what is the value of c such that the line y=2x+3 is tangent to the parabola y=cx^2

Answers

Answer 1

The value of [tex]c[/tex] such that the line [tex]y = 2\cdot x + 3[/tex] is tangent to the parabola [tex]y = c\cdot x^{2}[/tex] is [tex]-\frac{1}{3}[/tex].

If [tex]y = 2\cdot x + 3[/tex] is a line tangent to the parabola [tex]y = c\cdot x^{2}[/tex], then we must observe the following condition, that is, the slope of the line is equal to the first derivative of the parabola:

[tex]2\cdot c \cdot x = 2[/tex] (1)

Then, we have the following system of equations:

[tex]y = 2\cdot x + 3[/tex] (1)

[tex]y = c\cdot x^{2}[/tex] (2)

[tex]c\cdot x = 1[/tex] (3)

Whose solution is shown below:

By (3):

[tex]c =\frac{1}{x}[/tex]

(3) in (2):

[tex]y = x[/tex] (4)

(4) in (1):

[tex]y = -3[/tex]

[tex]x = -3[/tex]

[tex]c = -\frac{1}{3}[/tex]

The value of [tex]c[/tex] such that the line [tex]y = 2\cdot x + 3[/tex] is tangent to the parabola [tex]y = c\cdot x^{2}[/tex] is [tex]-\frac{1}{3}[/tex].

We kindly invite to check this question on tangent lines: https://brainly.com/question/13424370


Related Questions

5x + 8 + 3x + 4 = -40 +4

Answers

Answer:

x=-6

Step-by-step explanation:

Answer:

[tex]x=-6[/tex]

Step-by-step explanation:

[tex]5x+8+3x+4=-40+4[/tex]

⇒ Subtract 4 from both sides:

[tex]5x+8+3x+4-4=-40+4-4[/tex]

[tex]5x+8+3x=-40[/tex]

⇒ Combine like terms:

[tex]5x+3x=8x[/tex]

[tex]8x+8=-40[/tex]

⇒ Subtract 8 from both sides:

[tex]8x+8-8=-40-8[/tex]

[tex]8x=-48[/tex]

⇒ Divide both sides by 8:

[tex]\frac{8x}{8}=\frac{-48}{8}[/tex]

[tex]x=-6[/tex]

________________________

What is the y-intercept of the line shown below? Enter your answer as a coordinate pair.

Answers

Answer:

The x intercept is (-2,0)

the y intercept is (0,4)

Can someone help me with 8-grade math homework, please

Answers

Answer:

so y=7.25x+9.99 where y is the total money they spend, and the x is the total number of they want to bought jersey which is 20,

So here it's equation:

y=7.25(20)+9.99

y= 145+9.99

y=154.99, therefore the total is 154.99

and the second one is find and explain the mistake

the y values is the mistake when you equate the number of x to the equation given so the true answer of that table if you use the equation is:

X Y

2 0

3 -2

4 -4

5 -6

Write the equation of the line in slope-intercept form that passes through the given points.
(-1, 8) and (5,-2)

Answers

Answer:

y = -5/3x + 19/3

Step-by-step explanation:

y2 - y1 / x2 - x1

-2 - 8 / 5 - (-1)

-10/6

= -5/3

y = -5/3x + b

8 = -5/3(-1) + b

8 = 5/3 + b

19/3

20 < 5 (F – 32) < -15
solve the compound inequalities

Answers

Answer:

no solution

Step-by-step explanation:

20 < 5(F - 32) < -15

-15 can never be greater than 20, thus the answer is no solution

Mr. Reyes broke his bicycle. He asked Renato to fix it. Renato charged 350 php for the
new parts of the bicycle and 150 php per hour for labor to repair the bicycle. If Renato
spent 4 hours repairing Mr. Reyes’ bike, what is the total amount he needs to pay?

a. What is asked?
b. What are the given numbers?
c. What are the operations needed?
d. Write the number sentence.
e. Solve. Show your solution.​

Answers

Answer:

950 php

Step-by-step explanation:

a. What is asked?

Find the total amount for repair of the bike.

b. What are the given numbers?

350 php for parts and 150 php per hour for labor. Total 4 hours repair duration.

c. What are the operations needed?

Multiplication and addition

d. Write the number sentence.

Find the labor charge by multiplying the rate by the number of hours and add to the cost of parts.  

e. Solve. Show your solution.​

350 + 150*4 = 350 + 600= 950 php

A group of students left school at 8:00 am on a field trip to a science museum 90 miles away. Which best the average speed of the bus if they arrived at 10:00

Answers

Answer:

45 mph

Step-by-step explanation:

90 / 2 = 45 mph

HELP ME ASAP!!!!!!

See pic attached

Answers

Step-by-step explanation:

a ) 9 × 2 = 18 18 + 3 = 21

o/p = 21

b) 17 - 3 = 14 14/2 = 7

i/p = 7

hope this answer helps you dear!

