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2 years ago

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HELP QUICK!

1 answer:

USPshnik [31]2 years ago

3 0

Answer:

Eric will win if Nita chooses 7 and he chooses and number that is less than 17 (ex. n<17).

Nita will win if Eric chooses 17 and she chooses a number less than 8 (ex. n<8).

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Use Euler's formula to derive the identity. (Note that if a, b, c, d are real numbers, a + bi = c + di means that a = c and b =

storchak [24]

Answer with Step-by-step explanation:

We have to prove that

$sin 2\theta=2sin\theta cos\theta$ by using Euler's formula

Euler's formula : $e^{i\theta}=cos\theta+isin\theta$

$e^{i(2\theta)}=(e^{i\theta})^2$

By using Euler's identity, we get

$cos2\theta+isin2\theta=(cos\theta+isin\theta)^2$

$cos2\theta+isin2\theta=(cos^2\theta-sin^2\theta+2isin\theta cos\theta)$

$(a+b)^2=a^2+b^2+2ab, i^2=-1$

$cos2\theta+isin2\theta=cos2\theta+i(2sin\theta cos\theta)$

$cos2\theta=cos^2\theta-sin^2\theta$

Comparing imaginary part on both sides

Then, we get

$sin2\theta=2sin\theta cos\theta$

Hence, proved.

8 0

2 years ago

A water tank has a square base with each side of length 4 meters. water enters through a hose at a constant rate of 20 liters pe

levacccp [35]

43.66 minutes

4^2*5+20*x-x^2/2=0
Or
Initial volume of water plus rate of water in minus rate of water out

8 0

2 years ago

A craftsman can sell 10 jewelry sets for $500 each. He knows

liraira [26]

Answer:15

Step-by-step explanation:

Given

Craftsman sell 10 Jewelry set for $500 each

For each additional set he will decrease the price by $ 25

Suppose he sells n set over 10 set

Earning $=\text{Price of each set}\times \text{no of set}$

Earning $=(500-25n)(10+n)$

$E=5000+500n-25n^2-250n$

differentiate to get the maximum value

$\frac{dE}{dn}=-50n+250$

Equate $\frac{dE}{dn}$ to get maximum value

$-50n+250=0$

$n=\frac{250}{50}$

$n=5$

Thus must sell 5 extra set to maximize its earnings.

5 0

2 years ago

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ

SOVA2 [1]

$y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}$

The arc length of the curve is

$\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx$

which has a value of about 5.99086.

Let $f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}$ . Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

$\ell_i=\dfrac{i-1}2$

$r_i=\dfrac i2$

with $1\le i\le10$ .

These subintervals have midpoints given by

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

Over each subinterval, we approximate $f(x)$ with the quadratic polynomial

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that the integral we want to find can be estimated as

$\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that

$\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6$

so that the arc length is approximately

$\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086$

5 0

2 years ago

Eric created a rectangular patio using 1 foot square paving stones which are sold in batches by the Dozen the patio measures 7 f

Verdich [7]

Eric need 5 batches of paving stones to created his patio.

6 0

2 years ago