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1 year ago

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Select all quantities that are proportional to the diagonal length of a square. A. Area of a square B. Perimeter of a square C.

Side length of a square

1 answer:

viva [34]1 year ago

6 0

Answer:

B.Perimeter of a square

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hichkok12 [17]

Answer: 345.02

Step-by-step explanation:

8 0

2 years ago

School lunches cost PHP 135.50 per week. About how much would 15.5 weeks of lunches cost?

Pavlova-9 [17]

Answer: $2,100.25

Step-by-step explanation:

$135.50 x 15.5 = $2,100.25

7 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

Every day, the number of network blackouts has a distribution (probability mass function)

boyakko [2]

Expected Mean, E(X), is obtained by multiplying each pair of $x$ and its $P(x)$ and add up the answers

E(X) = (0×0.7) + (1×0.2) + (2×0.1) = 0.4

The formula to calculate the variance, Var(X), is given by E(X)² - (E(X))²

E(X²) = (0²×0.7) + (1²×0.2) + (2²×0.1) = 0+0.2+0.4 = 0.6
(E(X))² = (0.4)² = 0.16

Var(X) = 0.6 - 0.16 = 0.44

Translating these answers into the context we have

E(Y) = 0.4×500 = $200
Var(Y) = $110

3 0

2 years ago

Which option lists an expression that is not equivalent to 4 2/3?

I am Lyosha [343]

Answer:

Option A and Option B are not equivalent to the given expression.

Step-by-step explanation:

We are given the following expression:

$4^{\frac{2}{3}}$

Applying properties of exponents and base:

$(a^x)^y = a^{xy}\\a^{-x}= (\frac{1}{a})^x\\$

A. Using the exponential property $a^{-x}= (\frac{1}{a})^x\\$ , we can write:

$0.25^{\frac{3}{2}} = (\frac{1}{0.25})^{\frac{-3}{2}} = (4)^{\frac{-3}{2}}$

which is not equal to the given expression.

B. Using the exponential property $a^{-x}= (\frac{1}{a})^x\\$ , we can write:

$(0.25)^{\frac{-3}{2}} = (\frac{1}{0.25})^{\frac{3}{2}} = (4)^{\frac{3}{2}}$

which is not equal to the given expression.

C. First we convert the radical form into exponent form. Then by using the property $(a^x)^y = a^{xy}$ of exponent, we can write the following:

$^3\sqrt{16} = (16)^{\frac{1}{3}} = (4^2)^{\frac{1}{3}} = 4^{\frac{2}{3}}$

which is equal to the given expression.

D. First we convert the radical form into exponent form. Then by using the property $(a^x)^y = a^{xy}$ of exponent, we can write the following:

$(^3\sqrt{4})^2 = (4^{\frac{1}{3}})^2 = 4^{\frac{2}{3}}$

which is equal to the given expression.

Option D and Option C are equivalent to the given expression.

7 0

2 years ago

Read 2 more answers