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Blizzard [7]
2 years ago
7

Really need help

Mathematics
1 answer:
Ket [755]2 years ago
4 0
3n - 80 = 5n + 8\\3n=5n + 88\\ -2n = 88\\\\ n = -44
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EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi
Valentin [98]

If there is such a scalar function <em>f</em>, then

\dfrac{\partial f}{\partial x}=4y^2

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}

\dfrac{\partial f}{\partial z}=16ye^{4z}

Integrate both sides of the first equation with respect to <em>x</em> :

f(x,y,z)=4xy^2+g(y,z)

Differentiate both sides with respect to <em>y</em> :

\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}

\implies\dfrac{\partial g}{\partial y}=4e^{4z}

Integrate both sides with respect to <em>y</em> :

g(y,z)=4ye^{4z}+h(z)

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

f(x,y,z)=4xy^2+4ye^{4z}+h(z)

\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}

\implies\dfrac{\mathrm dh}{\mathrm dz}=0

Integrate both sides with respect to <em>z</em> :

h(z)=C

So we end up with

\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}

7 0
2 years ago
IT IS DUE AT 11:59PM. PLEASE HELP!!!!
kaheart [24]

Hello from MrBillDoesMath!

Answer:   b = 4, h = 13

Discussion:

For a triangle with base b" and height "h, the area formula is

A=  (1/2)bh.

In our case A = 26, h = 5b-7, so

26 = (1/2) b (5b-7).  Multiply both sides by 2:

26*2 = b(5b-7) =>

52 = b(5b-7)  =>

52 = 5b^2 - 7b =>           (subtract 52 from both sides)

5b^2 - 7b - 52 = 0.   This factors as follows:

(b - 4) (5 b + 13) = 0        (use quadratic formula to find this)

so b = 4 and h = 5b -7 = 5*4 - 7 = 13


Thank you,

MrB


3 0
2 years ago
Read 2 more answers
What's the value of x y z
lions [1.4K]
They are algebraic symbols or known as unknown number. There is no true value for them. The value of algebraic symbols are based on equations

ie. 1+x = 2

First, we isolate the x by canceling the +1 FROM BOTH SIDES(Balance method) by -1 ON BOTH SIDES.

1+x-1 = 2-1

So we are left with the x on the left side, and a single number on the right side. Therefore, our calculation is complete.

x = 1


More complex cases would be

2y-3 = 45

First, we need to isolate the algebraic symbol, which is 2y (yx2) by +3 ON BOTH SIDES

2y-3+3 = 45+3

2y = 48

WE ARE NOT DONE! 2y=48 is still an equation. Therefore, to isolate the y, we need to divide BOTH SIDES by 2

2y/2 = 48/2

y = 24

There is no true or absolute or definite value for algebraic symbols like x,y,z,a,c,t,h,d etc. They are used to represent unknown numbers.


Hope this helped!
8 0
3 years ago
A drugstore charges customers 40 cents to print a photograph. Regina spends $4.80 to print photographs at this store.
Marrrta [24]

Answer:

12 photos

Step-by-step explanation:

x will represent the number of photos

4.80=.4x

divide 4.80 by .4

x= 12

she printed 12 photos

6 0
2 years ago
The interquartile range of a data set is 10 units. What does this represent?
babunello [35]
The central 50 percent of data around average
4 0
3 years ago
Read 2 more answers
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