Find the coordinates of the point at which the normal to the curve y = x ^ 2 at x = 1 meets the curve again

Answers

Answer 1

Answer:

[tex](-\frac{3}{2},\frac{9}{4})[/tex]

Step-by-step explanation:

A normal line is a line perpendicular to the tangent line, so we must take the derivative of the function to find the slope of the tangent line, and then take the opposite reciprocal of this slope, to find the slope of the normal line. The equation of a normal line will be in the form of [tex]y=mx+b[/tex]:

[tex]f(x)=x^2\\\\f'(x)=2x\\\\f'(1)=2(1)\\\\f'(1)=2[/tex]

Hence, the opposite reciprocal is [tex]-\frac{1}{2}[/tex], which is our slope for the normal line. Now, we find the y-intercept by plugging in the given coordinate point [tex](1,1)[/tex] since [tex]f(1)=1^2=1[/tex]:

[tex]y=-\frac{1}{2}x+b\\\\1=-\frac{1}{2}(1)+b\\ \\1=-\frac{1}{2}+b\\ \\b=\frac{3}{2}[/tex]

Thus, the equation of the normal line is [tex]y=-\frac{1}{2}x+\frac{3}{2}[/tex]. Using this information, we can now find the coordinates where the normal of the curve at x=1 meets the curve again:

[tex]x^2=-\frac{1}{2}x+\frac{3}{2}\\ \\ x^2+\frac{1}{2}x-\frac{3}{2}=0\\ \\ 2x^2+x-3=0\\\\(x-1)(2x+3)=0\\\\x=1,\: x=-\frac{3}{2}[/tex]

Since we only care about [tex]x=-\frac{3}{2}[/tex] since [tex]x=1[/tex] was already accounted for, the y-coordinate would be:

[tex]y=x^2\\\\y=(-\frac{3}{2})^2\\\\y=\frac{9}{4}[/tex]

Therefore, the coordinates are [tex](-\frac{3}{2},\frac{9}{4})[/tex].

In the graph attached below, you can see the tangent line [tex]y=2x-1[/tex] and how it is perpendicular to [tex]y=\frac{1}{2}x-\frac{3}{2}[/tex].

Find The Coordinates Of The Point At Which The Normal To The Curve Y = X ^ 2 At X = 1 Meets The Curve

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helpppppppppppppp with this

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Answer:

1.

7 -3n

2.

2(p -10)

3.

4(3 +x)

4.

10 - 2w

5.

C = 45h + 125

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3n ÷ 4+n

Camila had a large collection of basketball cards. She gave half of them to her friend Erin and a sixth of them to her brother. She still has 150 cards left. How many cards did she start with?

Answers

Answer:

300

Step-by-step explanation:

SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114.

1) What percentage of SAT scores is between 287 and 857?

2) What percentage of SAT scores is greater than 629?

Please explain!

Answers

1) For our first job, PROBLEM A, it has a mean of 515 points and a standard deviation of 114 points. We're given the goal of calculating what % belongs between 401 and 629. As we can see, if we remove 515, then subtract 114 from 515, we obtain our first value of 401, then if we add our standard deviation tournament, we get our second number of 629. So, using the empirical rule, we know that in this scenario, 68 of our data points will fall inside this range.

2) Part B requires us to identify the scores that are less than 401 and larger than 629. So, in part A, we have the inclusive section of this, and now we have the exclusive section. Simply remove 60 percent from 100 percent, and we get 32 percent outside of this range.

Which of the following is equivalent to
60
5?
BD
2
VGO
60
- -
/60

Answers

Answer:

second choice: √60

Step-by-step explanation:

60^(1/2) is equal to √60

Three kids, Alberto, Bernadette, and Carlos, decide to share 11 cookies. They wonder how many ways they could split the cookies up provided that none of them receive more than 4 cookies (someone receiving no cookies is for some reason acceptable to these kids).

How many ways do they find?

Answers

Using the arrangements formula, it is found that they find 46200 ways.

What is the arrangements formula?

The number of arrangements of n elements is given by:

[tex]A_n = n![/tex]

If they repeat in [tex]n_1, n_2, \cdots, n_n[/tex] ways, the number of arrangements is given by:

[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2!\cdots n_n}[/tex]

In this problem, 11 elements are arranged with repetitions of 4, 3 and 3, hence:

[tex]T = \frac{11!}{4!3!3!} = 46200[/tex]

They find 46200 ways.

More can be learned about arrangements at https://brainly.com/question/2259733

A recipe for strawberry punch calls for 3/7 qt of ginger ale and 1/7 qt of strawberry soda. How much liquid is​ needed?
If the recipe is​ doubled, how much is​ needed?
If the recipe is​ halved, how much is​ needed?

