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Harman [31]
3 years ago
14

Suppose that y varies jointly with w and x and inversely with z and y = 32- when w = 6, x = 20, and z = 3. Write the equation th

at models the relationship
Mathematics
1 answer:
natulia [17]3 years ago
3 0
Y directly proportional to WX  and inversely to Z. 

Y=k(WX)/Z
Where k is the constant of proportionality. 
So, the first thing is to find the value of this constant. 

k = YZ/WX
  = (32×3)/(6×20)
  = 96/120
  = 0.8
The <span>equation that models the relationship will be;
Y = 0.8(WX/Z)</span>
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egoroff_w [7]

Answer:

it is -12

Step-by-step explanation:

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3 years ago
Complete a table with at least 5 points then graph the following quadratic on the coordinate plane. Identify all zeros.y = -2x2
Anna [14]

Answer:

See attached

Step-by-step explanation:

Given function:

  • y = -2x² + 5x + 8

Table and graph are attached

Zeros are included in the graph

<u>Zero's are obtained:</u>

x = 0 ⇒ y = 8

y = 0 ⇒  Solving quadratic equation

  • -2x² + 5x + 8 = 0
  • x = (-5 ± √(25 + 2*4*8))/-4
  • x = 3.608
  • x = -1.108

So zeros are (0, 8), (3.608, 0) and (-1.108, 0)

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3 years ago
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8 0
3 years ago
QUESTION 2<br> 84 is 30% of what number?
Tpy6a [65]

Answer: 280

Step-by-step explanation:

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5 0
3 years ago
Read 2 more answers
Suppose F⃗ (x,y)=(x+3)i⃗ +(6y+3)j⃗ . Use the fundamental theorem of line integrals to calculate the following.
Scorpion4ik [409]

In order to use the fundamental theorem of line integrals, you need to find a scalar potential function - that is, a scalar function <em>f(x, y)</em> for which

grad <em>f(x, y)</em> = <em>F</em><em>(x, y)</em>

This amounts to solving for <em>f</em> such that

∂<em>f</em>/d<em>x</em> = <em>x</em> + 3

∂<em>f</em>/∂<em>y</em> = 6<em>y</em> + 3

Integrating both sides of the first equation with respect to <em>x</em> gives

<em>f</em> = 1/2 <em>x</em> ^2 + 3<em>x</em> + <em>g(y)</em>

Differentiating with respect to <em>y</em> gives

∂<em>f</em>/∂<em>y</em> = d<em>g</em>/d<em>y</em> = 6<em>y</em> + 3

Solving for <em>g</em> gives

<em>g</em> = ∫ (6<em>y</em> + 3) d<em>y</em> = 3<em>y</em> ^2 + 3<em>y</em> + <em>C</em>

and hence

<em>f(x, y)</em> = 1/2 <em>x</em> ^2 + 3<em>x</em> + 3<em>y</em> ^2 + 3<em>y</em> + <em>C</em>

<em />

(a) By the fundamental theorem, the integral of <em>F</em> along any path starting at the point <em>P</em> (1, 0) and ending at <em>Q</em> (3, 3) is

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (3, 3) - <em>f</em> (1, 0) = 99/2 - 7/2 = 46

(b) Now we're talking about a closed path, so the integral is simply 0. We can verify this by checking the integral over the origin-containing paths:

• From the origin to <em>P</em> :

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (1, 0) - <em>f</em> (0, 0) = 7/2 - 0 = 7/2

• From <em>Q</em> back to the origin:

∫ <em>F</em><em>(x, y)</em> • d<em>r</em> = <em>f</em> (0, 0) - <em>f</em> (3, 3) = 0 - 99/2 = -99/2

Then the total integral is 7/2 + 46 - 99/2 = 0, as expected.

6 0
3 years ago
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