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3 years ago

May have to flip or look closely in order to see the question. Brainliest involved

Mathematics

1 answer:

Gwar [14]3 years ago

5 0

Answer:

The answer is step 5

Step-by-step explanation:

flip the sign

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A storage box with a square base must have a volume of 90 cubic centimeters. the top and bottom cost $0.60 per square centimeter

Paul [167]

Answer-

For side length of 3.56 cm and height of 7.10 cm the cost will be minimum.

Solution-

Let us assume that,

x represents the length of the sides of the square base,

y represent the height.

Given the volume of the box is 90 cm³, so

$\Rightarrow V=90\\\\\Rightarrow x^2\times y=90\\\\\Rightarrow y=\dfrac{90}{x^2}$

As the top and bottom cost $0.60 per cm² and the sides cost $0.30 per cm². Total cost C will be,

$C=\text{cost for top and bottom}+\text{cost for rest 4 sides}\\\\=(2x^2\times 0.6)+(4xy\times 0.3)\\\\=(2x^2\times 0.6)+(4x\times \frac{90}{x^2}\times 0.3)\\\\=1.2x^2+ \dfrac{108}{x}$

Then,

$C'=\dfrac{d}{dx}(1.2x^2+ \dfrac{108}{x})=2.4x-\dfrac{108}\\\\C''=\dfrac{d^2}{dx^2}(1.2x^2+ \dfrac{108}{x})=2.4+\dfrac{216}{x^3}$

As C'' has all positive terms so, for every positive value of x (as length can't be negative), C'' is positive.

So, for minima C' = 0

$\Rightarrow 2.4x-\dfrac{108}{x^2}=0\\\\\Rightarrow 2.4x=\dfrac{108}{x^2}\\\\\Rightarrow x^3=\dfrac{108}{2.4}=45\\\\\Rightarrow x=3.56$

Then,

$y=\dfrac{90}{x^2}$

$y=\dfrac{90}{3.56^2}$

$y=7.10$

Therefore, for side length of 3.56 cm and height of 7.10 cm the cost will be minimum.

4 0

4 years ago

Read 2 more answers

Use the substitution method to solve the system of equations

shusha [124]

Answer:

you need to give us the equation or we can't help you

Step-by-step explanation:

i'm sorry if this is not what you're looking for :(

7 0

3 years ago

Can anyone just explain how to do a distant rate time problems because I'm confused about them

Ulleksa [173]

Answer:

The formula for distance problems is: distance = rate × time or d = r × t. Things to watch out for: Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.

Step-by-step explanation:

Here is an example.

Two cars started from the same point, at 5 am, traveling in opposite directions at 40 and 50 mph respectively. At what time will they be 450 miles apart?

After t hours the distances D1 and D2, in miles per hour, travelled by the two cars are given by

D1 = 40 t and D2 = 50 t

After t hours the distance D separating the two cars is given by

D = D1 + D2 = 40 t + 50 t = 90 t

Distance D will be equal to 450 miles when

D = 90 t = 450 miles

To find the time t for D to be 450 miles, solve the above equation for t to obtain

t = 5 hours.

5 am + 5 hours = 10 am

4 0

3 years ago

For f(x) = -8x +8, find f(-3)

aniked [119]

Answer:

f(x)=-8x+8

f(-3)

ANSWER: 11/8

7 0

3 years ago

The number of trucks registered in a city increases by 10% each year. Initially, there were 100 trucks registered. There were 11

Alex787 [66]

Answer:

214 trucks

Step-by-step explanation:

Un= amount after a certain time period

Uo= initial amount

n= number of time periods

i= interest rate

Equation used : Un= Uo (1+i)^n

Un=100(1.1)^8 = 214.36 , but you can't have half a truck so round and the answer would simply be 214.

5 0

4 years ago