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3 years ago

What is the slope of a horizontal line? 0 undefined 1 -1

Mathematics

2 answers:

LenaWriter [7]3 years ago

3 0

the slope of a horizontal line is zero

umka21 [38]3 years ago

3 0

Answer:

Zero

Step-by-step explanation:

When a line is horizontal or you can say parallel to the x-axis, its slope is zero.

The reason being that there is no change in the value of y because the value of x is constant at each point of the line.

Slope = (change in y) / (change in x)

On the contrary, the slope of the line which is vertical or parallel to the y-axis has an undefined slope.

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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 f(x, y) for which

grad f(x, y) = F(x, y)

This amounts to solving for f such that

∂f/dx = x + 3

∂f/∂y = 6y + 3

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

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

Differentiating with respect to y gives

∂f/∂y = dg/dy = 6y + 3

Solving for g gives

g = ∫ (6y + 3) dy = 3y ^2 + 3y + C

and hence

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

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

∫ F(x, y) • dr = f (3, 3) - f (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 P :

∫ F(x, y) • dr = f (1, 0) - f (0, 0) = 7/2 - 0 = 7/2

• From Q back to the origin:

∫ F(x, y) • dr = f (0, 0) - f (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

In a certain year, there were 92 female officials in Congress, which is comprised of the House of Representatives and the Senate

crimeas [40]

Answer:

There are 78 female members of the House of Representatives and 14 female members of the Senate.

Step-by-step explanation:

Let h equal the amount of female members of the House of Representatives and s equal the amount of female members in the Senate.

Since the amount of female officials in Congress is 92, and is made up of the House of Representatives and the Senate, we can represent this as the equation h+s=92

Since there are 64 more female members in the House of Representatives than female Senators, the senators would need 64 more female members to have the same amount as the House of Representatives. We can represent this as h=s+64.

Substituting, we get s+64+s=92, which simplifies to 2s+64=92. Subtracting 64 from both sides, we get 2s=28, which equals to s=14. There are 14 female senators. Substituting back into h+s=92, 14+s=92, and s=78. Therefore, there are 78 female members of the House of Representatives and 14 female members of the Senate.

8 0

2 years ago

HELP! WILL GIVE BRAINLIEST

likoan [24]

Answer: area 24 perimeter/circumstance 32 meters

Step-by-step explanation:

3 0

3 years ago

Im Desparate! So Very Desparate xD Please Answer All!

notsponge [240]

2 - b.
3 - a.

I'm not sure about 4. Hope this helps!

4 0

2 years ago

If f(x)=x^1/2 and g(x)=2x^3-x^1/2, find f(x)-g(x)... HELP ITS URGENT

bija089 [108]

F(x) - g(x) =
x^1/2 - (2x^3 - x^1/2)=
x^1/2 - 2x^3 + x^1/2=
2x^1/2 - 2x^3

7 0

3 years ago