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Simora [160]
3 years ago
12

What is the defination of focus of a parabola on a coordinate grid

Mathematics
1 answer:
AleksAgata [21]3 years ago
4 0

Answer:

Focus of a Parabola. A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola and the line is called the directrix. The focus lies on the axis of symmetry of the parabola.

Step-by-step explanation:

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Use Green's Theorem to calculate the circulation of F =2xyi around the rectangle 0≤x≤8, 0≤y≤3, oriented counterclockwise.
Tamiku [17]

Green's theorem says the circulation of \vec F along the rectangle's border C is equal to the integral of the curl of \vec F over the rectangle's interior D.

Given \vec F(x,y)=2xy\,\vec\imath, its curl is the determinant

\det\begin{bmatrix}\frac\partial{\partial x}&\frac\partial{\partial y}\\2xy&0\end{bmatrix}=\dfrac{\partial(0)}{\partial x}-\dfrac{\partial(2xy)}{\partial y}=-2x

So we have

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_D-2x\,\mathrm dx\,\mathrm dy=-2\int_0^3\int_0^8x\,\mathrm dx\,\mathrm dy=\boxed{-192}

6 0
3 years ago
Find the degree measure of each angle in the triangle.
Alex777 [14]

Answer:

  • ∠R = 56°
  • ∠Q = 90°
  • ∠S = 34°

Step-by-step explanation:

The given triangle is a right angled triangle.

So, the angles in the triangle are :

  • 90°
  • (2x + 38)°
  • (5x - 11)°

Solving according to <u>angle sum property</u>,

Sum of all angles in a triangle is 180°

\longrightarrow 90° + (2x + 38)° + (5x - 11)° = 180°

\longrightarrow 117° + 7x = 180°

\longrightarrow 7x = 180° - 117°

\longrightarrow 7x = 63°

\longrightarrow x = 9

Angles =

\longrightarrow 2(9) + 38

\longrightarrow 56°

\longrightarrow 5(9) - 11

\longrightarrow 34°

  • ∠R = 56°
  • ∠Q = 90°
  • ∠S = 34°

The angles are 56°, 90° and 34°.

4 0
3 years ago
A pack or cardinal flower seeds cost $4.00 and a pack of petunia flower seeds cost $2.50. You buy the same number of packs of ea
jeyben [28]

Answer:

6 packs

Step-by-step explanation:

you add $4.00 and $2.50 together, and get 6.50 and then divide 39 bye $6.50

4 0
3 years ago
What do you predict the solution for the system 5x-6y=7 and 6x-7y=8 will be ?<br>​
Alenkinab [10]
System of Linear Equations entered :

[1] 5x - 6y = 7
[2] 6x - 7y = 8
Graphic Representation of the Equations :

-6y + 5x = 7 -7y + 6x = 8

Solve equation [2] for the variable x


[2] 6x = 7y + 8

[2] x = 7y/6 + 4/3
// Plug this in for variable x in equation [1]

[1] 5•(7y/6+4/3) - 6y = 7
[1] - y/6 = 1/3
[1] - y = 2
// Solve equation [1] for the variable y


[1] y = - 2
// By now we know this much :

x = 7y/6+4/3
y = -2
// Use the y value to solve for x

x = (7/6)(-2)+4/3 = -1
8 0
3 years ago
If x-y=9 and xy=2,find the value of (x square + y square)
kati45 [8]

Answer:

x² + y² = 85

Step-by-step explanation:

Using the expansion

(x - y)² = x² + y² - 2xy , then

x² + y² - 2xy = (x - y)² ( add 2xy to both sides )

x² + y² = (x - y)² + 2xy ← substitute given values

          = 9² + 2(2)

          = 81 + 4

          = 85

3 0
2 years ago
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