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4 years ago

11

For his long-distance phone service, Hans pays a $3 monthly fee plus .11 cents per minute. Last month, Hans's long-distance bill

was 19.96. For how many minutes was Hans billed?

1 answer:

Lera25 [3.4K]4 years ago

3 0

Answer:

about 154 minutes and 18 seconds

Step-by-step explanation:

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Compute the differential of surface area for the surface S described by the given parametrization.

AysviL [449]

With $S$ parameterized by

$\vec r(u,v)=\langle e^u\cos v,e^u\sin v,uv\rangle$

the surface element $\mathrm dS$ is

$\mathrm dS=\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

We have

$\dfrac{\partial\vec r}{\partial u}=\langle e^u\cos v,e^u\sin v,v\rangle$

$\dfrac{\partial\vec r}{\partial v}=\langle -e^u\sin v,e^u\cos v,u\rangle$

with cross product

$\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\langle ue^u\sin v-ve^u\cos v,-ve^u\sin v-ue^u\cos v,e^{2u}\cos^2v+e^{2u}\sin^2v\rangle$

$\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\langle e^u(u\sin v-v\cos v),-e^u(v\sin v+u\cos v),e^{2u}\rangle$

with magnitude

$\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=\sqrt{e^{2u}(u\sin v-v\cos v)^2+e^{2u}(v\sin v+u\cos v)^2+e^{4u}}$

$\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=e^u\sqrt{u^2+v^2+e^{2u}}$

So we have

$\mathrm dS=\boxed{e^u\sqrt{u^2+v^2+e^{2u}}\,\mathrm du\,\mathrm dv}$

8 0

3 years ago

How do I answer this question on khan academy.

yarga [219]

If $b$ is Ben's age and $i$ is Ishaan's age, then

present day: $b=4i$
6 years ago: $b-6=6(i-6)$

Rewrite the second equation as

$b-6=6(i-6)\implies b-6=6i-36\implies b+30=6i$

Substitute $b=4i$ into this equation to solve for $i$ :

$b+30=6i\implies4i+30=6i\implies30=2i\implies i=15$

Then

$b=4i\implies b=4\cdot15=60$

So Ben is 60 years old now.

8 0

4 years ago

Felicia has $350 to deposit into two different savings accounts. Felicia will deposit $200 into Account I, which earns 4.5% annu

Alisiya [41]

Total price after 6 years in Account I is :

$P _1=P_o+\dfrac{P_ort}{100}\\\\P_1=200+\dfrac{200\times 4.5 \times 6}{100}\\\\P_1=\$254$

Total price after 6 years in Account II is :

$P_2=P_o(1+\dfrac{r}{n})^{nt}\\\\P_2=150(1+\dfrac{3.34}{1})^{1\times 6}\\\\P_2=\$1002373.64$

Total balance, $T=P_1+P_2=1002373.64+254=\$1002627.64$

Hence, this is the required solution.

5 0

3 years ago

I subtract 3 from a certain number, multiply the result by 5 and then add 9

mr_godi [17]

Answer:

The number is 5x-6

Step-by-step explanation:

Let the number be x.

Then,

Subtracting 3,

x - 3

Multiplying by 5,

(x-3)5
5(x-3)

Adding 9:

5(x-3)+9

Solving Further:

5x-15+9
5x-6

3 0

2 years ago

Read 2 more answers

Work out 4x-5=9 ..............................................................

iragen [17]

Answer:

Step-by-step explanation:

4x-5=9

4x=14

x=14/4. or 7/2 if you want to simplify it

3 0

3 years ago

Read 2 more answers