Answer:
The width is 50 yards and the length is 141 yards.
Step-by-step explanation:
Let's call: L the length of the field and W the width of the field.
From the sentence, the perimeter of the rectangular playing field is 382 yards we can formulate the following equation:
2L + 2W = 382
Because the perimeter of a rectangle is the sum of two times the length with two times the width.
Then, from the sentence, the length of the field is 9 yards less than triple the width, we can formulate the following equation:
L = 3W - 9
So, replacing this last equation on the first one and solving for W, we get:
2L + 2W = 382
2(3W - 9) + 2W = 382
6W -18 +2W = 382
8W - 18 = 382
8W = 382 + 18
8W = 400
W = 400/8
W = 50
Replacing W by 50 on the following equation, we get:
L = 3W - 9
L = 3(50) - 9
L = 141
So, the width of the rectangular field is 50 yards and the length is 141 yards.
Answer:
A Pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm and 96 cm but does not resonate at any wavelengths longer than these. This pipe is:
A. closed at both ends
B. open at one end and closed at one end
C. open at both ends.
D. we cannot tell because we do not know the frequency of the sound.
The right choice is:
B. open at one end and closed at one end
.
Step-by-step explanation:
Given:
Length of the pipe, 
= 120 cm
Its wavelength 
= 480 cm
= 160 cm and 
= 96 cm
We have to find whether the pipe is open,closed or open-closed or none.
Note:
- The fundamental wavelength of a pipe which is open at both ends is 2L.
- The fundamental wavelength of a pipe which is closed at one end and open at another end is 4L.
So,
The fundamental wavelength:
⇒ 
It seems that the pipe is open at one end and closed at one end.
Now lets check with the subsequent wavelengths.
For one side open and one side closed pipe:
An odd-integer number of quarter wavelength have to fit into the tube of length L.
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
So the pipe is open at one end and closed at one end
.
Answer:
7
Step-by-step explanation:
you need to use PEMDAS
3 x 3 x 3 = 27 divided by 9 is 3 and 10-3=7
Answer: 28
Step-by-step explanation:
Simplifying
2x + 16 = 3x + -12
Reorder the terms:
16 + 2x = 3x + -12
Reorder the terms:
16 + 2x = -12 + 3x
Solving
16 + 2x = -12 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
16 + 2x + -3x = -12 + 3x + -3x
Combine like terms: 2x + -3x = -1x
16 + -1x = -12 + 3x + -3x
Combine like terms: 3x + -3x = 0
16 + -1x = -12 + 0
16 + -1x = -12
Add '-16' to each side of the equation.
16 + -16 + -1x = -12 + -16
Combine like terms: 16 + -16 = 0
0 + -1x = -12 + -16
-1x = -12 + -16
Combine like terms: -12 + -16 = -28
-1x = -28
Divide each side by '-1'.
x = 28
Simplifying
x = 28
A^2+b^2=c^2
5^2+b^2=12^2
25+b^2=144
b^2=144-25
b^2=119
SQUARE ROOT BOTH SIDES:
b=10.9
The answer is c.
