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taurus [48]
3 years ago
14

Geometry question please help meeee

Mathematics
1 answer:
garik1379 [7]3 years ago
6 0
Answers:
Scale factor is 8:5
Area ratio is 64:25
Volume ratio is 512:125

=================================================

Explanation:

Divide the second surface area (375) over the first surface area (960) to get
375/960 = 0.390625
Then take the square root of this to get
sqrt(0.390625) = 0.625
The decimal value 0.625 converts to the fraction 5/8, which turns into the scale factor 8:5 

-----------------

Once you know the scale factor, you can square both sides to get the area ratio
8:5
8^2:5^2
64:25

The area ratio is 64:25

Then go back to the scale factor, and cube each part to get the volume ratio
8:5
8^3:5^3
512:125

The volume ratio is 512:125

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Solve the system of equations:x + 3y - z = -4 2x - y + 2z = 13 3x - 2y - z = -9
tatiyna

Answer:

The solution to the system of equations is

\begin{gathered} x=\frac{179}{13} \\  \\ y=-\frac{279}{39} \\  \\ z=-\frac{48}{13} \end{gathered}

Explanation:

Giving the system of equations:

\begin{gathered} x+3y-z=-4\ldots\ldots\ldots\ldots\ldots\ldots..........\ldots\ldots\ldots\ldots.\ldots\text{.}\mathrm{}(1) \\ 2x-y+2z=13\ldots\ldots...\ldots\ldots\ldots\ldots..\ldots..\ldots\ldots\ldots\ldots\ldots.(2) \\ 3x-2y-z=-9\ldots\ldots\ldots.\ldots\ldots\ldots\ldots....\ldots\ldots.\ldots\ldots\ldots\text{.}\mathrm{}(3) \end{gathered}

To solve this, we need to first of all eliminate one variable from any two of the equations.

Subtracting (2) from twice of (1), we have:

5y-4z=-21\ldots\ldots\ldots\ldots\ldots.\ldots.\ldots..\ldots..\ldots\ldots.\ldots..\ldots\text{...}\mathrm{}(4)

Subtracting (3) from 3 times (1), we have

3y-5z=-3\ldots\ldots...\ldots\ldots..\ldots\ldots\ldots\ldots\ldots.\ldots\ldots\ldots\ldots\ldots..\ldots\ldots(5)

From (4) and (5), we can solve for y and z.

Subtract 5 times (5) from 3 times (4)

\begin{gathered} 13z=-48 \\  \\ z=-\frac{48}{13} \end{gathered}

Using the value of z obtained in (5), we have

\begin{gathered} 3y-5(-\frac{48}{13})=-3 \\  \\ 3y+\frac{240}{13}=-3 \\  \\ 3y=-3-\frac{240}{13} \\  \\ 3y=-\frac{279}{13} \\  \\ y=-\frac{279}{39} \end{gathered}

Using the values obtained for y and z in (1), we have

\begin{gathered} x+3(-\frac{279}{39})-(-\frac{48}{13})=-4 \\  \\ x-\frac{279}{13}+\frac{48}{13}=-4 \\  \\ x-\frac{231}{13}=-4 \\  \\ x=-4+\frac{231}{13} \\  \\ x=\frac{179}{13} \end{gathered}

8 0
1 year ago
Their sum is −7 and their difference is 14 what are my numbers
Mashcka [7]

Answer:

Answer: 3 1/2 and -10 1/2 are the two numbers.

Step-by-step explanation:

Let x and y be the two unknown numbers.

x+y=-7 [Given]

x-y=14 [Given]

x-y=14 [Given]

x=y+14 [Add y to both sides]

x+y=-7 [Given]

(y+14)+y=-7 [Subtitution]

2y+14=-7 [Combine like terms]

2y=-21 [Subtract 14 from both sides]

y=-21/2 [Divide both sides by 2]

y=-10 1/2 [Division]

x-y=14 [Given]

x=y+14 [Add y to both sides]

x=-10 1/2 + 14 [Substitution]

x= 3 1/2 [Addition]

Check:

x+y=-7 [Given]

3 1/2 + -10 1/2?=-7 [Substition]

-7=-7 [Addition]

QED

x-y=14 [Given]

3 1/2 - -10 1/2?=14 [Substitution]

3 1/2 + 10 1/2?=14 [Change the sign of the subtrahend and add]

14=14 [Addition]

QED

Answer: 3 1/2 and -10 1/2 are the two numbers.

8 0
3 years ago
From a hot-air balloon, Madison measures a 36^{\circ}
krek1111 [17]

The balloon’s vertical distance above the ground is 570.3 feet

<h3>Angle of elevation and depression</h3>

Given the following parameters

The angle of depression = 36 degrees

Base distance =  785 feet

<h3>Required</h3>

vertical distance above the ground (H)

Using the SOH CAH TOA identity

tan 36 = H/785
H = 785tan36

H = 570.3 feet

Hence  the balloon’s vertical distance above the ground is 570.3 feet

Learn more on SOH CAH TOA here: brainly.com/question/20734777

3 0
2 years ago
Find the flow rate through a tube of radius 6 cm, assuming that the velocity of fluid particles at a distance r cm from the cent
vaieri [72.5K]

Answer:

791.68 cm/s

Step-by-step explanation:

The volume flow rate can be interpreted as the integral of fluid velocity over area

\dot{V} = \int\limits^6_0 {v(r) 2\pi r} \, dr\\\dot{V} = 2\pi\int\limits^6_0 {(25-r^2)r} \, dr\\\dot{V} = 2\pi\int\limits^6_0 {25r-r^3} \, dr\\\\\dot{V} = 2\pi[12.5r^2 - r^4/4]_0^6\\\dot{V} = 2\pi(12.5*6^2 - 6^4/4 - 12.5*0 - 0)\\\dot{V} = 2\pi*126 = 791.68 cm/s

7 0
3 years ago
0.8342 as a fraction?
ratelena [41]

Answer:

4171/5000

Step-by-step explanation:

When diving 4171 by 5000, you get the answer of 0.8342. If you are using a calculator, you can use a button that allows you to convert decimals to fractions and vice versa.

5 0
3 years ago
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