In case of Nina:
slope of graph = speed = 48-32/6-4 = 16/2 =8
y-32 =8(x-4)
y-32=8x-32
y=8x
d=8t
at x= 0 i.e at t= 0
d= 0m
In case of Ryan:
slope =speed = 47.5-35=6-4 = 12.5/2 =6.25
y-35=6.25(x-4)
y-35=6.25x-25
y=6.25x+10
d=6.25t+10
at t = 0, d= 10m
RYAN had a head start of 10 m
Answer:
<em>Answer: A. 0.2</em>
Step-by-step explanation:
<u>Probability</u>
The circle graph shows the distribution of the makeup of the Riverside Municipal Choir.
The total number of choir sections is: 8+10+10+12=40
To calculate the probability of a member chosen at random comes from the alto section, we use the formula:
![\displaystyle P=\frac{8}{40}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20P%3D%5Cfrac%7B8%7D%7B40%7D)
Calculating:
P = 0.2
Answer: A. 0.2
Answer:
m + 6
Step-by-step explanation:
The words 'a sum' indicate addition since a sum is the answer to an addition problem. Therefore, the expression is m + 6.
Answer:
Work done = 1.69 lb-ft.
Step-by-step explanation:
Work required to stretch a spring 2 feet beyond its natural length W = 12 ft-lb
By Hook's law
![W=\int\limits^2_0 {kx} \, dx](https://tex.z-dn.net/?f=W%3D%5Cint%5Climits%5E2_0%20%7Bkx%7D%20%5C%2C%20dx)
![12=k[\frac{x^{2} }{2}]^{2}_0](https://tex.z-dn.net/?f=12%3Dk%5B%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B2%7D%5D%5E%7B2%7D_0)
12 = ![\frac{k}{2}(2)^{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bk%7D%7B2%7D%282%29%5E%7B2%7D)
12 = 2k
k = 6 lb per feet
Now we have to find the work done to stretch the spring 9 inch or
feet beyond its natural length.
We again use the Hook's law.
![W=\int\limits^\frac{3}{4} _0 {kx} \, dx](https://tex.z-dn.net/?f=W%3D%5Cint%5Climits%5E%5Cfrac%7B3%7D%7B4%7D%20_0%20%20%7Bkx%7D%20%5C%2C%20dx)
![W=k\int\limits^\frac{3}{4} _0 {x} \, dx](https://tex.z-dn.net/?f=W%3Dk%5Cint%5Climits%5E%5Cfrac%7B3%7D%7B4%7D%20_0%20%20%7Bx%7D%20%5C%2C%20dx)
![W=6\int\limits^\frac{3}{4} _0 {x} \, dx](https://tex.z-dn.net/?f=W%3D6%5Cint%5Climits%5E%5Cfrac%7B3%7D%7B4%7D%20_0%20%20%7Bx%7D%20%5C%2C%20dx)
![W=6[\frac{x^{2} }{2}]^{\frac{3}{4}}_{0}](https://tex.z-dn.net/?f=W%3D6%5B%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B2%7D%5D%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D_%7B0%7D)
![W=3(\frac{3}{4})^{2}](https://tex.z-dn.net/?f=W%3D3%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7B2%7D)
lb-ft
Therefore, work done to stretch the spring 9 in. beyond the its natural length will be 1.69 lb-feet.
Answer:
x = 4 , x = 3
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
(11)
18x + 5 = 46 - 1 + 8x
18x + 5 = 45 + 8x ( subtract 8x from both sides )
10x + 5 = 45 ( subtract 5 from both sides )
10x = 40 ( divide both sides by 10 )
x = 4
(13)
15x + 5 + 22x + 4 = 120
37x + 9 = 120 ( subtract 9 from both sides )
37x = 111 ( divide both sides by 37 )
x = 3