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2 years ago

I kind of need this answer now .-.

Mathematics

1 answer:

alex41 [277]2 years ago

6 0

Answer: 11 centimeters per day

Step-by-step explanation:

Level increase is 55cm

Days it took to increase is 5 days

Increase rate in cm/day = 55/5 = 11cm/day.

Glad to help

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The function f(x) = –4x2 represents the path of a whale as it surfaces for air and dives again. Select all the observations that

lara31 [8.8K]

Answer:

The correct option is;

E. The whale touches the surface at the maximum

Please find attached the whale motion diagram

Step-by-step explanation:

The given function is f(x) = -4·x²

Therefore, we have;

x, f(x)

-5, -100

-4, -64

-3, -36

-2, -16

-1, -4

0, 0

1, -4

2, -16

3, -36

4, -64

5, -100

Which is the gives the singular maximum value for f(x) at x = 0, which is the surface of the water where the whale reaches for air

The errors in the other options are

A. The domain is always real

B. The range is (-∞, 0)

C. There is only one point where the whale touches the surface at x = 0

D. The values of f(x) initially rises, hen descends as the whale moves to the surface of the water and then descends.

3 0

3 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

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

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2 years ago

Polynomial function F(x)=2-11x+2x²

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Answer:

should be 4

Step-by-step explanation:

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3 years ago

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Answer:

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

because it as the information triangle y

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2 years ago