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3 years ago

Explain how you can use long division to see that the rational number is

1 answer:

8 0

To use division to find the decimal equivalent of a rational number, divide the top number by the bottom number. You will get a decimal number.

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A box with a square base and no top is to be built with a volume of 1638416384 in33. Find the dimensions of the box that require

julsineya [31]

Answer:

$512\ \text{in}^2$

Step-by-step explanation:

x = Length and width of base

y = Height of box

Volume of the box is $16384\ \text{in}^3$

$x^2y=16384\\\Rightarrow y=\dfrac{16384}{x^2}$

Surface area is given by

$s=x^2+4y\\\Rightarrow s=x^2+4\times \dfrac{16384}{x^2}\\\Rightarrow s=x^2+\dfrac{65536}{x^2}$

Differentiating with respect to x we get

$s'=2x-\dfrac{131072}{x^3}$

Equating with 0 we get

$0=2x^4-131072\\\Rightarrow x=(\dfrac{131072}{2})^{\dfrac{1}{4}}\\\Rightarrow x=16$

$s''=2+\dfrac{393216}{x^4}$

at $x=16$

$s''=2+\dfrac{393216}{16^4}=8>0$

So the function is minimum at x = 16

$y=\dfrac{16384}{x^2}=\dfrac{16384}{16^2}\\\Rightarrow y=64$

The material required is

$s=x^2+4y=16^2+4\times 64\\\Rightarrow s=512\ \text{in}^2$

The minimum amount of material required is $512\ \text{in}^2$ .

6 0

3 years ago

THIS IS DUE TOMORROW HELPPPP

bogdanovich [222]

Answer:

Answers are below

Step-by-step explanation:

1. For every 4 boys, there are 3 girls.

2a. 14-p

2b. (d+f)/8

2c. 2x+5

2d. c/6

3a. 2a+2b

3b. 21d+12e

3c. 8a+24b

4. Speed = distance/time

5a. 101 boys and 121 girls

5b. 8 won + 4 lost = 12 games in total

6a. 65

6b. 657

6c. 98

7a. 49.99

7b. 110.92

Hope these answers are correct! Please mark me as brainliest!

3 0

3 years ago

Given an exponential function for compounding interest, A(x) = P(.96)x, what is the rate of change?

uranmaximum [27]

Answer:

The rate of change is positive 96%

Step-by-step explanation:

.96 = 96%

4 0

3 years ago

Solve and show your work: |4x − 1| = 13 <br> PLEASE HELP ME

Damm [24]

Answer: x=7/2, x=-3

Step-by-step explanation:

First lets do look at it without the absolute value marks

4x-1=13

4x=14

x=7/2

Now lets do the same but assume 13 is negative,

4x-1=-13

4x=-12

x=-3

5 0

3 years ago

Jason ran for days last week on Monday he ran 3.45 miles on Wednesday here and 0.82 miles farther than he went on Monday on Frid

disa [49]

15.82 miles
3.45 + 4.27 + 4.65 + 3.45 = 15.82 miles

4 0

3 years ago

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