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3 years ago

A pencil case with a cylinder shape with diameter= 10 cm

Mathematics

1 answer:

Mila [183]3 years ago

4 0

Answer:

length of the longest pencil that can fit must be less than 13cm

Step-by-step explanation:

To get the longest pencil that fit the case, we will use the pythagoras theorem;

diameter = 10cm

radius = 10/2

radius = 5cm

Height = 12cm

Get the length of the longest side

l² = r²+h²

l² = 5²+12²

l² = 25 + 144

l² = 169

l = √169

l = 13cm

Hence the length of the longest pencil that can fit must be less than 13cm

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A rectangle had a length of 4.5 units and a width of 2.67 units.

Nady [450]

Answer:

I have no answer.

Step-by-step explanation:

You need to add more information.

3 0

4 years ago

A chemist has a 40% alcohol solution and a 25% alcohol solution. How much of each should he mix together to get 50 liters of a 3

ludmilkaskok [199]

Answer:

33 1/3 L of the 40% solution, 16 2/3 L of the 25% solution

Step-by-step explanation:

Set up two equations...

Let x represent the number of Liters of the 40% solution

Let y represent the number of Liters of the 25% solution

We need 50 liters total, so

x + y = 50

and we need the 50 L to be 35% solution, so

0.4x = 0.25y = 0.35(50)

Solve the first equation for one variable...

x = 50 - y (subtract y from both sides in equation 1)

Now substitute that value into the second equation...

0.4(50 - y) + 0.25y = 17.5 (x becomes 50 - y, 0.35(50) = 17.5)

Now solve for y...

20 - 0.4y + 0.25y = 17.5

-0.15y = -2.5

y = 16.66666667

y = 16 2/3 L

So we need to plug that into the first equation to find 'x'

x + 16 2/3 = 50

x = 50 - 16 2/3

x = 33 1/3

3 0

3 years ago

Read 2 more answers

The total cost (in hundreds of dollars) to produce x units of a product is c(x) = (3x-2) / (8x+1), find the average cost for eac

olya-2409 [2.1K]

Answer:

a) $\frac{74}{10025}$

b) $\frac{3x-2}{x(8x+1)}$

c) $\frac{-24x^2+32x-2}{(8x^2+x)^2}$

Step-by-step explanation:

For total cost function $c(x)$ , average cost is given by $\frac{c(x)}{x}$ i.e., total cost divided by number of units produced.

Marginal average cost function refers to derivative of the average cost function i.e., $\left ( \frac{c(x)}{x} \right )'$

Given: $c(x)=\frac{3x-2}{8x+1}$

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

At x = 50 units,

$\frac{c(50)}{50}=\frac{150-2}{50(400+1)}=\frac{148}{50(401)}=\frac{74}{10025}$

Average cost = $\frac{c(x)}{x}=\frac{3x-2}{x(8x+1)}$

Marginal average cost:

Differentiate average cost with respect to $x$

Take $f=3x-2\,,\,g=8x^2+x$

using quotient rule, $\left ( \frac{f}{g} \right )'=\frac{f'g-fg'}{g^2}$

Therefore,

$\left ( \frac{c(x)}{x} \right )'=\left ( \frac{3x-2}{8x^2+x} \right )'\\=\left ( \frac{3(8x^2+x)-(16x+1)(3x-2)}{(8x^2+x)^2} \right )\\=\frac{24x^2+3x-48x^2-3x+32x+2}{(8x^2+x)^2}\\=\frac{-24x^2+32x-2}{(8x^2+x)^2}$

3 0

3 years ago

Line t has a slope of -9/2 line u is parallel to t what is the slope of u

erik [133]

Answer:

the slope of the parallel line would also be -9/2

Step-by-step explanation:

5 0

3 years ago

2. Six cell phones weigh 46.2 ounces.

Zigmanuir [339]

Answer:

Yes, they're proportional and the constant of proportionality is 7.7.

Step-by-step explanation:

They are proportional because 46.2÷6=7.7 and 107.8÷14 also equals 7.7. This also means that 7.7 is the constant of proportionality.

6 0

3 years ago

Read 2 more answers