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dem82 [27]
3 years ago
7

Definition n of product rule

Mathematics
1 answer:
Vladimir [108]3 years ago
5 0
A product rule is a formal rule for differentiating problems where one function is multiplied by another.

Hope this helps!!!   :)
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Read 2 more answers
Why did I get this question wrong?
Talja [164]

Answer:

9.25

Step-by-step explanation:

M₄ means the area using 4 rectangles with heights equal to the function evaluated at the midpoints.

The width of each rectangle is (4−0)/4 = 1.

The area of each rectangle is:

M₁ = (1) (1.12) = 1.12

M₂ = (1) (1.80) = 1.80

M₃ = (1) (2.69) = 2.69

M₄ = (1) (3.64) = 3.64

The total area is therefore:

M = 1.12 + 1.80 + 2.69 + 3.64

M = 9.25

7 0
3 years ago
a car recently sold for $32,345. if there is a 6% sales tax on automobile sales, how much tax will be added to the price of the
geniusboy [140]
6% of $32,345 is $1,940.70, your decimal point is off by 1 place :)
7 0
3 years ago
You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod
lorasvet [3.4K]

Answer:

a. y=830*(0.87)^x

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: y=a*b^x, where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

13\%=\frac{13}{100}=0.13

Upon substituting our given values in exponential decay function we will get

y=830*(1-0.13)^x

y=830*(0.87)^x

Therefore, the exponential model y=830*(0.87)^x represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

y=830*(0.87)^2

y=830*0.7569

y=628.227\approx 628.23

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be \frac{830}{2}=415.

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

415=830*(0.87)^x

Upon dividing both sides of our equation by 830 we will get,

\frac{415}{830}=\frac{830*(0.87)^x}{830}

0.5=0.87^x

Let us take natural log of both sides of our equation.

ln(0.5)=ln(0.87^x)

Using natural log property ln(a^b)=b*ln(a) we will get,

ln(0.5)=x*ln(0.87)

\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}

\frac{ln(0.5)}{ln(0.87)}=x

\frac{-0.6931471805599}{-0.139262067}=x

x=4.977286\approx 4.98

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

5 0
3 years ago
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