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2 years ago

Point P(1,7) is located on circle C. The center of circle C is (−2,3). What is the radius of the circle?

Mathematics

1 answer:

Mumz [18]2 years ago

4 0

Answer: 5

Step-by-step explanation:

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Evaluate the line integral, where C is the given curve. (x + 6y) dx + x2 dy, C C consists of line segments from (0, 0) to (6, 1)

Dima020 [189]

Split $C$ into two component segments, $C_1$ and $C_2$ , parameterized by

$\mathbf r_1(t)=(1-t)(0,0)+t(6,1)=(6t,t)$

$\mathbf r_2(t)=(1-t)(6,1)+t(7,0)=(6+t,1-t)$

respectively, with $0\le t\le1$ , where $\mathbf r_i(t)=(x(t),y(t))$ .

We have

$\mathrm d\mathbf r_1=(6,1)\,\mathrm dt$

$\mathrm d\mathbf r_2=(1,-1)\,\mathrm dt$

where $\mathrm d\mathbf r_i=\left(\dfrac{\mathrm dx}{\mathrm dt},\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt$

so the line integral becomes

$\displaystyle\int_C(x+6y)\,\mathrm dx+x^2\,\mathrm dy=\left\{\int_{C_1}+\int_{C_2}\right\}(x+6y,x^2)\cdot(\mathrm dx,\mathrm dy)$

$=\displaystyle\int_0^1(6t+6t,(6t)^2)\cdot(6,1)\,\mathrm dt+\int_0^1((6+t)+6(1-t),(6+t)^2)\cdot(1,-1)\,\mathrm dt$

$=\displaystyle\int_0^1(35t^2+55t-24)\,\mathrm dt=\frac{91}6$

6 0

3 years ago

Solve the equation y=2x^2-x-6 using the quadratic formula show the steps to solving

saul85 [17]

Answer:

$x1 = 2 \\ x2 = - \frac{3}{2}$

Step-by-step explanation:

$x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{1 + - \sqrt{ {( - 1)}^{2} - 4(2)( - 6) } }{2(2)} \\ x = \frac{1 + - \sqrt{1 + 48} }{4} \\ x = \frac{1 + - \sqrt{49} }{4} \\ x = \frac{1 + - 7}{4} \\ \\ x1 = \frac{1 + 7}{4} = \frac{8}{4} = 2 \\ x2 = \frac{1 - 7}{4} = - \frac{6 }{4} = - \frac{3}{2}$

7 0

3 years ago

3x -4y -2 +2x+6 simplify each expression

jasenka [17]

Answer:

5x-4y+4

Step-by-step explanation:

3x-4y-2+2x+6

Gathers like terms together:

3x+2x= 5x

-4y= -4y

-2+6= 4

Put it together:

5x-4y+4

8 0

3 years ago

13. Writing in Math Write three different improper fractions that equal 4 2/3

nikklg [1K]

14/3 28/6 42/9 all these fractions are improper and equivalent to 4 2/3 when simplified

6 0

3 years ago

Games Made x

Fudgin [204]

The type of function that best models the data in the table is the quadratic function

<h3>How to determine the function type?</h3>

The table of values is represented as:

x: 4 6 8 10 12

y : 118 142 150 142 118

From the above table, we can see that:

The y values increase from 118 to 150
The y values then decrease to 118
The x values increase

This is only possible in a quadratic function

Hence, the type of function that best models the data in the table is the quadratic function

Read more about quadratic function at:

brainly.com/question/1214333

#SPJ1

5 0

2 years ago