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3 years ago

15

Lacey has a 20% off coupon for Bed Bath and Beyond She wants to buy a beach towel priced at $15. If she uses her coupon what is

the cost of the towel before
tax?

1 answer:

horsena [70]3 years ago

8 0

10% of $15 = 15/10= 1.5
1.5 x 2= 3 = 20%
15-3=12
Therefore the towel will be $12 with a 20% of coupon

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The length of a rectangular rug is 4 feet less than twice its width. The perimeter of the rug is 40 feet. Write a system of equa

Brrunno [24]

Answer:

Step-by-step explanation:

L=2W-4

40=2L+2W

The first equation uses the information that the length of a rectangular rug is 4 feet less than twice its width.

The second equation is using your standard perimeter equation of 2L+2W=perimeter of a rectangle.

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7x+6>1+2x

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Fiesta28 [93]

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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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3 years ago