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alekssr [168]
3 years ago
13

The answer to the problem

Mathematics
1 answer:
Blababa [14]3 years ago
7 0
2 5/9 +1 2/3
= 2 5/9 + 1 6/9
= 3 11/9
= 4 2/9
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Consider the function V=g(x), where g(x) =x(6-2x)(8-2x), with x being the length of a cutout in cm and V being the volume of an
Andrej [43]

Answer:

The maximum volume of the open box is 24.26 cm³

Step-by-step explanation:

The volume of the box is given as V=g(x), where g(x)=x(6-2x)(8-2x) and 0\le x\le3.

Expand the function to obtain:

g(x)=4x^3-28x^2+48x

Differentiate  wrt  x to obtain:

g'(x)=12x^2-56x+48

To find the point where the maximum value occurs, we solve

g'(x)=0

\implies 12x^2-56x+48=0

\implies x=1.13,x=3.54

Discard x=3.54 because it is not within the given domain.

Apply the second derivative test to confirm the maximum critical point.

g''(x)=24x-56, g''(1.13)=24(1.13)-56=-28.88\:

This means the maximum volume occurs at x=1.13.

Substitute x=1.13 into g(x)=x(6-2x)(8-2x) to get the maximum volume.

g(1.13)=1.13(6-2\times1.13)(8-2\times1.13)=24.26

The maximum volume of the open box is 24.26 cm³

See attachment for graph.

6 0
3 years ago
A bunch of ballons contains many different colors. red 17 purple 11 orange 3 green 1 yellow 2 What is the probability that a ran
4vir4ik [10]

Answer: 1/2

Step-by-step explanation:

Number of red balloons = 17

Number of purple balloons = 11

Number of orange balloons = 3

Number of green balloons = 1

Number of yellow balloons = 2

Total number of balloons = 34

The probability that a randomly selected balloon will be red will be:

= Number of red balloons/Total number of balloons

= 17/34

= 1/2

5 0
3 years ago
Convert the polar equation to rectangular form r=2/1+sin( theta)
Nataly_w [17]
r=\dfrac2{1+\sin\theta}
r+r\sin\theta=2
\implies \sqrt{x^2+y^2}+y=2
8 0
2 years ago
Polly has 7 cucumbers to sell at the market. She has 3 times more carrots than cucumbers. She sells 6 carrots at the market. How
NeX [460]

Answer:

15

Step-by-step explanation:

7x3=21

21-6=15

the word times means to multiply a number the said amount of times for example

cat has 5 sticks. Roger has 2 times as many sticks as cat. the equation is 5 × 2 that would equal 10. :)

5 0
2 years ago
I know this might be hard but how do you make 0.12 into a fraction
hichkok12 [17]

first you put 12 over 100 and that is 12/100 and then simplify

7 0
2 years ago
Read 2 more answers
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