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3 years ago

Please help!

Mathematics

1 answer:

frosja888 [35]3 years ago

7 0

a. The center of the circle will be the coordinate point of the marked point inside the circle.

center: (3,-5)

The radius is the distance between the center and any point on the circle.

radius: 4 units

b. standard form for circles: (x-h)²+(y-k)²=r² where (h,k) is the center

standard form: (x-3)²+(y+5)²=16

c. Simplify equation in standard form to get general form.

(x-3)²+(y+5)²=16

x²-6x+9+y²+10y+25=16

general form: x²+y²-6x+10y+18=0

Hope u find this useful!

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photoshop1234 [79]

Substitute $u=x^2+4$ and $du=2x\,dx$ . Then the integral transforms to

$\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}$

Apply the power rule.

$\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C$

Now put the result back in terms of $x$ .

$\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}$

3 0

2 years ago

Can I have some help

Brums [2.3K]

$\frac{100}{40} = \frac{z + 69}{z} \\ 100z = 40z + 2760 \\ 60z = 2760 \\ z = 46$

6 0

3 years ago

A circle is described by the equation x2 y2 14x 2y 14 = 0. what are the coordinates for the center of the circle and the length

bearhunter [10]

Answer:

length is (-7,-1) and radius is 6

Step-by-step explanation:

We are given the expression of the equation of a circle that is

x2 + y2 + 14x + 2y + 14 = 0.

Using completing the squares:

x2 + y2 + 14x + 2y + 14 = 0(x+7)^2 + (y+1) ^2 = -14 + 49 + 1(x+7)^2 + (y+1) ^2 = 36 center thus is at (-7,-1) and the radius is equal to square root of 36 equal to 6.

6 0

10 months ago

the store where henry's family. shops sold 10 3 times as many pounds of corn as henry's family bought. the weight of the corn is

saveliy_v [14]

Times it by 3 and see what u get try see if it work

7 0

3 years ago

Given the geometric sequence where a1 = 3 and r = √2 find a9

Zigmanuir [339]

Answer:

$a_9=48$

Step-by-step explanation:

we are given

sequence is geometric

so, we can use nth term formula

$a_n=a_1(r)^{n-1}$

we have

$a_1=3$

$r=\sqrt{2}$

we have to find a9

so, we can plug n=9

we get

$a_9=3(\sqrt{2})^{9-1}$

$a_9=2^4\cdot \:3$

$a_9=48$

8 0

2 years ago