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
PLEASE HELP WILL GIVE BRAINLIEST!!!!! ASAP
GEOMETRY picture of problem below!!!!
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Answer:
12
Step-by-step explanation:
X x Y =20 So 12 Then 12 - 12 + 12 = 12
Please help and If you can have a good night
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Answer:
Please help and If you can have a good night
SSSWhich of the following numbers is irrational?
0.13
✓3
-0.3
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14x - 43 = 71 + 8x look for x show work please
Answers
Answer:
x=19
Step-by-step explanation:
14x-43=71+8x problem
14x=114+8x add 43 to both sides
6x=114 subtract 8x from both sides
x=19 divide by 6 to both sides (114/6 =19) x=19
A line passes through the points (-5, 2) and (10,-1). Which is the equation of the line?
o y=-3x+1
O y-zx=3
O y = -5x – 23
O y = 5x + 27
HURRY
Answers
Solve for
50
15
None of the above
Other
Answers
A librarian sorts 450 books at a constant rate. After 4 days, the librarian still has 150 books to sort. How much time does it take to sort the books from start to finish?
Answers
Answer:
6 days
Step-by-step explanation:
hope this helps
A librarian sorts 450 books at a constant rate. After 4 days, the librarian still has 150 books to sort. Then 6 days time does it take to sort the books from start to finish
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The librarian sorted at a constant rate, then they sorted the same amount of books all 4 days.
450-150=300
If they still have 150 books left to sort, then they sorted 300 books over 4 days.
300/4=75
This means that they sorted 75 books per day.
150 divided by 75 is 2
So it will take 2 more days to finish sorting all the books.
So altogether, it will take 6 days to sort all of the books.
Hence 6 days time does it take to sort the books from start to finish
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Anthony is shopping at a discount store. He really wants to buy a jacket that costs $129.99. The jacket is on sale for 25% off. Anthony also has a coupon for 35% off any item in the store. If the sales tax is 7.2% after discounts, what is the final sale price of the jacket?
Take the discounts off one at a time in the order listed, and then add on the tax. Round to the nearest cent.
Price after the first discount:
Price after both discounts:
Price after adding tax:
Answers
Answer:
dats alot
Step-by-step explanation:
What is the missing number in the solution to 958 ÷ 10?
Answers
Answer:
B.)58?
Step-by-step explanation:
Hope I helped..
Answer:
b: 58
Step-by-step explanation:
752 second graders went to
see Hansel and Gretel on
Friday. 25% of the students
went to the bathroom during
the movie. How many kids
went to the bathroom?
Answers
see Hansel and Gretel on
Friday. 25% of the students
went to the bathroom during
the movie. How many kids
went to the bathroom?
Answer:
188
Step-by-step explanation:
752 x 25% = 188
the area of rectangle is x^2-3x+2. Find a possible length and width of the rectangle.
Answers
Answer:
x - 2 and x - 1 can be possible length and width of the rectangle.
Step-by-step explanation:
Area = x² - 3x + 2
◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇
To find possible length and width we can factorize the above expression.
◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇
x² - 3x + 2 ( 2 = -1 × -2 )
x² - x - 2x + 2 ( 3 = -1 + -2 )
x(x - 1) + -2(x - 1)
(x - 2) (x - 1)
◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇
x - 2 and x - 1 can be possible length and width of the rectangle.
_________________________________
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Chocolate sprinkles cost as much per pound as sugar. Find 1 10 the baker's total cost for 100 pounds of chocolate sprinkles. Explain the number of zeros and the placement of the decimal in your answer using a place value chart.
Answers
116=$0.05
hope this helps
The total cost of chocolate sprinkles is $800
What are Place value charts?This is an implementation of the numeral system that shows the value of each digit in a number using their positions
Given that, Chocolate sprinkles cost as much per pound as sugar.
From the complete question, we have the following parameters:
Unit rate = $8.00
Total pounds = 100
Total cost of chocolate sprinkles
So, the total cost of chocolate sprinkles is calculated using the following formula;
Unit = Total / Pounds
This gives
$8.00 = Total / 100
Total = $800
Hence, the total cost of chocolate sprinkles is $800
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19 - (- 41)
plzzzzzz help fast!
Answers
Answer:
60
Step-by-step explanation:
Is because when you have two negative -- signs it became positive
19 + 41 = 60
Answer:
60
Step-by-step explanation:
19 - (- 41) by the power of math, it turns into a positive and the subtraction sign to an addition
19 + (+41)
19+40= 60
What is 2x+8x=6? Please answer accurately???
