Answer:
The percentage that the coat was reduced is 25%.
Step-by-step explanation:
A percentage is always out of a factor of 100.
40 x 2.5 = 100
30 x 2.5 = 75
75/100 = 3/4
1/4 is missing, which is the percentage.
1/4 = 0.25, or 25%
Hope This Helps!
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
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Answer:
Calvin will paint the entire area in 92 minutes or 1 hour 32 minutes.
Step-by-step explanation:
First of all we know that the total surface are that Calvin is painting is 115 square feet.
The rate at which Calvin is painting refers to the surface area he covers every 2 minutes. This is 2.5 square feet every 2 minutes.
we can set up a relation to solve this problem
If Calvin paints
in 2 minutes
He will paint
in
minutes
By cross multiplying, we have 
Hence Calvin will paint the entire area in 92 minutes or 1 hour 32 minutes.
Answer:
x = 6
Step-by-step explanation:
8x + 2 + 70 + 60 = 180
8x + 132 = 180
8x = 48
x = 6
1128 feet = 1128/5280 miles
it travels at 1128/5280 miles per second
to convert to miles / hour we multiply by 3600
so speed of the bullet = (1128 * 3600) / 5280 = 769.1 mph to nearest tenth.