There are 35 boys in 6th grade. The number of girls in 6th grade is 40. Emma says that means the ratio of the number of boys in 6th grade to the number of girls in 6th grade is 3:4. Is Emma correct? If not, what is the correct answer?theses are the answers you chose froma: correct ratiob:7:8c: 5;8d: 8:7

Answers

Answer:

No, Emma is not correct.

Step-by-step explanation:

because if we put 35 and 42 in rational form we can write it to its simple form by dividing it

35 / 7 = 5

42 / 7 = 6

after dividing we get the answer as 5:6.

Hope it helps ☺️

1/5d=-3 help I'm confused

Answers

Answer:

d=-15

Step-by-step explanation:

1/5d= -3

d= -3×5

d= -15

Hope this helps you. Have a nice day. Please mark as brainliest. It helps a lot. ^_^

express 23/15-7/10 as a percentage​

Answers

Answer:

83.3%

Step-by-step explanation:

PLZZZ HELPPPP ILL MARK BRAINLIEST TO FIRST AND CORRECT ANSWER THAT HAS WORK AND A THX TO SECOND AND CORRECT ANSWER.

Answers

Answer:

well I think it is none of these because the square root would be 9^2

Step-by-step explanation:

Answer:

9^2

Step-by-step explanation

if the are is 81 then you have to think for th numbers like if the are was 20

it would be 5x4=20cm sorry i can't type in anything special  ti won'y let me

b^(3) * b^(4) write without exponents

Answers

Answer:

(b×b×b)×(b×b×b×b)

Step-by-step explanation:

Writing the equation out is the only way to remove the exponents.

The answer would be (b*b*b) * (b*b*b*b)

please help me someone

Answers

That’s the answer
Just like this

It costs 4.99 for 2lbs of bacon and 6.99 for 5lbs of bacon.which is a better buy?

Answers

The 5lbs. $6.99 divided by 5 is 1.40 aprox. and $4.99 divided by 2 is 2.40. for one pound.

Answer:

The 5lbs is a better buy

Step-by-step explanation:

Find the price per pound:

4.99/2= $2.49

6.99/5= $1.39

3) if the cost of 1 pen is Rs.10, find the cost of 5 pen​

Answers

Answer: 5 pens cost Rs.50

Explanation: Since 1 pen costs Rs.10, you will need to multiply the number of pens (1) and the cost of that number of pens (Rs.10) by the amount of pens you must find the cost for (5). Since 10 times 5 is 50, that means that 50 is the cost of 5 pens.

I hope this helps!

factor [tex]x^{2} + 2x[/tex]

Answers

Answer:

the answer is x(x+2)

what the slope of a line

Answers

Answer:

The slope of a line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.

Hope it helps.

4) Ashley's Bikes rents bikes for S13 plus $5

per hour. Mary paid $38 to rent a bike.

For how many

hours did she rent the bike?

Answers

Answer:

6 hours.

Step-by-step explanation:

1st hour - 13

2nd hour - add 5 = 18

3rd hour - 23

4th hour - 28

5th hour - 33

6th hour - 38 (which is the end total)

Can someone pls help me out

Answers

>> Answer

___________

[tex] \: [/tex]

[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]

This is Question no picture, soo iam work in question before^^

Step by step :

x² = 12² + 10²

x² = 144 + 100

x² = 244

x = 15,6m

solve for r to find the missing term in geometric sequence

hi can someone please answer my question. thank you ❤️​

Answers

Step-by-step explanation:

given :

120, 60, 30, _, _, _

find r!

solution :

r = 60/120 = ½.

=> 120,60,30, 15, 15/2 , 15/4 , ...

Step-by-step explanation:

Calcute the ratio :

r = Un/Un-1

r = 60/120

r = ½

Calculate 4th term :

Un = ar^n-1

U4 = 120 × ½^4-1

U4 = 120 × ½³

U4 = 120 × 0.125

U4 = 15

Calculate 5th term :

Un = ar^n-1

U5 = 120 × ½^5-1

U5 = 120 × ½⁴

U5 = 120 × 0.0625

U5 = 7.5

Calculate 6th term :

Un = ar^n-1

U6 = 120 × ½^6-1

U6 = 120 × ½⁵

U6 = 120 × 0.03125

U6 = 3.75

80°
50°
Зc +2°
C=.

Can i get a step by step or a video on this?

Answers

Answer:

C= 19.333333(Its infinite)

Solve for x.

9(x + 1) = 25 + x

x = 2
x = 3
x = 4
x = 5

Answers

Answer:

x = 2

Give me the brainlest, please?

