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olga55 [171]
2 years ago
8

Suppose the value R(d) of d dollars in euros is given by R(d)-d The cost P(n) in dollars to purchase and ship n purses is given

by P(n)- 66n+23. Write a formula for the cost Q(n) in euros to purchase and ship n purses. It is not necessary to simplify Q(n) D
Mathematics
1 answer:
S_A_V [24]2 years ago
8 0

<u>Corrected Question</u>

Suppose the value R(d) of d dollars in euros is given by R(d)=\dfrac67 d. The cost in dollars to purchase and ship n purses is given by P(n)=66n+23. Write a formula for the cost, Q(n) in euros to purchase and ship n purses.

Answer:

Q(n)=\dfrac67(66n+23)

Step-by-step explanation:

The value R(d) of d dollars in euros is given by R(d)=\dfrac67 d

Therefore:

R(1)=\dfrac67

T$hat is, 1  dollars =\dfrac67$ euros

The cost P(n) in dollars to purchase and ship n purses is given by:

P(n) = 66n+23.

Therefore, the cost, Q(n) in euros to purchase and ship n purses

=\dfrac67 \cdot P(n)\\Q(n)=\dfrac67(66n+23)

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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,
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32.66 units

Step-by-step explanation:

We are given that

y=6x^2+14x

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

\frac{dy}{dx}=12x+14

We know that length of curve

s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx

We have a=-2 and b=1

Using the formula

Length of curve=s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

dt=12dx

dx=\frac{1}{12}dt

Length of curve=s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt

We know that

\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C

By using the formula

Length of curve=s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})

Length of curve=s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})

Length of curve=s=32.66

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2 years ago
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