All categories

3 years ago

Evaluate 4r/ s if r=9 and s=2

Mathematics

1 answer:

Nataliya [291]3 years ago

3 0

Just replace the variables with the numbers and solve

You might be interested in

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

3 years ago

THE PRODUCT (x-10)(x+2) is equivalent to

marissa [1.9K]

You can use the FOIL method when you have two binomials. First, outer, inner, last

7 0

3 years ago

What does endpoint mean

emmasim [6.3K]

Where you stop/finish. hope that helps :)

6 0

3 years ago

Read 2 more answers

A 25 foot ladder is leaning against a house. It makes a 75 degree angle with the ground. How far is the base of the ladder from

Oduvanchick [21]

Look at the picture.

$\cos 75^\circ =\frac{x}{25} \\
25 \cos 75^\circ = x \\
25 \times 0.2588 \approx x \\
x \approx 6.47$

The base of the ladder is 6.47 feet from the house.

4 0

3 years ago

The vertices of ABC are A(2, -3), B(-3,-5), and C(4,1). For each translation,

Snezhnost [94]

Answer:

all of ABOVW

Step-by-step explanation:

6 0

2 years ago

Evaluate 4r/ s if r=9 and s=2​

Evaluate 4r/ s if r=9 and s=2