Step-by-step explanation:

Answer:  x=2

Step-by-step explanation:

9(x+1)=25+x   (Distribute the 9)

9x+9=25+x     (Work both sides to isolate the variable)

-9        -9

9x=16+x

-x       -x

8x=16

/8   /8

x=2

Caroline wears a suit to work everyday. Caroline has 6 suits, 3 overcoats, and 4 pairs of shoes. How many different outfits can Caroline create? *

Answers

Caroline needs 1 suit, 1 overcoat, and 1 pair of shoes for an outfit. To find the number of different outfits, we can multiply the number of options for each group. 6 x 3 x 4 = 72 outfit options.

We can also think about it logically. For each suit, they have 3 different coats to wear. For each suit and coat combination, they have 4 different pairs of shoes to wear. So for each suit, there are 3 x 4 = 12 coat/shoe combinations. Since there are 6 different suits, they have 6 x 12 = 72 options.

please answer, it’s a test

Answers

Answer:

A

Step-by-step explanation:

The inverse of 2x would be 1/2 x and the inverse of +6 would be -6.

What can divided 62 and 30

Answers

62- 1,2, 31,62
30-1,2,5,6,10,15,30

A number that multiplies a variable in a term is a_____.

A. factor
B. coefficient
C. term
D. variable

Answers

Answer:

coefficient

Step-by-step explanation:

Answer: Answer:

Step-by-step explanation:

Help me pls and thx and have a nice day

Answers

Answer: the answer should be the last one

Step-by-step explanation:

8+7+5+7+9



Mathematics middle school


Answers

Answer:

36

Step-by-step explanation:

hope this helps

8+7+5+7+9

15+5+7+9

20+7+9

27+9

36

= 8+7+5+7+9

= 15+5+7+9

= 20+7+9

= 27+9

= 36

The answer is 36.

HELPPPP PLEASEEEE!!!!

Answers

Answer:

B

Step-by-step explanation:

C I think sorry if it may be wrong ☹️
Other Questions
Which of the following elements is an Alkali Metal?A) LithiumB) NeonFluorineD Beryllium (sin+cos)^2(sincos)^2 Construct the bisector of the following figures A washer and a dryer cost $885 combined. The washer costs $65 less than the dryer. What is the cost of the dryer? 10 active volcanoes across the world and their tectonic plate or boundary it's located solve the inequality Questions about KeralaWhat is the capital of Kerala?State flower of Kerala?state bird of Kerala?Districts in keralafood culture of Keralano. of rivers in Keraladistrict with the longest coastline in Kerala A line with a slope of 7 passes through the points (7,3) and (8,f). What is the value of f? how many beats will a half note get ina 2/4 time signature WHO ANSWERS I WILL MARK BRAINLIESTJarvis works in a garage for $9 an hour.If he works on Saturday he is paid time and a half.If he works on Sunday he is paid time and three quarters.Last weekend Jarvis worked for FIVE hours on Saturday and TWO hours on Sunday.Hours paid on Saturday ( Mixed fraction ) =Hours paid on Sunday ( Mixed fraction ) =Total hours paid ( Mixed fraction ) =How much was Jarvis paid last weekend altogether? Please answer this question this homework is for today HELP A CHICKEN NUGGET OUT!What is the value of x9? 14x(x+2)=14 Enter your answer in the box. x9= Why is Search Engine helpful in our daily lives and how does Search engine works? 2. How should this sentence be changed?Coffee is very popular in most countries: however, in a few, tea is the warmbeverage of choice.A. Delete the comma after the word howeverB. Change the colon to a semicolonC. Insert a semicolon after the word teaO D. No change needs to be made to this sentence When a material is heated, the change in temperature depends on the kind of material and its mass. Different objects can absorb and release different amounts of energy when heated and cooled. This property is called heat capacity. How might scientists apply this property to design something useful in the real world? Give one or two examples.ill give 50 points for this answer please help In no more than 50 words, give a brief history of theater. Plato!!! Please help ~_~Type the correct answer in the box. If necessary, use / for the fraction bar.A solid wooden block in the shape of a rectangular prism has a length, width, and height of 3/8 centimeter, 1/8 centimeter, and 5/8 centimeter,respectively,The volume of the block is () cubic centimeter. The number of cubic wooden blocks with a side length of 1/8 centimeter that can be cutfrom the rectangular block is()Answer goes in the () Is shape 1 similar to shape 2? Why or why not? The weight of an empty pickup truck is 2.1 times the weight of an empty car. If the empty car weighs 1.8 tons, how many tons does the pickup weigh carrying a 0.5 ton load? (IF I SEE RANDOM LETTERS IT WILL BE DELETED AND THE PERSON WILL BE REPORTED.) Destiny and Franijza are at the swimming pool. They decide to walk to the ice cream shop. They walk north at a pace of 6 km/h * r for 20 minutes, and then east at the same pace for 10 minutes. If the swimming pool is at the origin (0, 0) what is the position of the ice cream shop?