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3 years ago

Write the Recursive form and next of the following sequence8,10,12,14,16...

Mathematics

1 answer:

Serggg [28]3 years ago

5 0

Answer:

Step-by-step explanation:

The recursive form is a(n + 1) = a(n) + 2, with a(1) = 8.

The next term is a(6) = a(5) + 2, which heere is a(6) = 16 + 2 = 18

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Evaluate the integral Integral from (5 comma 2 comma 4 )to (7 comma 9 comma negative 3 )y dx plus x dy plus 3 dz by finding para

padilas [110]

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_{(5,2,4)}^{(7,9,-3)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz$

Parameterize the line segment (call it $C$ ) by

$\vec r(t)=(1-t)(5\,\vec\imath+2\,\vec\jmath+4\,\vec k)+t(7\,\vec\imath+9\,\vec\jmath-3\,\vec k)$

$\vec r(t)=(2t+5)\,\vec\imath+(7t+2)\,\vec\jmath+(4-7t)\,\vec k$

with $0\le t\le1$ . Then

$\vec r'(t)=2\,\vec\imath+7\,\vec\jmath-7\,\vec k$

and the line integral is

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^1((7t+2)\,\vec\imath+(2t+5)\,\vec\jmath+3\,\vec k)\cdot\vec r'(t)\,\mathrm dt$

$=\displaystyle\int_0^1((2t+5)+2(7t+2)-21)\,\mathrm dt$

$=\displaystyle\int_0^1(28t+18)\,\mathrm dt=\boxed{32}$

Alternatively, if we can show that $\vec F$ is conservative, then we can apply the fundamental theorem of calculus. We need to find $f$ such that $\nabla f=\vec F$ , which requires

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

Integrating both sides of the first equation with respect to $x$ gives

$f(x,y,z)=xy+g(y,z)$

Differentiating both sides wrt $y$ gives

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

Differentiating wrt $z$ gives

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}$

$\implies h(z)=3z+C$

So we have

$f(x,y,z)=xy+3z+C$

and $\vec F$ is conservative. By the FTC, we find

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=f(7,9,-3)-f(5,2,4)=\boxed{32}$

5 0

3 years ago

Can someone help me find x

nadya68 [22]

Answer:

Step-by-step explanation:

2 equal 90° angles, we can use an equation

x + 15 = 90

x = 90 - 75

x = 15°

-------------------------

check

90 = 15 + 75

90 = 90

the answer is good

7 0

3 years ago

In a survey examining eating habit 34 women over 40 years old and a 54 women 40 and under responded to the survey. What’s the ra

Rina8888 [55]

Answer:

17:27

Step-by-step explanation:

You would start with 34:54

this reduces to 17:27

4 0

3 years ago

Plz help me thank you

lana [24]

√5.√8

=√40

√2×2×2×5

2√10

option A is correct

8 0

3 years ago

Read 2 more answers

Use part 1 of the fundamental theorem of calculus to find the derivative of the function. y = cos x (3 + v5)8 dv sin x

dexar [7]

It looks like

$y(x)=\displaystyle\int_{\cos x}^{\sin x}(3+v^5)^8\,\mathrm dv$

(If the limits are in the wrong order, just multiply the result by -1)

Split the integral at an arbitrary value between $\cos x$ and $\sin x$ , and write $y(x)$ as

$y(x)=\displaystyle\left\{\int_{\cos x}^c+\int_c^{\sin x}\right\}(3+v^5)^8\,\mathrm dv$

$y(x)=\displaystyle\int_c^{\sin x}(3+v^5)^8\,\mathrm dv-\int_c^{\cos x}(3+v^5)^8\,\mathrm dv$

Then by the FTC,

$\dfrac{\mathrm dy}{\mathrm dx}=(3+\sin^5x)^8\cdot\dfrac{\mathrm d\sin x}{\mathrm dx}-(3+\cos^5x)^8\cdot\dfrac{\mathrm d\cos x}{\mathrm dx}$

$\dfrac{\mathrm dy}{\mathrm dx}=\cos x(3+\sin^5x)^8+\sin x(3+\cos^5x)^8$

7 0

4 years ago