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LuckyWell [14K]
3 years ago
7

Write the standard equation of each circle below

Mathematics
1 answer:
almond37 [142]3 years ago
8 0
Okay so if you answer me in the comments I can help you but I need more explanation than that :)
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Jacob is a plumber. Due to increased material costs, he puts all his prices up by 7%. He now chargers R320 per hour for her serv
Lorico [155]

Answer:

R290.1

Step-by-step explanation:

Let

x = charge before he put his prices up

New charge = R320

Percentage increase in price = 7%

x + 7% of x = 320

x + 0.07 * x = 320

x + 0.07x = 320

1.07x = 320

x = 320/1.07

x = 299.06542056074

Approximately

x = R290.1

Charge before he put his prices up = R290.1

4 0
2 years ago
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
What is the value of y when the value of x is 1 Car mileage for a hybrid car
Svetllana [295]

Answer: 60

Step-by-step explanation:

Just got the wrong answer to see what it was

8 0
3 years ago
A box is 12 cm wide 12 cm long and 15 cm tall what is the total surface area of 4 such boxes
Mnenie [13.5K]
Surface area = 2(12*12+15*12+15*12) = 1008

1008 * 4 = 4032
4 0
3 years ago
Find the area of a rhombus with diagonals 9 ft. and 12 ft
aleksklad [387]
The answer would be 54, because A= PQ over 2 = 9 x 12 over 2 = 54
3 0
3 years ago
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