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snow_lady [41]
3 years ago
9

Half a number increased by 15 is equal to the sum of 5 and the product of 3 and the number.

Mathematics
1 answer:
son4ous [18]3 years ago
3 0

Answer:

(x/2) + 15 = 5 + 3x

Step-by-step explanation:

Follow the steps in the equation. X is your number. First you halve it, then you add 15. Next, set it equal to the other side. The second side is 5 + (because it is the sum) and 3x (the product of 3 and x means multiply them)

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Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)
babunello [35]

\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k

We want to find f(x,y,z) such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=x^2+y

\dfrac{\partial f}{\partial y}=y^2+x

\dfrac{\partial f}{\partial z}=ze^z

Integrating both sides of the latter equation with respect to z tells us

f(x,y,z)=e^z(z-1)+g(x,y)

and differentiating with respect to x gives

x^2+y=\dfrac{\partial g}{\partial x}

Integrating both sides with respect to x gives

g(x,y)=\dfrac{x^3}3+xy+h(y)

Then

f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)

and differentiating both sides with respect to y gives

y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C

So the scalar potential function is

\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}

By the fundamental theorem of calculus, the work done by \vec F along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it L) in part (a) is

\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}

and \vec F does the same amount of work over both of the other paths.

In part (b), I don't know what is meant by "df/dt for F"...

In part (c), you're asked to find the work over the 2 parts (call them L_1 and L_2) of the given path. Using the fundamental theorem makes this trivial:

\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3

\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4

8 0
3 years ago
2x^3 + 3x^2 -11x -6 divided by x - 2
Gnesinka [82]

p(x)= x-2

g(x)= 2x^3 + 3x^2 - 11x - 6

first we have to find the zero of the polynomial of x-2

p(x)= x-2 = 0

         x=2

therefore,

p(x)= 2x^3 + 3x^2 - 11x - 6

p(2)= 2*2^3 + 3*2^2 - 11*2 - 6

      = 2*8 + 3*4 - 11*2 - 6

      = 16 + 12 - 22 - 6

      = 28-28

     = 0

Hope it helped u, ^_^.

3 0
3 years ago
11. find the value of x in the kite below.<br> E<br> (6x + 6)<br> F<br> Р<br> G
cluponka [151]

14.

Step-by-step explanation:

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6x=90-6

6x=84

x= 84/6

x=14.

8 0
3 years ago
A+(−1.3)=−4.5 i dont know the answer i need help plsss
DochEvi [55]
A+(-1.3)=-4.5
Add 1.3 to both sides of the equation
a=-3.2
5 0
2 years ago
each letter of the alphabet is written on a piece of paper and put it in a hat. If a piece of paper is chosen at random, what is
iris [78.8K]

Answer:

3/13 or 0.230769231

Step-by-step explanation:

How many vowels are in the alphabet? 6

How many letters are in the alphabet? 26

What is 6/26? 3/13 or 0.230769231

HOPE THIS WAS HELPFUL!!!

6 0
3 years ago
Read 2 more answers
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