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3 years ago

7

Claudia's skis are 150 centimeters long. how many millimeters is this?

2 answers:

alex41 [277]3 years ago

6 0

the answer to this question is 1500 millimeters

artcher [175]3 years ago

3 0

it would be 1500 millimeters

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A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

3 years ago

What is the diameter of a hemisphere with a volume of 2233\text{ cm}^3,2233 cm 3 , to the nearest tenth of a centimeter?

Agata [3.3K]

Answer:

The diameter of the hemisphere is 20.4 centimeters.

Step-by-step explanation:

The volume of an hemisphere is given by:

$V = \frac{2 \pi r^{3}}{3}$

In this problem, we have that:

$V = 2233$

So

$\frac{2 \pi r^{3}}{3} = 2233$

$2\pi r^{3} = 3*2233$

$r^{3} = \frac{3*2233}{2\pi}$

$r = \sqrt[3]{\frac{3*2233}{2\pi}}$

$r = 10.2$

The radius is 10.2 centimeters.

The diameter is double the radius. So:

2*10.2 = 20.4

The diameter of the hemisphere is 20.4 centimeters.

5 0

3 years ago

Solving systems of equations by substitution -2x-3(6-11)=-7

Papessa [141]

Answer:

11

Step-by-step explanation:

Simplify both sides of the equation.

Subtract 15 from both sides.

Divide both sides by -2.

x = 11

3 0

3 years ago

Which statement is true for the equation 5n − 4 = 5n − 3?

Andrew [12]

It has one solution that is the answer

5 0

3 years ago

Read 2 more answers

Simplify the expression. 3(8j + 6) + 2j

kvv77 [185]

Answer: 3 x 16j

Step-by-step explanation:

3(8j +6) +2j

3 x 14j+2j

3 x 16j

4 0

3 years ago