1. The circle C has centre (5,k), where k is a constant. The line y = 2x + 1 is tangent to C at point
A (3,7). Find the equation of C.
Answers
Answer:
[tex](x-5)^2+(y-6)^2=5[/tex]
Step-by-step explanation:
Equation of the Circle
A circle centered at (h,k) and radius r can be written with the equation:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We are given the center (5,k), thus:
[tex](x-5)^2+(y-k)^2=r^2[/tex]
We know the point (3,7) belongs to the circle. This means the distance between the center and this point is the radius.
Given two points (x1,y1) and (x2,y2), the distance between them satisfies:
[tex]d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Calculating the radius, we have:
[tex]r^2=(7-k)^2+(3-5)^2[/tex]
[tex]r^2=(7-k)^2+4\qquad\qquad [1][/tex]
Now we use the fact that the line y=2x+1 and the circle are tangent at (3,7). The radius and the line are perpendicular at that point. Two perpendicular lines with slopes m1 and m2 satisfy the condition:
[tex]m_1\cdot m_2=-1[/tex]
The line y=2x+1 has a slope of m1=2, thus the slope of the segment from (5,k) to (3,7) has a slope of -1/2:
The slope is calculated as:
[tex]\displaystyle \frac{7-k}{3-5}=-\frac{1}{2}[/tex]
Operating:
[tex]\displaystyle \frac{7-k}{-2}=-\frac{1}{2}[/tex]
Multiplying by -2
[tex]\displaystyle 7-k=1[/tex]
Solving:
k=6
From [1] the radius is:
[tex]r^2=(7-6)^2+4[/tex]
[tex]r^2=1+4[/tex]
[tex]r^2=5[/tex]
Finally, substituting into the equation of the circle:
[tex]\mathbf{(x-5)^2+(y-6)^2=5}[/tex]
The graph can be seen in the figure below.
Answer:
Step-by-step explanation:
Related Questions
A news report says that 9% of middle school students are on the track team. There are 600 students in your middle school How many students in your school would you expect to be on the track team? HE Pad SATTE BAR HG West nus SAUNA w 1
Answers
Answer: 54
9% of 600 would be 54.
Which of these statements best describes the relation shown in Item 1?
A- A function that is one-to-one
B-A function that is many-to-one
C-A function that is one-to-many
D-A relation that is not a function
Answers
Answer:
The relation is 'a function that is one-to-many'.
Step-by-step explanation:
From the table, we can see that element 10 i.e. y=10 in the range, corresponds to two elements i.e. x=-5, and x=5 in the domain.
In other words, the given table represents the many-to-one function as an element of the range y = 10 corresponds to more than one element in the domain.
Therefore, the relation is 'a function that is one-to-many'.
The statements that best describe the relation shown in Item 1 is one to many. Option C is correct
Functions are represented as mappings to relate the domain of the given function with the co-domain.
For instance, the function y= x + b has a domain of x and the codomain of "y"
Mappings can be one to one, where each value of the domain is a unique value in the co-domain
Many to one where one element in the domain have more than one element in the codomain
From the given table, we can see that when y = 10, the corresponding x values are 5 and -5. his shows that the codomain value (10) has more than one unique value in the domain.
Hence the statements that best describe the relation shown in Item 1 is a one to many
Learn more here: https://brainly.com/question/22738955
help plz (I give you brainlist)
Answers
Answer:
58.3825
Step-by-step explanation:
Add all 4 numbers together and divided by how many numbers are there (4)and you get your answer
please help me out....
Answers
Answer:
It is the first one, so
7u + 5v
Answer:
7u+5v (A)
Step-by-step explanation:
3u+4u=7u
7v-2v=5v
7u+5v
PLS GIVE BRAINLIEST
Emma borrowed $89.40 from her sister. She determines that she can pay her back the total over six months. Which number reflects the monthly change in her balance?
Answers
Answer:
$14.9
Step-by-step explanation:
Step one:
given data
we are told that Emma borrowed $89.40 from her sister to pay her back in 6 months.
let us solve for the amount she is to pay her sister every month.
amount to be paid per month= 89.40/6
=$14.9
So that every month she pays back her sister $14.9
we don't know her balance but every month there will be a deduction.
