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Tanya [424]
2 years ago
6

The Smith family goes out for lunch, and the price of the meal is $45.The sales tax on the meal is 6%, and the family also leave

s a 20%tip on the pre-tax amount. What is the total cost of the meal?
Mathematics
1 answer:
Zinaida [17]2 years ago
3 0

Answer:

$56.70

Step-by-step explanation:

45 x 6% = 2.7 Multiply price of meal with the percentage of sales tax

45 x 20% = 9 Multiply price of mean with the percentage of tip

$9 is the tip amount

$2.70 is the sales tax

$45 + $2.70 + $9 = $56.70. Add the price of the meal with the sales tax and tip amount to get the total cost of the meal.

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What 2 number when you multiply is 14 and when added is -9
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Answer: -7 -2


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3 years ago
Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview
svetlana [45]

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

y=e^{mt} be an auxiliary solution of equation (i).

Then, we have

y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.

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}.

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3 years ago
2 times 2.1-(2.8 times 1.5)
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5 0
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Find the unit rate of 183 miles in 3 hours
klio [65]
30. find the unit rate of 183 miles in 3 hours IF you want me to show the unit rate in miles per hour here is the method to do that: => 183 miles / 3 hours = 61 miles per hour. Thus the unit rate is 61 miles per hour or 61 miles /h Now, if you want to see the unit rate in miles per minute then here is the method to do that: => 1 hour = 60 minutes => 3 hours = 180 minutes => 183 miles / 180 minutes = 1.02 miles per minute
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