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Tpy6a [65]
3 years ago
6

+4.31. Let a(s) be a unit speed curve with kt = 0. Prove there is a curve

Mathematics
1 answer:
yanalaym [24]3 years ago
6 0

Answer:

It is proved

Step-by-step explanation:

A curve immersed in the three-dimensional sphere is said to be a Bertrand curve if there exists another curve and a one-to-one correspondence between and such that both curves have common principal normal geodesics at corresponding points.

See attachment for the step by step solution of the given problem.

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To offer scholarships to children of employees, a company invests $13,000 at the end of every three months in an annuity that pa
Andreyy89

Annuities

Suppose a fixed investment R is done every fixed number of periods m per year for t years at a constant rate r.

a.

The final value of the investments plus the interest is calculated as follows:

FV=R\cdot\frac{(1+i)^n-1}{i}

Where:

n = number of total periods of the investment.

n = m*t

i=\frac{r}{m}

The company invests R = $13,000 for t = 10 years at the end of every quarter (3 months), thus m = 4. The interest rate is r = 9% = 0.09.

The interest rate compounds quarterly.

Calculate:

n = 4*10 = 40

i = 0.09 / 4 = 0.0225

\begin{gathered} FV=\$13,000\cdot\frac{(1+0.00225)^{40}-1}{0.0225} \\ FV=\operatorname{\$}13,000\times\frac{(1.00225)^{40}-1}{0.0225} \\ FV=\operatorname{\$}13,000\times\frac{2.435188965-1}{0.0225} \\ FV=\operatorname{\$}13,000\cdot63.786176 \end{gathered}

Calculating:

FV = $829,220

The company will have $829,220 in scholarship funds

b. The interest can be found by subtracting the final value and the initial value. We have to calculate the latter:

\begin{gathered} A=FV(1+i)^{-n} \\ A=\$829,220(1.0225)^{-40} \\ A=\$340,516 \end{gathered}

Thus, the interest is:

welcI = $829,220 - $340,516

I = $488,704

The interest is $488,704

5 0
11 months ago
Paul bought : student discount card for the bus. The card allows him to buy daily bus passes for $1.40.
tekilochka [14]
Paul spend 22.4 on student discount card.
8 0
2 years ago
A researcher at a school of nursing decides to investigate the correlation between a pre- admission HESI examination, high schoo
Nataly_w [17]

Answer: D. Predictive validity

Step-by-step explanation: Predictive validity can be explained as a method of determining the degree or level of correctness of a prediction using pre-existing information or data and values obtained from the actual measurement.

In the scenario above, the researchers investigates the correlation or relationship between the predicted value obtained using a pre- admission HESI examination, high school GPA, and SAT scores and the actual grade received upon completion of the first year. This process is to analyze or determine the validity of our prediction.

4 0
3 years ago
How many feet is 20% of 4 miles
Nataliya [291]
1 mile=5280 feet
4 miles=21120 feet

21120×20÷100=4224. As a result, 20% of 4 miles is 4224 feet. Hope it help!
3 0
3 years ago
Read 2 more answers
Mrs. Stern washed
bekas [8.4K]

Answer:

Mrs. Stern washed more

\frac{7}{20} laundry still needs to be washed.

Step-by-step explanation:

Total amount of laundry: \frac{20}{20}

\frac{20}{20} -\frac{2}{5}-\frac{1}{4} =

\frac{20}{20} - \frac{8}{20} -\frac{5}{20} =

\frac{7}{20} of the laundry still needs to be done.

Mrs. Stern washed \frac{8}{20} of the laundry.

Her son washed \frac{5}{20} of the laundry.

Mrs. Stern washed more laundry than her son.

8 0
3 years ago
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