Answer:
Joseph used ![5\frac{2}{3}\ yards\ of\ cape](https://tex.z-dn.net/?f=5%5Cfrac%7B2%7D%7B3%7D%5C%20yards%5C%20of%5C%20cape)
Step-by-step explanation:
Total fabric available = 17 yards
fraction used = one-third = 1/3
Let us convert this fraction to actual number
He used one-third of total
= ![\frac{1}{3}\ of\ 17\\=\frac{1}{3} \times \frac{17}{1} = \frac{17}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5C%20of%5C%20%2017%5C%5C%3D%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20%5Cfrac%7B17%7D%7B1%7D%20%3D%20%5Cfrac%7B17%7D%7B3%7D)
To convert to mixed number, look for the closest number to the numerator that the denominator in the fraction can divide, and write it as the whole number in the mixed fraction, the remainder becomes the numerator of the new fraction:
The closest number to 17 that 3 can divide without a remainder is 15 and 3 can divide 15, 5 times, while the remainder becomes 2
![\therefore \frac{17}{3} = 5\frac{2}{3}\ yards\ of\ cape](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cfrac%7B17%7D%7B3%7D%20%3D%205%5Cfrac%7B2%7D%7B3%7D%5C%20yards%5C%20of%5C%20cape)
A vertical stretching<span> is the </span>stretching<span> of the graph away from the x-axis.
It means you simply need to multiply the scale factor with the x-values.
</span>If point H is located at <span>(-2, 0),and the scale factor is 2,then the stretch would be (-2*2.5,0)
Hence,the new point will be:
A.(-5,0).
</span>
It's 768 sqaure centimeters
Answer:
a = L
b = MT^(-1)
c = LT^(-1)
k = MT^(-2)
f = MLT^(-2)
S = T^(-1)
Step-by-step explanation:
x (0) = a
x is denoted by displacement in vibration analysis hence attains units of x.
Hence, a = L
b is the damping coefficient:
![b = \frac{F}{\frac{dx}{dt} } \\= MLT^(-2) / LT^(-1)\\= MT^(-1)](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7BF%7D%7B%5Cfrac%7Bdx%7D%7Bdt%7D%20%7D%20%5C%5C%3D%20MLT%5E%28-2%29%20%2F%20LT%5E%28-1%29%5C%5C%3D%20MT%5E%28-1%29)
x'(0) = c
dx/dt = velocity hence c attains the units of velocity
c = LT^(-1)
Coefficient k is the stiffness:
![k = \frac{F}{x} = \frac{MLT^(-2)}{L} = MT^(-2)](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7BF%7D%7Bx%7D%20%20%3D%20%5Cfrac%7BMLT%5E%28-2%29%7D%7BL%7D%20%3D%20MT%5E%28-2%29)
Coefficient f is the magnitude of the exciting force
![F = m*acceleration = MLT^(-2)](https://tex.z-dn.net/?f=F%20%3D%20m%2Aacceleration%20%3D%20MLT%5E%28-2%29)
Coefficient S is the angular frequency
angular frequency is displacement in radians per seconds; hence,
S = T^(-1)
Answer:
10a < 25b
Step-by-step explanation: