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olga55 [171]
3 years ago
7

C++ the length of a rectangle is stored in a double variable named length, the width in one named width. write an expression who

se value is the length of the diagonal of the rectangle.
Mathematics
1 answer:
Blizzard [7]3 years ago
7 0
Sqrt(pow(width,2) + pow(length ,2)
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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
A book is in the shape of a right rectangular prism. It measures 8 1/2 inches tall, 7 inches wide, and 2 1/2 inches thick. What
Alenkasestr [34]
Hello!

The formula for volume of a rectangular prism is:

V = lwh

Let's convert the dimensions to decimals, and then use the formula to solve.

8 1/2 = 8.5 as a decimal.

7 = 7 as a decimal.

2 1/2 = 2.5 as a decimal.

Multiply:

V = 8.5 × 7 × 2.5

V = 59.5 × 2.5

V = 148.75

148.75 = 148 3/4 as a fraction because if you convert 3/4 to a decimal by dividing the numerator by the denominator, it equals 0.75.

ANSWER:

The volume of the book is 148 3/4 inches cubed.

6 0
2 years ago
Read 2 more answers
4 2/3 divided by 4 1/5
Galina-37 [17]
(4 2/3) / (4 1/5) = 1.111
8 0
3 years ago
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The system of equations is graphed on the coordinate plane. y=−12x−1y=14x−4 A graph with a blue line passing through coordinates
Anika [276]
We have that

 case 1)
<span>system of equations is
</span><span>y=−12x−1
y=14x−4

using a graph tool
see the attached figure

the solution of the system  is the point (0.115,-2.385)

case 2)
</span>system of equations is
<span>blue line passing through coordinates A (0, -4) and B (4, -3)
</span><span>red line passing through coordinates   C(0, -1) and  D (4, -3)

</span>using a graph tool
see the attached figure

the solution of the system  is the point (4,-3)<span>

</span>

8 0
3 years ago
Please help! WILL GIVE THE BRAINLIEST!!!
Mariana [72]
Hey there,

Your question states: <span>The coordinates of A, B, and C in the diagram are A(p, 4), B(6, 1), and C(9, q). Which equation correctly relates p and q? 

Your correct answer would be </span><span>D. p − q = 7 BECAUSE . . .we would have to back the number up because we would need to basically subtract </span>P-Q which would give you 7. So D.) would be your answer.

Hope this helps.

~Jurgen
7 0
3 years ago
Read 2 more answers
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