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3 years ago

3 Terrence uses pieces of wood that are 10 inches long to

Mathematics

1 answer:

Alchen [17]3 years ago

3 0

Answer:

146 whistles

Step-by-step explanation:

First, convert 122 feet to inches, by multiplying it by 12

122(12)

= 1464

Divide this by 10 to find how many whistles he can make

1464/10

= 146.4

Since we can only have a whole number of whistles, we have to round down to 146.

So, he can make 146 whistles

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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

HELP!!!! 15 points and marked brainliest!!!!

nikitadnepr [17]

Answer:

Step-by-step explanation:

LN = LM + MN

=> 22 = 3z + 1 + 3z + 1

20 = 6z

z = 10/3

LM = (10/3)*3+1 = 11

:(((

8 0

3 years ago

Help me please I don't understand

Arturiano [62]

Step-by-step explanation:

hope this helps you out with the problems

3 0

3 years ago

An object is moving at a speed of 7300 inches every 3 seconds. Express this speed in miles per day.

AleksAgata [21]

Answer:

Since there are 60 seconds in one minute, we can write this as 146,000 inches per minute. Since there are 60 * 60 = 3600 minutes in one day, we can write it as 525,600,000 inches per day. Since there are about 63360 inches in one mile, the answer is about 8295 miles per day.

4 0

4 years ago

Read 2 more answers

El precio de un automovil $696.000 y se puede pagar de dos maneras distintas.

Svet_ta [14]

I’m sorry i don’t speak Spanish!

7 0

3 years ago