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lapo4ka [179]
3 years ago
13

Quesuon 18 of 40

Mathematics
1 answer:
dimulka [17.4K]3 years ago
7 0

Answer:

answer is a cylinder I hope it will help you please follow

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Write the equation of the circle in general form. Show all of your work
finlep [7]
<h2>1. What are the center and equation of the circle?</h2>

In this exercise we have the general form of the equation of a circle, which is given by:

x^2+y^2+18x+4y+49=0

The ordinary equation of a circle is:

(x-h)^2+(y-k)^2=r^2 \\ \\ Developing \ this \ equation: \\ \\ x^2+y^2-2hk-2ky+h^2+k^2-r^2=0

But this can be written as:

x^2+y^2+Dx+Ey+F=0 \\ \\ D=-2h, \ E=-2k, \ and \ F=h^2+k^2-r^2

From the original equation we know that:

D=18, \ E=4, \ and \ F=49 \\ \\ So: \\ \\ h=-\frac{18}{2}=9, \ k=-\frac{4}{2}=2, \ and \ r=\sqrt{9^2+2^2-49}=6

Finally:

\boxed{CENTER: \ (h,k)=(9,2)} \\ \\ \boxed{RADIUS: \ 6}

<h2>2. Write the equation of the circle in general form.</h2>

We need to write this equation in the form:

x^2+y^2+Dx+Ey+F=0

Since:

D=-2h, \ E=-2k, \ and \ F=h^2+k^2-r^2

Then we need to find the center and radius in order to get D, E and F then. From the graph, it is easy to know that the center is (h,k)=(-3,4) and the radius is 2. Therefore:

D=-2(-3)=6, \ E=-2(4)=-8, \ and \ F=(-3)^2+(4)^2-(2)^2=21

Finally, the general form of the equation is:

\boxed{x^2+y^2+6x-8y+21=0}

<h2>3. Write the equation of the parabola</h2>

A parabola is the set of all points in a plane that are equidistant from  a fixed line called the directrix and a fixed point called the focus that does not lie on the line. Since the directrix is x=2 then this is a horizontal axis. So the standard for of the equation of a parabola that matches this form is:

(y-k)^2=4p(x-h) \ \ p \neq 0

The vertex is (h,k)=(-5,8) so our goal is to find p:

(y-8)^2=4p(x+5)

We can find the absolute value of p as follows:

\left|p\right|=2-(-5)=7

Since the directrix is to the left of the vertex, the parabola opens to the left and hence:

p.

Finally, the equation is:

(y-8)^2=4(-7)(x+5) \\ \\ \boxed{(y-8)^2=-28(x+5)}

8 0
4 years ago
Read 2 more answers
How do you solve this? ASAP please help me. <br> a^2+2.1^2=2.9
ss7ja [257]
Convert decimal to fraction
a^2+(21/10)^2=2.9
Use exponent rules
a^2+441/100=2.9
Move constant to the right
a^2=2.9-441/100
Calculate
a^2=-151/100
This equation has no solution.
3 0
3 years ago
Please Help<br> Find the circumferences of of both circles to the nearest hundredth.
torisob [31]

Step-by-step explanation:

small circle

C= pi D

C = 3.1415(9)

C= 28.3 ft

large circle

C= 2(3.1415)(7)

C = 44 ft

Add 28.3 + 44 = 72.3 ft

7 0
3 years ago
To finish a project, you need to paint the lateral surfaces of a cube with side length 2.5 inches. Find the area that you need t
valentina_108 [34]

Answer:

25 in^2

Step-by-step explanation:

We want to find the lateral surface area of the cube.

The lateral surface area of a cube is given as:

A = 4a^2

where a = length of side of the cube

Therefore, given that the length of the side of the cube is 2.5 inches, the area you need to paint is:

A = 4 * 2.5^2\\A = 25 in^2

6 0
3 years ago
Please help me asap thx a bunch
Nimfa-mama [501]
It would be 53%. The biased survey is survey 2. The other surveys give 50%, 54%, and 54%
5 0
3 years ago
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