answer.
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
Sedaia [141]
2 years ago
7

If the radius of the circle x² + y2 - 4x - 6y - k = 0 is4 units, find the value of k.​

Mathematics
1 answer:
meriva2 years ago
5 0

Answer: 3

Step-by-step explanation:

Given

The equation of the circle is x^2+y^2-4x-6y-k=0

Using completing the square method

\Rightarrow x^2+y^2-4x-6y+4-4+9-9-k=0\\\Rightarrow \left( x^2-4x+4\right)+\left( y^2-6y+9\right)-\left( k+4+9\right)=0\\\Rightarrow \left( x-2\right)^2+\left( y-3\right)^2=\left( k+13\right)

on comparing with standard form,  r^2=k+13

Insert the value of r

\Rightarrow 4^2=k+13\\\Rightarrow k=16-13\\\Rightarrow k=3

You might be interested in
Ellie completed an algebraic proof to show that V12 + V108 = 8 - 31.
lorasvet [3.4K]

Answer:

The answer to your question is given below.

Step-by-step explanation:

To know the correct answer to the question, do the following:

√12 + √108

= 12^½ + 108^½

= 4^½ • 3^½ + 36^½ • 3^½

Factorise

3^½ (4^½ + 36^½)

Recall:

4^½ = √4 = 2

36^½ = √36 = 6

Therefore,

3^½ (4^½ + 36^½) = 3^½ (2 + 6)

= 3^½ • 8

8 0
2 years ago
Two vehicles are driving along a straight roadway at a constant speed. At a certain point in time, a car is 1.2 miles away from
Maurinko [17]

Answer:

The expression for the total distance between the car and the landmark in terms of the number of hours spent driving is given as follows;

1.2 = 65 × t

Where t = 1.2/65 = 0.0185 h = 66.46 seconds

Step-by-step explanation:

The parameters given are;

Distance, d between car and landmark = 1.2 miles

Speed of car = 65 miles/hr

Distance between truck and landmark = 0.7 miles

Speed of car = 55 miles/hr

The expression for the total distance between the car and the landmark as a function of time t is given as follows;

Distance, d = Speed, v × Time, t

Therefore, the expression for the total distance between the car and the landmark in terms of the number of hours spent driving is given as follows;

1.2 = 65 × t

Where t = 1.2/65 = 0.0185 h = 66.46 seconds.

7 0
2 years ago
Which expression represents a factorization of 32m+56mp
Lana71 [14]
8m(4+7p). (The greatest common factor is 8.).
3 0
2 years ago
Read 2 more answers
Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to excee
aivan3 [116]

Answer: 8x + 14

Step-by-step explanation:

3x + 2 + 3x + 2 + x + 5 + x + 5 = 2(4x + 7) = 8x + 14

3 0
2 years ago
Based on Pythagorean identities, which equation is true? sine squared theta minus 1 = cosine squared theta secant squared theta
Naddik [55]

Answer:

Cot^2\theta-Csc^2\theta=-1

Step-by-step explanation:

The only Pythagorean identities are:

1. \ Sin^2\theta+Cos^2\theta=1

2. \ 1+Tan^2\theta=Sec^2\theta

3. \ 1+Cot^2\theta=Csc^2\theta

4. \ Sin^2\theta=1-Cos^2\theta\\  \ \ Cos^2\theta=1-Sin^2\theta

 

Therefore,Cot^2\theta-Csc^2\theta=-1 is correct as it's one of the pythagorean identities.

4 0
2 years ago
Read 2 more answers
Other questions:
  • The sum of two consecutive multiples of 10 is 210. find the smaller multiple.
    14·2 answers
  • The table shows the maximum daily temperatures, in degrees Fahrenheit, recorded in a Texas town in May. 84 86 84 88 83 85 90 84
    5·2 answers
  • Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k. k = ______ Graph of two lines. f of x equa
    10·1 answer
  • You have a litre bottle of water and drink 375 millilitres.<br><br> How much is left?
    13·1 answer
  • Find the distance between lines 8x−15y+5=0 and 16x−30y−12=0.
    11·1 answer
  • Which method should be used to solve for x?
    15·1 answer
  • How did the Germanic tribes contribute to the decline of the Western Roman Empire? Write your answer in a paragraph of 125 words
    14·1 answer
  • A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base
    5·1 answer
  • A roller coaster at an amusement park rises to a height of 196 feet above the ground. So far, it has risen 36% of this height. T
    14·2 answers
  • Which of the following represent the distance formula? Select all that apply.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!