1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Svet_ta [14]
3 years ago
12

Given the circle with the equation (x + 1)2 + y2 = 36, determine the location of each point with respect to the graph of the cir

cle. In your final answer, state whether each point is on the interior, exterior, or circumference of the circle. Include your calculations as proof of each point’s location. A. (-1, 1) B. (-1, 6) C. (4, -8)
Mathematics
2 answers:
weqwewe [10]3 years ago
4 0

Answer:

Step-by-step explanation:

First, we need to plug these points into the equation given to find our inequality. If the answer is lower then the number the equation equals (36) it's on the interior, if it's equal, it's on the circumference, and if it's greater its on the exterior.

A. (-1 + 1)^2 + 1^2 =? 36

0^2 + 1 =? 36

0 + 1 =? 36

We get the value

1 < 36

This point is on the interior of the circle

B. (-1 + 1)^2 + 6^2 =? 36

0^2 + 36 =?36

0 + 36 =? 36

we get the value

36 = 36

This point is on the circumference of the circle

C. (4 + 1)^2 + -8^2 =? 36

5^2 + 64 =? 36

25 + 64 =? 36

we get the value

89 > 36

this point is on the exterior of the circle.

kati45 [8]3 years ago
3 0
\bf \textit{equation of a circle}\\\\ &#10;(x- h)^2+(y- k)^2= r^2&#10;\qquad &#10;center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad &#10;radius=\stackrel{}{ r}\\\\&#10;-------------------------------\\\\&#10;(x+1)^2+y^2=36\implies [x-(\stackrel{h}{-1})]^2+[y-\stackrel{k}{0}]^2=\stackrel{r}{6^2}~~~~&#10;\begin{cases}&#10;\stackrel{center}{(-1,0)}\\&#10;\stackrel{radius}{6}&#10;\end{cases}

so, that's the equation of the circle, and that's its center, any point "ON" the circle, namely on its circumference, will have a distance to the center of 6 units, since that's the radius.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad &#10;%  distance value&#10;d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}&#10;\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(1-0)^2}\implies d=\sqrt{(-1+1)^2+1^2}&#10;\\\\\\&#10;d=\sqrt{0+1}\implies d=1

well, the distance from the center to A is 1, namely is "inside the circle".

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(6-0)^2}\implies d=\sqrt{(-1+1)^2+6^2}&#10;\\\\\\&#10;d=\sqrt{0+36}\implies d=6

notice, the distance to B is exactly 6, and you know what that means.

\bf ~~~~~~~~~~~~\textit{distance between 2 points}&#10;\\\\&#10;(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad &#10;C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})&#10;\\\\\\&#10;\stackrel{distance}{d}=\sqrt{[4-(-1)]^2+[-8-0]^2}\implies d=\sqrt{(4+1)^2+(-8)^2}&#10;\\\\\\&#10;d=\sqrt{25+64}\implies d=\sqrt{89}\implies d\approx 9.43398

notice, C is farther than the radius 6, meaning is outside the circle, hiking about on the plane.
You might be interested in
Im not sure how to do this or what function to use SIN, COS, or TAN but if you could walk me through it that would be so so so a
Elanso [62]

Answer: 3.8

Step-by-step explanation:first, you need to figure out what side you’re looking for. Side AC is opposite of the angle you’re given. They also give you length of side AB which is 4. That is the hypotenuse (side directly across from right angle). So, you have the hypotenuse, and need the find the opposite side measure. Which option uses opposite and hypotenuse? That’s Sin. So, you would do: sin70 = ? / 4.

sin (of given angle)= opposite / hypotenuse.

Sin (70 degrees) = ? / 4

Then you solve for “?”

Type sin70 into your calculator, then multiply both sides by 4 to get “?” by itself. You should get 3.758770483, which rounds to 3.8

5 0
2 years ago
Like in Utah, license plates in the great state of Wisconsin consist of 2 letter and 4 digits. However, only digits can repeat a
sveta [45]

Answer:

The correct option is B) 26x26x10^4.

Step-by-step explanation:

Consider the provided information.

It is given that the Wisconsin consist of 2 letter and 4 digits. And two letters always precede the digits.

There are 26 Alphabet so that means for alphabets we have 26 choices also we for digits we have 10 choices (0 to 9).

However, only digits can repeat. For first letter we have 26 choices for second we have only 25 choices left, similarly for digits we have 10 choices but repetition is allow so we can choose same number.  the number of possible plates are:

26×25×10×10×10×10

Which also can be written as:

26 \times 25 \times 10^{4}

Hence, the correct option is B) 26x26x10^4.

8 0
3 years ago
If Mark got 6 questions out of 40 incorrect, what percent of the questions did he get correct?
romanna [79]
6/40 6.0/40.0 because it’s decimal and percentage wiser
6 0
3 years ago
How to solve word problems wit fractions
AURORKA [14]

Your answer is 1/5 Hope this helps :D

7 0
3 years ago
To the nearest millimeter, a cell phone is 105 mm long and 66 mm wide. What is the ratio of the width to the length?
makvit [3.9K]

Answer:

22:35

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 66 and 105 is 3

Divide both the numerator and denominator by the GCD

66 ÷ 3/105 ÷ 3

Reduced fraction:

22/35

therefore the ratio will be 22:35

3 0
3 years ago
Other questions:
  • Cgc,gvmbmbbvvhvvhhjjjbu
    12·2 answers
  • A(1) = 20<br> (a(n) = a(n − 1) – 17<br> Find the 3rd term in the sequence.
    7·1 answer
  • I got a black bag with 3 green apples, 5 yellow apples, 7 green pears, and 2 yellow pears. Filecio randomly grabs the fruits one
    8·1 answer
  • 64 is 128% of what number?
    12·2 answers
  • Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in ord
    7·2 answers
  • 8 crabs are on the beach.<br> 3 more crabs come.<br> 7 more crabs come.<br> How many crabs in all?
    12·2 answers
  • The area of a right triangle is 39.6cm2 , and the base of the triangle is 12in . Which of the following values is the height of
    6·1 answer
  • Solve<br> 4/√7-1 +2/√7+1
    15·2 answers
  • brantty works 21.5 hours every week . if she earns 8.50 per hour how much does she earn in one week round part a to the nearest
    7·1 answer
  • Which triangle are congruent by AAS?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!