Hence the monthly change in her balance is reflected by a deduction of $14.9
3.
Lakpa buys 20 items for Rs 6000. He sells them at Rs 390 each. Calculate:
(a)
His total profit on the deal.
(b)
His percentage of profit on the deal
Answers
Helpp pleaseeee i will make brainliest!
Answers
Answer:
d and a
Step-by-step explanation:
Two angles are said to be supplementary when the sum of the two angles is 180°. When a transversal intersects with two parallel lines eight angles are produced. The eight angles will together form four pairs of corresponding angles:)
Question 1
Solve the equation formed when f (x) = g(x).
f (x) = 3x – 4
g(x) = -2x + 1
X = -4
X = -1
X = 1
X = 4
Answers
Answer:
X= -4
PLEASE MARK BRAINLIEST I ONLY NEED 1 MORE!!!!!!!!!!!!!!!!
f) 16 - p = 12
g) 18 - 2p = 6
h)p2+ 4 = 9
i)p4- 3 = 1
**MUST SHOW YOUR WORK**
Answers
4 - p = 0 plus p
p = 4
g) 18 - 2p = 6 divide by -2
-9 + p = -3 plus 9
p = 6
h) p x 2 + 4 = 9 divided by 2
p + 2 = 4.5 minus 2
p = 2.5
i) p x 4 - 3 = 1 plus 3
p x 4 = 4 divided by 4
p = 1
what is 99,765 divided by 5?
Answers
Answer:
It is 19,953. Your welcome
Answer:
99,765/5= 19953 :)
Step-by-step explanation:
A scientist walking through a forest recorded as integers the heights of 5 trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?
Answers
Answer:
A) 22.2
Step-by-step explanation:
I took AMC 8 and got it right. ^^
3/13% of a quantity is equal to what fraction of the quantity?
Answers
Answer: 3/1300
Sorry I’m late !!
what is the answer?
Answers
a triangle equals 180 degrees, 2 angles are given 47 degrees and the 90 degree angle that makes a right square. 90+47=137. 180-37=43.
PLEASEE HELP I WILL BRAINLISTT Question 2: Given the function defined by y = x^2, which of the following is its average rate of change from x = 2 to x = 10? *
A.5/2
B.2
C.8/3
D.12
Answers
12 is its average rate of change from x = 2 to x = 10.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
Given the function defined by y = x^2
now,
its average rate of change from x = 2 to x = 10,=
=10^2-2^2/10-2
=100-4/8
96/8
=12
Hence, 12 is its average rate of change from x = 2 to x = 10.
To learn more on division click:
brainly.com/question/21416852
#SPJ2
Abdul made $252 for 12 hours of work.At the same rate,how many hours would he have to work to make $105
Answers
Answer:
5 hours
Step-by-step explanation:
252 divided by 12= 21
21x5=105
hehe i need help with the whole quiz basically:I
Find the decimal that is equivalent to:
A. 1.714
B. 0.583
C. 0.0583
D.
Answers
Answer:
a
Step-by-step explanation:
math
Answer:
Don't cheat that's lame
Liam has a bag of b beads. He gives 20 beads to his sister. He then makes 4 necklaces with the same of beads on each necklace using all of the remaining beads. Write an expression that represents the number of beads on each necklace. Show your work.
Answers
Given :
Liam has a bag of b beads.
He gives 20 beads to his sister.
He then makes 4 necklaces with the same of beads on each necklace using all of the remaining beads.
To Find :
Write an expression that represents the number of beads on each necklace.
Solution :
Number of necklace remains after giving 20 beads to his sister is ( b - 20 ).
Number of beads on each necklace using all of the remaining beads is :
[tex]N=\dfrac{b-20}{4}[/tex]
Hence, this is the required solution.
What is the sum of 3(x + 3) and -2(x - 5)?
A. x - 2
B. x - 1
C. x + 8
D. x + 19
Answers
Answer:
The answer is D
Step-by-step explanation:
find the value of the x intercept -x+y=-5
Answers
Answer:
x=-5=(5,0)
Step-by-step explanation:
Answer:
X-intercept is five. The point is (5,0)
Step-by-step explanation:
X-intercept is when the line crosses the x-axis, ie when y is o. Sub zero in for y.
