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2 years ago

Evaluate the expression. ab if a = 6 and b = 7

Mathematics

2 answers:

Shtirlitz [24]2 years ago

6 0

Answer:

Step-by-step explanation:

ab is a x b

$a \times b$

$6 \times 7 = 42$

Misha Larkins [42]2 years ago

4 0

Answer:

Step-by-step explanation:

6x7=42

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How many terms are there in the following expression:

sweet [91]

3 terms

when you combine like terms you are left with 10x + y + 8 which is 3 terms.

7 0

2 years ago

Can anyone please tell me how to do this

andrew11 [14]

Hello there, this problem is just basic addition, here is what it would look like

$52.31+25.90$

Solve it and we get 78.21

5 0

2 years ago

Read 2 more answers

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

2 years ago

5 1/6 + (7 1/3)l <60

agasfer [191]

Answer:

$l$

Step-by-step explanation:

Given the inequality

$5\dfrac{1}{6}+7\dfrac{1}{3}l$

First, convert mixed numbers to improper fractions:

$5\dfrac{1}{6}=\dfrac{5\cdot 6+1}{6}=\dfrac{31}{6}\\ \\7\dfrac{1}{3}=\dfrac{7\cdot 3+1}{3}=\dfrac{22}{3}$

Now the inequality looks like

$\dfrac{31}{6}+\dfrac{22}{3}l$

Multiply it by 6:

$\dfrac{31}{6}\cdot 6+\dfrac{22}{3}l\cdot 6$

7 0

3 years ago

Pls help me. i need it

Juli2301 [7.4K]

Answer:

option 2 is correct

Step-by-step explanation:

5 0

3 years ago