:

$\frac{x}{-1.5} * -1.5=21*-1.5$

x = -31.5

Note that the value of x must be negative because we are dividing by a negative number and the quotient is positive (-ve/-ve is +ve and +ve/-ve is -ve)

Hope this helps :)

3 0

3 years ago

Mike's Bikes charges an initial fee of $10 to rent a bike plus $5 per hour (h) of use. If the total cost (t) can be determined u

Juli2301 [7.4K]

Answer:

It is 3 hrs.

Step-by-step explanation:

because the ten dollars of initial fee takes off the 25 dollars, we have 15 left, and mike's bikes charges $5/hour, so 15/3+=5

6 0

3 years ago