-x+y=-5
-x+0=-5
-x=-5
x=5
hey ok i need help on this question ive been stuck on it for a couple minutes haha
Answers
Answer:
The side s has a length of 4 and side q has a length of 4[tex]\sqrt{3}[/tex] ⇒ F
Step-by-step explanation:
In the 30°-60°-90° triangle, there is a ratio between its sides
side opp (30°) : side opp (60°) : hypotenuse
1 : [tex]\sqrt{3}[/tex] : 2
In the given triangle
∵ The side opposite to 30° is s
∵ The side opposite to 60° is q
∵ The hypotenuse is 8
→ Use the ratio above to find the lengths of s and q
side opp (30°) : side opp (60°) : hypotenuse
1 : [tex]\sqrt{3}[/tex] : 2
s : q : 8
→ By using cross multiplication
∵ s × 2 = 1 × 8
∴ 2s = 8
→ Divide both sides by 2
∴ s = 4
∴ The length of s is 4
∵ q × 2 = [tex]\sqrt{3}[/tex] × 8
∴ 2q = 8[tex]\sqrt{3}[/tex]
→ Divide both sides by 2
∴ q = 4[tex]\sqrt{3}[/tex]
∴ The length of q is 4[tex]\sqrt{3}[/tex]
What is the sum of 6 and y
Answers
Answer:
6+y
Step-by-step explanation:
6+y is the ans as the question has asked to sum of them but it has not given any other clues
Answer:
i got 6y
Step-by-step explanation:
pleaseee helpp i have 20 mins for a unit testt
Answers
Answer: Its c
Step-by-step explanation:
I think
One of the slowest fish is the blenny
fish. The function y = 0.5x describes
how many miles y the fish swims in
x hours. Graph the function. Use the
graph to estimate the number of miles
the fish swims in 3.5 hours.
.
Answers
Answer:
It swims 1.75 miles in 3.5 hours. X stands for hours so x=3.5. Y stands for miles so y=1.75.
Step-by-step explanation:
your equation is y=0.5x
we know x=3.5
so y= 0.5(3.5)
solve and you get y= 1.75
so in (x,y) intercept format (3.5,1.75) and you can make a graph and label your x intercepts hours and your y intercepts miles traveled.
The number of miles the fish swims in 3.5 hours is 1.75 miles.
The equation of a straight line is:
y = mx + b;
y, x are variables, m is the slope of the line and b is the y intercept.
Given the function: y = 0.5x;
where y represent the miles the fish swims in x hours.
The graph of the function is plotted using geogebra online graphing tool.
From the graph, the number of miles the fish swims in 3.5 hours is 1.75 miles.
Find out more at: https://brainly.com/question/13911928
The figure is cut into 6 equal pieces. shade 2/3 of the figure
Answers
Answer:
you need to shade 4/6
Step-by-step explanation:
find three consecutive numbers whose sum is 84
Answers
Answer:
three consecutive numbers that add up to 84 are 27,28 and 29
Step-by-step explanation:
27+28=55
55+29-=84
How many halves are in 8/10
Answers
Answer:
1 half with 3/10 left over.
Step-by-step explanation:
1/2 is also 5/10, so that means that there is one 5/10 is 8/10, with 3/10 left over
DUE 10:00 PM HELP ASAP. When Sarah left your house this morning her cell phone was 80% charged and then it started to lose 8% charge for each hour there after write an equation for B in terms of tea representing the charge remaining in series battery as percentage t hours after Sara left her house
Answers
Answer:
The answer would be B=-8>80
Step-by-step explanation:
Which equation below has no solution?
A) 3(6x + 8) = 24 + 18x
B) 8(x + 4) = 12x - 6
C) 5x - 4 = 2(4x + 8) - 3x
Answers
Answer:
B
Step-by-step explanation:
The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle? 27° 36° 54° 72°
Answers
Answer:72
Step-by-step explanation:
Answer:
The answer is D) 72
Step-by-step explanation:
I got the questions right on edge 2020. good luck everyone. please rate the question.
What do you call the pairs of roots of quadratic
equation with complex solutions?
Math
Answers
Imaginary numbers contain complex solutions (a +- bi)