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1 year ago

8

what is the volume of the largest sphere that you could carve out of a wooden block whose edges measure 8 m by 8 m by 8 m? Use t

he Pi and round to the nearest tenth

1 answer:

Papessa [141]1 year ago

7 0

Given data:

The given cube .

The expression for the volume of the sphere is,

$\begin{gathered} V=\frac{4}{3}\pi(\frac{8}{2}m)^{3^{}} \\ =268.0826m^3 \\ \approx261m^3 \end{gathered}$

Thus, the volume of the sphere is 261 cubic-m.

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Create a matrix for this system of linear equations, The determinant of the coefficient matrix is

marin [14]

Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation: The given system of linear equations is :

$2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

$D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.$

Now, from equations (ii) and (iii), we have

$x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

$2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.$

From equations (iv) and (v), we get

$y=\dfrac{11-3}{2}=4,\\\\z=10-3\times3=1.$

Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

3 0

3 years ago

point T"(-2,5) is a vertex of triangle T"O"P". The original image was rotated 90° counterclockwise around the origin and rhen tr

emmainna [20.7K]

ANSWER

T(-2,1)

EXPLANATION

Let T(a,b) be the coordinates.

When this point is rotated 90° counterclockwise about the origin,

Then,

$T(a,b)\to \: T'( - b,a)$

If this point is then translated using the rule;

$(x,y)\to (x-1,y+7)$

then,

$T(a,b)\to \: T'( - b,a) \to T"( - b - 1,a + 7)$

It was given that, T"(-2,5)

This implies that,

-b-1=-2

-b=-2+1

-b=-1

b=1

a+7=5

a=5-7

a=-2

Therefore the coordinates of T are:

(-2,1)

4 0

4 years ago

Read 2 more answers

The sides of a rectangle are in the ratio 2:5. The perimeter of the rectangle is 70 cm. What is the width of the rectangle?

EleoNora [17]

Width = 10cm

Length = 25cm

<u>Explanation: </u>

Given, width:length = 2:5

Let width = 2x ,

So, length = 5x

Perimeter of rectangle = 2x(length + width)

According to the question,

$70cm = 2X(5x + 2x)\\70cm = 2X(7x)\\35cm = 7x\\x = 5cm$

Hence,

Width = 10cm

Length = 25cm

4 0

3 years ago

What is the slope of the graph?

Nookie1986 [14]

Answer: The slope is $\frac{3}{5}$

Step-by-step explanation:

The slope of a line can be calculated with the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Observe the graph provided in the exercise.

You can notice that these two points are on the line:

$(2,3)$ and $(7,6)$

Then you can identify that:

$y_2=3\\y_1=6\\\\x_2=2\\x_1=7$

Knowing these coordinates, you can substitute values into the formula for calculate the slope.

Then, you get that the slope of the graph is:

$m=\frac{3-6}{2-7}\\\\m=\frac{-3}{-5}\\\\m=\frac{3}{5}$

4 0

3 years ago

John is building his daughter a doll house that is a miniature model of their house. The front of their house has a circular win

n200080 [17]

Answer:

see the procedure

Step-by-step explanation:

we know that

The scale factor of the model is 1/30

That means ----> 1 unit in the model represent 30 units in the actual

so

using proportion

Find out how much represent 5 ft in the model

Convert feet to inches

Remember that

$1\ ft=12\ in$

so

$5\ ft=5(12)=60\ in$

Let

x -----> the diameter of the circular window in the model house in inches

$\frac{1}{30}=\frac{x}{60}\\\\x=\frac{60}{30}\ in$

Simplify

$2\ in$

therefore

The diameter of the circular window in the model house is 2 inches

see the attached figure to better understand the problem

8 0

3 years ago