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4 years ago

Solve for the value of x. 1.x+8=-10 2.X-5=7 3.5x=30 4.X over 5 =-8

Mathematics

1 answer:

BabaBlast [244]4 years ago

8 0

-18 negative eighteen
6 positive six
12 positive twelve
-40 negative forty

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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the

Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

3 0

4 years ago

SOMEONE PLSSS HELPP MEE

evablogger [386]

Answer:

Step-by-step explanation:

∛6t^2= (6t^2)^1/3=

also if you want further

6^1/3 t^2/3

8 0

3 years ago

On a field trip, there were five girls for every eight boys. How many girls attended the 130 student field trip

yarga [219]

26 because 5 gose in to 13 2 times and you have 3 left bring down the zero for 30 and 6 gose in to it evenly

6 0

3 years ago

SOMEONE HELP PLEASE

yan [13]

I have this same question, can anyone answer it?

7 0

4 years ago

Read 2 more answers

A college sends a survey to members of the class of 2012. Of the 1254 people who graduated that year, 672 are women, of whom 124

Svetllana [295]

Answer:

a) $P(F) = \frac{672}{1254}=\frac{112}{209}=0.536$

b) $P(M) = \frac{582}{1254}= \frac{97}{209}=0.464$

c) $P(A') = 1-P(A) = 1- \frac{124}{672}= \frac{137}{168}=0.815$

Step-by-step explanation:

For this case we have a total of 1254 people. 672 are women and 582 are female.

We know that 124 women wnat on to graduate school.

And 198 male want on to graduate school

We can define the following events:

F = The alumnus selected is female

M= The alumnus selected is male

A= Female and attend graduate school

And we can find the probabilities required using the empirical definition of probability like this:

Part a

$P(F) = \frac{672}{1254}=\frac{112}{209}=0.536$

Part b

$P(M) = \frac{582}{1254}= \frac{97}{209}=0.464$

Part c

For this case we find the probability for the event A: The student selected is female and did attend graduate school

$P(A) =\frac{124}{672}=\frac{31}{168}=0.185$

And using the complement rule we find P(A') representing the probability that the female selected did not attend graduate school like this:

$P(A') = 1-P(A) = 1- \frac{124}{672}= \frac{137}{168}=0.815$

4 0

4 years ago