Answers
Answer:
x = 3/5
Step-by-step explanation:
2x + 8x = 6
10x = 6
x = 3/5
10x=6
6/10=0.6 or 3/5
3/5 or .6
Hurry, I need help and please explain
Answers
Answer:
Question 18
=$3.33
Step-by-step explanation:
i)
26/100 x 4.5
=1.17
(the discount price)
ii)
$4.5-$1.17
=$3.33
Answer:
QUESTION 18
The original price is $4.50
The discount is 26%
They are asking for the sale price which the price after the discount.
So,
The original price means 100% of the cost, like there is no discount at all.
But then we have to apply a 26% discount which means to subtract 26% (the discount) from 100% (the original price)
The new price of the item has to be 74% of the original price.
74% of $4.50 is the same as saying 26% discount.
But what is the number?
To calculate 74% of $4.50, turn 74% into a decimal which is 0.74, then multiply it by 4.50.
0.74 x 4.50 = 3.33
In conclusion, after a 26% discount on an item that is originally $4.50, the new price (sale price) of the item is now $3.33
f(x)5x + 4
Find f(6)
Answers
[tex]\sf{Hello!}[/tex]
[tex]f(x) = 5x + 4[/tex]
[tex]f(6) = ---- [/tex]
[tex]f(6) = 5(6) + 4[/tex]
[tex]f(6) = 30 + 4[/tex]
[tex]f(6) = 34[/tex]
Have a nice day!
Ans: 28
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:
Please help if you are good at math!!
Answers
Answer:
Y intercept= (0,15)
X intercept= ([tex]\frac{3}{4}[/tex],0) , (5,0)
Vertex= -[tex]\frac{b}{2a}[/tex]
Step-by-step explanation:
PLEASE MARK BRAINLIEST
given the equation 9x+3Y=7 which equation is perpendicular to an equation with a y intercept of 12
Answers
S
You have $18 to spend on lip balm and hand sanitizer. The equation 1.5x + 2.5y = 18 represents this situation, where x is tubes of
lip balm and y is bottles of hand sanitizer. How many tubes of lip balm can you buy when you do not buy any bottles of hand
sanitizer?
Answers
Answer:
(1.5×5) + (2.5×4)
Step-by-step explanation:
if 1.5 + 2.5 is 4.0, and you have $18 and you would see how many times 4 can go into 18 (18÷4) which has four times then you have $2 left so you can get another lip balm so x equals 5 and Y equals 4. I hope this helps! :D
y-intercept. y = -3/2x
Answers
Answer:
i hope you find the answer but unfortunaatly im not sure
Step-by-step explanation: thankyou for the points though :)
where the dot needa go ?
Answers
Answer:
where the green circle is where it goes
Completely factor f(x)=2x^4+11x^3+2x^2-15x given that f(-3/2)=0
Due today please help
Answers
Answer:
There isn't a picture
Step-by-step explanation:
£100 will buy lunches for 80 school children for 5 days
work out the cost of buying lunch for one school child for one day
I will only mark brainest and rate a 5 star if you show working out pls and the correct answer and working out
Answers
80 children x 5 days = 400 total lunches.
£100 / 400 lunches = £0.25 per lunch
The cost for one lunch for one student is £0.25
solve the question, thank you
Answers
Answer:
A . m = 11/6
its going to be a
I need help pleaseeee
Answers
Decimal is 0.4
Percent is 40%
If f(x) = 4x - 8, what is the value of f(-3)?
Answers
Answer:
-20
Step-by-step explanation:
f(x)= 4x-8 f(-3)
y= 4(-3) -8
y= -12 -8
y= -20
Which is the correct decimal representation of 13/40
Answers
Answer:
.325
Step-by-step explanation:
Answer:
0.325 is a decimal
Step-by-step explanation:
Addy is buying a new pair of aeropostale jeans for $40. They are on sale for 25% off. what is the sale price of the jeans?
Answers
Answer:
Step-by-step explanation:
40*25%= 10 off
40-10= $30.00 sale price
Perform the indicated operations. 2−26 −48−16 07−6 76 −200 −73 Arrow −48−16 07−6 −200 −73 1−13 −48−16 07−6 38 −200 −73 Arrow 1-13 07−6 38 −73
Answers
Not certain if this question is complete
Answer and Step-by-step explanation:
We perform the operations given, using the rules of subtraction and addition on the number line:
Two negative signs adds up to a negative result, one negative number and positive number may add up to a negative or positive value depending on which is bigger :
2-26= -24( the positive value 2 reduces negative value by 2 and we are left with -24)
-48-16= -64( two negative values add up to a negative value)
07-6= 1( seven is bigger than 6 hence positive result)
We use the above method to solve the given expressions
+76-200-73= -124-73=-192
-48-16=-64
+7-6-200-73=-199-73=-272
+1-13=-12
-48-16=-64
+07-6=1
+38-200-73=-162-73=-235
1-13=-12
07-6=1
38-73= -35
1, -1, 3, 38 & 0, 2, -2, -24