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2 years ago

Find the simplest pattern and insert the missing term(s) of each sequence. 4, 7, 12, 21, 38, ___

Mathematics

1 answer:

Arte-miy333 [17]2 years ago

7 0

Answer:

Step-by-step explanation:

4, 7, 12, 21, 38, ...

2+2=2¹+2
4+3= 2²+3
8+4= 2³+4
16+5= 2⁴+5
32+6= 2⁵+6

next term:

2⁶+7= 64+7=71

nth term:

2ⁿ+(n+1)

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Find the average value of f(x+y)=sin(x+y) over

Troyanec [42]

For each given region $D$ , the average value of $f$ over $D$ is the integral of $f$ over $D$ divided by the area of $D$ . In both cases, $D$ is a rectangle so the area is trivial.

a. The area of $D$ is $\dfrac\pi3\cdot\dfrac{5\pi}3=\dfrac{5\pi^2}9$ . The integral of $f$ over $D$ is

$\displaystyle\int_0^{5\pi/3}\int_0^{\pi/3}\sin(x+y)\,\mathrm dx\,\mathrm dy$

$\displaystyle=\int_0^{5\pi/3}\left(\cos y-\cos\left(y+\dfrac\pi3\right)\right)\,\mathrm dy$

$=\sin\dfrac{5\pi}3-\sin\left(\dfrac{5\pi}3+\dfrac\pi3\right) - \sin0+\sin\dfrac\pi3=0$

So the average value of $f$ over this region is 0.

b. The area of $D$ is $\dfrac{2\pi}3\cdot\dfrac{7\pi}6=\dfrac{7\pi^2}9$ . The integral of $f$ is

$\displaystyle\int_0^{7\pi/6}\int_0^{2\pi/3}\sin(x+y)\,\mathrm dx\,\mathrm dy$

$=\displaystyle\int_0^{7\pi/6}\left(\cos y-\cos\left(y+\frac{2\pi}3\right)\right)\,\mathrm dy$

$=\sin\dfrac{7\pi}6-\sin\left(\dfrac{7\pi}6+\dfrac{2\pi}3\right) - \sin0+\sin\dfrac{2\pi}3=\dfrac{\sqrt3}2$

The average vale of $f$ over this region is then $\dfrac{\frac{\sqrt3}2}{\frac{7\pi^2}9}=\dfrac{9\sqrt3}{14\pi^2}$ .

4 0

3 years ago

PLEASE HELP I WANT TO PASS THIS LESSON PLS

zmey [24]

Answer:

ok ok so its the first one at the top(least), then the third one, then the second one, then the fourth one at the bottom(greatest)

Step-by-step explanation:

1= 88/63 least

2= 95/18 third

3=70/27 second

4= 95/4 greatest

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3 years ago

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Classify each number below as a rational number or an irrational number.

artcher [175]

Answer:

-15pi = irrational

square root of -3 = irrational

square root of -4 = rational

-1/11 = rational

-27.92 repeated = rational

Step-by-step explanation:

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2 years ago

5) Consider the sequence of steps to solve the equation: 2(x − 4) + 5x = 9x − 10 Given ⇒ 2(x − 4) + 6x = 9x − 10 Step 1 ⇒ 2x − 8

vlada-n [284]

<span>The answer to this question is Step 7.
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This is where 10 is being added to both sides. It is not Step 4 as that uses the Subtraction Property of Equality (which can be proved true by taking the addition of a negative number).
</span>

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3 years ago

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olga_2 [115]

Answer:

Step-by-step explanation:

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