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anzhelika [568]

3 years ago

15

you are building a rectangular wading pool you want the area of the bottom to be 90 ft squared you want the length of the pool t

o be 3 ft longer than twice its width what will the dimensions of the pool be

1 answer:

Sindrei [870]3 years ago

5 0

L=2W+3, A=LW, using L from the first in the second gives you:

A=(2W+3)W

A=2W^2+3W, and we are told A=90 so

2W^2+3W=90

2W^2+3W-90=0

2W^2-12W+15W-90=0

2W(W-6)+15(W-6)=0

(2W+15)(W-6)=0, since W>0 for all real possibilities,

W=6ft, and since L=2W+3

L=15ft

So the pool will be 6 ft wide by 15 ft long.

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18. The Sahara Desert is the largest desert in the world. It covers 3,500,000 square miles. The Australian Desert is the second

ruslelena [56]

Solution:
3,500,000 - 2,030,000 = 1,470,000 square miles
Explanation:
Let's fully understand what this word problem is saying. Break it down.
The Sahara Desert is the largest desert in the world.
The Australian Desert is the second largest desert.
This means that the Australian Desert has an area that is less than the Sahara desert.
We are given the size of the Sahara, which is 3,500,000 square miles, but not the size of the Australian desert.The area of the Australian desert is less by 2,030,000 square miles.This is the amount we have to subtract from the area of the Sahara to find the size of the Australian desert:
3,500,000-2,030,000= 1,470,000 square miles. Hope this helps!

6 0

3 years ago

Hello, can somebody please help me with this word problem? Thanks.

erastovalidia [21]

We are given that this is an ideal gas, and that the volume and presumably the number of moles of gas are constant. We can use Gay-Lussac's Law, which describes volume and pressure. We have that pressure is directly proportional to volume. For a change in a gas, we can write the equation as
$\dfrac{P_i}{T_i} = \dfrac{P_f}{T_f}$ ,
where i denotes initial and f denotes final.

We have that $T_i=600 \ K$ , $T_f=800 \ K$ , and $P_f=30 \ atm$ . We need to find $P_i$ . To do so, let's first rearrange Gay-Lussac's equation to solve for $P_i$ .

$\dfrac{P_i}{T_i} = \dfrac{P_f}{T_f} \\\\P_iT_f=P_fT_i\\\\P_i= \dfrac{P_fT_i}{T_f}$

Now, we plug in our values to get $P_i$ .

$P_i= \dfrac{P_fT_i}{T_f}=\dfrac{30\ atm \ 600 \ K}{800 \ K} = 22.5 \ atm$ .

This seems like a reasonable value, because as temperature goes up, pressure goes up, and an increase in temperature corresponds to an increase in pressure.

Technically, you were given values with only one significant figure, so you can only report the value as $20 \ atm$ , but this depends on how your instructor usually does these problems!

4 0

3 years ago

Due to a manufacturing error, 2 cans of regular soda were accidentally filled with diet soda and placed into a24 -pack.

Gennadij [26K]

Answer:

a) 1/48 or 2.0833%

b) 46/48 or 95.8333%

no it would not be unusual

c) I'm not sure sorry

5 0

3 years ago

Find the reduced row echelon form of the following matrices and then give the solution to the system that is represented by the

GaryK [48]

Answer:

a)

Reduced Row Echelon:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&0&1&-4\end{array}\right]$

Solution to the system:

$x_3=-4\\x_2=-\frac{7}{4}x_3=7\\x_1=-\frac{1}{2}x_2=-\frac{7}{2}$

b)

Reduced Row Echelon:

$\left[\begin{array}{cccc}4&3&0&7\\0&0&2&-17\\0&0&2&-17\end{array}\right]$

Solution to the system:

$x_3=-\frac{17}{2}\\x_1=\frac{7-3x_2}{4}$

x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.

Step-by-step explanation:

To find the reduced row echelon form of the matrices, let's use the Gaussian-Jordan elimination process, which consists of taking the matrix and performing a series of row operations. For notation, R_i will be the transformed column, and r_i the unchanged one.

a) $\left[\begin{array}{cccc}0&4&7&0\\2&1&0&0\\0&3&1&-4\end{array}\right]$

Step by step operations:

1. Reorder the rows, interchange Row 1 with Row 2, then apply the next operations on the new rows:

$R_1=\frac{1}{2}r_1\\R_2=\frac{1}{4}r_2$

Resulting matrix:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&3&1&-4\end{array}\right]$

2. Set the first row to 1

$R_3=-3r_2+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&0&1&-4\end{array}\right]$

3. Write the system of equations:

$x_1+\frac{1}{2}x_2=0\\x_2+\frac{7}{4}x_3=0\\x_3=-4$

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

$x_3=-4\\x_2=-\frac{7}{4}x_3=7\\x_1=-\frac{1}{2}x_2=-\frac{7}{2}$

b)

$\left[\begin{array}{cccc}4&3&0&7\\8&6&2&-3\\4&3&2&-10\end{array}\right]$

1. $R_2=-2r_1+r_2\\R_3=-r_1+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}4&3&0&7\\0&0&2&-17\\0&0&2&-17\end{array}\right]$

2. Write the system of equations:

$4x_1+3x_2=7\\2x_3=-17$

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

$x_3=-\frac{17}{2}\\x_1=\frac{7-3x_2}{4}$

x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.

7 0

3 years ago

What is the inverse of the function f(x)

tresset_1 [31]

Step-by-step explanation:

For the inverse function put f(x) =y.

Then exchange x by y and then again separate y. The new value of y is the inverse function of f(x).

You have not written the value of function in the question so I have given just tips to solve it.

8 0

3 years ago