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AnnZ [28]
3 years ago
14

What is $49.90 at 10% off

Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
4 0
$44.91 would be the answer because if you take the original price times the discount percentage over (divided) by 100 you would get 4.99 which you then would subtract from your total. Leaving you with 44.91
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Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
Vera_Pavlovna [14]

Split up the integration interval into 4 subintervals:

\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]

The left and right endpoints of the i-th subinterval, respectively, are

\ell_i=\dfrac{i-1}4\left(\dfrac\pi2-0\right)=\dfrac{(i-1)\pi}8

r_i=\dfrac i4\left(\dfrac\pi2-0\right)=\dfrac{i\pi}8

for 1\le i\le4, and the respective midpoints are

m_i=\dfrac{\ell_i+r_i}2=\dfrac{(2i-1)\pi}8

  • Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

T_i=\dfrac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)

so that

\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4T_i\approx\boxed{3.038078}

  • Midpoint rule

We approximate the area for each subinterval by

M_i=f(m_i)(\ell_i-r_i)

so that

\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4M_i\approx\boxed{2.981137}

  • Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial p_i(x), where

p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m)\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

\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx

It so happens that the integral of p_i(x) reduces nicely to the form you're probably more familiar with,

S_i=\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))

Then the integral is approximately

\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4S_i\approx\boxed{3.000117}

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

3 0
3 years ago
Round the following to the nearest cent: $16.997
Paul [167]
\$16.99\underbrace{7}_{>5}\approx\$17.00
7 0
3 years ago
Human beings have discovered an inhabitable planet and soon after, they find 10 more inhabitable planets. Of these 11, only 5 ar
Tatiana [17]

5 of the planets are earth like and 2 are mars like

5 * 2 = 10

<u>1 * 2 = 2</u>

Total 12

4 earth like and 4 mars like

Earth = 4*2 = 8

<u>Mars = 4 * 1 = 4</u>

Total 12

3 Like Earth 6 like mars

Earth 3 * 2 = 6

<u>Mars 6 * 1 = 6</u>

Total 12

Those answers are the only ones possible.

3 0
4 years ago
Can someone help me with this f(g(x))=2(3x-4)^2+5?
Greeley [361]

Answer:

f(x)=349525

Step-by-step explanation:

f(x)=2(3x-4)^2+5

f(x)= 6x - 8^7

f(x)= 6x - 2,097,152

f(-6x)= - 2,097,152

/-6x       /-6x

f(x)=349525


I hope I am not terribly wrong but I probably am good luck

7 0
3 years ago
Mary buys a reel of thread for sewing. There are 10 m of thread on the reel. She uses 210 cm. How much is left on the reel in ce
galben [10]
10meters=1000cm
1000-210=890
Mary has 890 centimeters of thread left on the reel.
5 0
4 years ago
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