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3 years ago

9

Kathy purchased a new purse that sold for $48.00 and was subject to a 7 percent sales tax. The total amount that Kathy paid for

the purse was?

1 answer:

pshichka [43]3 years ago

7 0

$51.36 should be the total amount Kathy paid for the purse.

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Last year, a beauty magazine had a total of 2,650 subscribers. This year, after its parent company made some changes, it had 3,2

lilavasa [31]

Answer:

22%

Step-by-step explanation:

Divide 2,650 by 100:

2,650/100=26.5

Then divide 3233 by the dividend:

122=122%

Now you can see that there is a 22% percent increase over 100%, theefore making our answer 22%.

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3 years ago

Let z = ln(x 2 + y), x = ret . and y = ter . Use the Chain Rule to compute ∂z ∂r and ∂z ∂t at the point where (r, t) = (1, 2).\

Natali [406]

By the chain rule,

$\dfrac{\partial z}{\partial u}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial u}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial u}$

where $u\in\{r,t\}$ .

We have component partial derivatives

$\dfrac{\partial z}{\partial x}=\dfrac{2x}{x^2+y}=\dfrac{2re^t}{r^2e^{2t}+te^r}$

$\dfrac{\partial z}{\partial y}=\dfrac1{x^2+y}=\dfrac1{r^2e^{2t}+te^r}$

$\dfrac{\partial x}{\partial r}=e^t$

$\dfrac{\partial x}{\partial t}=re^t$

$\dfrac{\partial y}{\partial r}=te^r$

$\dfrac{\partial y}{\partial t}=e^r$

Putting the appropriate pieces together and setting $(r,t)=(1,2)$ , we get

$\dfrac{\partial z}{\partial r}(1,2)=\dfrac{2e^3+2}{e^3+2}$

$\dfrac{\partial z}{\partial t}(1,2)=\dfrac{2e^3+1}{e^3+2}$

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