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ololo11 [35]
3 years ago
11

A hardware store had 300 gallons of white paint on the shelves at the beginning of the month. At the end of the month, there wer

e 252 gallons of white paint. What is the percent decrease in the number of gallons of white paint from the beginning of the month to the end?
Mathematics
1 answer:
kirza4 [7]3 years ago
3 0
Set an equation.
252/300=x/100
Cross multiply
25200=300x
Divide by 300
x=84

So the percent of white paint left is 84. To find the decrease, subtract 84 from 100.

Answer: The percent decrease of white paint from the beginning of the month to the end is 16.

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Answer:  The required solution is

y=(-2+t)e^{-5t}.

Step-by-step explanation:   We are given to solve the following differential equation :

y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)

Let us consider that

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Substituting these values in equation (i), we get

m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.

So, the general solution of the given equation is

y(t)=(A+Bt)e^{-5t}.

Differentiating with respect to t, we get

y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.

According to the given conditions, we have

y(0)=-2\\\\\Rightarrow A=-2

and

y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.

Thus, the required solution is

y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.

6 0
3 years ago
PLEASE HELP ME!
Westkost [7]

Answer:

75.09%

Step-by-step explanation:

1st week: 1060

2nd week: 950

3rd week: 1090

4th week: 795

Percent decrease from first to fourth week is 75.09%

Hope this helps!

Plz Mark Brainliest!

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