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2 years ago

Test 4,580 for divisibility by 2, 3, 5, 9, and 10.

Mathematics

1 answer:

Hatshy [7]2 years ago

5 0

Answer:

Find the X and Y Intercepts 3x-5y=-20

Find the X and Y Intercepts 3x-5y=-20. 3x−5y=−20 3 x - 5 y = - 20. Find the x-intercepts. Tap for more steps

Step-by-step explanation:

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EM Company produces two types of laptop computer bags. The regular version requires $32 in capital and 4 hours of labor and sell

expeople1 [14]

Answer:

Step-by-step explanation:

Given that EM company produces two types of laptop computer bags.

Let regular version produced be R and deluxe version be D

Total capital required

= $32R+38D\leq 2100$

Total labor hours required

= $4R+6D\leq 280$

Sales revenue = $46R+55D$

Solving the two constraints we have

10D $\leq$ 140

D can be atmost 14 and hence R can be 49

Otherwise if D is made 0, R = 65 maximum

If R is made 0, D maximum is 46

Thus corner points are (65,0) (0.,46) or (49,14)

Sales revenue for (65,0) = 2990

(0,46) is 2530

(49,14) is 3024

Maximum when R =14 and D is 49

5 0

3 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

Write as a fraction 56:120

Fudgin [204]

56:120 = 56/120 = 7/15

7 0

3 years ago

Read 2 more answers

Write the equation of the line in fully simplified slope-intercept form.

FrozenT [24]

Step-by-step explanation:

y — yı = m(x – xı) equation of a line

Points A(1,3) and B(2,1)

Slope (m) = (y2 – y1) / (x2 – x1)

(1 –3) / (2 – 1)

–2/1

–2

Thus, y –3 = –2 (x – 1)

y – 3 = –2x + 2

y –3 + 3 = –2x + 2 + 3

y = –2x + 5

5 0

2 years ago

Inessa05 [86]

Step-by-step explanation

8 0

2 years ago

Read 2 more answers