Answers

Answer:4.7 qt of liquid is needed. If doubled, 8/7 qts of liquid is needed. if halved, 2/7 qts of liquid is needed.

Step-by-step explanation:

Add the two amounts of liquid to get the total amount of liquid:

1/7 qt + 3/7 qt = 4/7 qt (cannot be simplified further)

To double the recipe, multiply the total liquid amount by 2.

4/7 * 2/1 = 8/7

To half the recipe, multiply the total liquid amount by 1/2.

4/7 * 1/2 = 4/14 --> 2/7

MARKING AS BRAINLIEST! LAST ATTEMPT! ) show ur work

Answers

Answer:

√x³=√(x²·x)=x√x

√xy³z=√(x·y²·y·z)=y√xyz

√18x²y=√(3²·2·x²·y)=3x√2y

√32x⁴y²=√(2⁴·2·x⁴·y²)=2²x²y√2=4x²y√2

2√16x⁷y³z⁴=2√(2⁴·x⁶·x·y²·y·z⁴)=2³x³yz²√xy=8x³yz²√xy

-3√180x⁵y=-3√(3²·2²·5·x⁴·x·y)=-3(3)(2)x²√5xy=-18x²√5xy

5√108xyz²=5√(2²·3²·3·x·y·z²)=5(2)(3)z√3xy=30z√3xy

3x√xy¹⁰z⁷=3x√x·y¹⁰·z⁶·z)=3xy⁵z³√xz

x²√x³y²=x²√(x²·x·y²)=x²·x·y√x=x³y√x

show your work. pleasee and thank you everyone!!

Answers

Answer:

i dont know but i reallyyy hope someone helpsss

Step-by-step explanation:

I need help answering this question . Please help

Answers

Answer:

the 3rd option

Each person will have 2 slicles in total from 6 pieces.

Answer:

4 peco or slices this may not be right

Last question and then I’ll take care of the rest on my own ^^^^

Answers

Answer:

  (c)  5/2

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

  a^-b = 1/a^b

__

Using these rules, we can simplify the expression as follows:

  (5^-3)(2^2)(5^6)/((2^3)(5^2)) = (5^(-3+6-2))(2^(2-3)) = (5^1)(2^-1)

  = 5/2

Unit 6 Lesson 7 Exit Ticket
1. Gwyneth takes 753 steps to get to the bus stop each morning. Her sister Beth takes 647
steps to get to the subway each morning. How many more steps does Gwyneth take
than Beth in the morning?
Answer.
2. On the number lines below, show how you could use subtraction AND addition to solve
this problem. For each strategy, circle the answer to the question above.
Subtraction:
Addition:
O
K

Answers

Answer:

1. 106 steps more than Beth.

Help help help math math

Answers

Answer:

add x to both sides. once you do this, you will get x+y=15

Add x to both sides.

y = -x + 15 —> y + x = 15

So, the final answer is x + y = 15.

Juan's dog stands 2 feet and 3 inches tall. Peter's dog stands 9 inches tall. Use what you have learned about fractions to calculate how much taller Juan's dog is than Peter's dog. Remember that there are 12 inches in one foot.
PLEASE WRITE IT!

Answers

Answer:

2 feet and 3 inches = 27 inches

27 - 9 = 18 inches which also equal to 1 foot and 6 inches

Answer:

Juan's dog = 2 feet 3 inches = 27 inches Peter's

dog = 9 inches so to find how taller Juan's dog

hight is

by

27-9 = 18 inches or 1 feet and 6 inches.

hope I

helped u by my answer

Step-by-step explanation:

#ITZADMIRER

If f(x)=x^2+9x and g(x)=3x+1 find f(g(x)) and g(f(x))

Answers

Answer:

see explanation

Step-by-step explanation:

to find f(g(x)) , substitute x = g(x) into f(x)

f(g(x))

= f(3x + 1)

= (3x + 1)² + 9(3x + 1) ← expand parenthesis

= 9x² + 6x + 1 + 27x + 9 ← collect like terms

= 9x² + 33x + 10

----------------------------------------------

to find g(f(x)), substitute x = f(x) into g(x)

g(f(x))

= g(x² + 9x)

= 3(x² + 9x) + 1 ← distribute parenthesis

= 3x² + 27x + 1

Help me please! I will give brainliest!!

Answers

Answer: 1/4

Step-by-step explanation: we need a common denominator of 3 and 12, by multiplying 3 x 4 = 12 then 1 x 4, we then have the fraction 4/12. subtract 1/12 then you have 3/12 we then simplify by dividing the numerator and denominator by the same number = 1/4

Answer:

1/3 - 1/12 = 4/12 - 1/12= 3/12

Step-by-step explanation:

- Get 1/3 the same denominator as the 1/12

- to do that you multiply the 3 by 4 you get 1/12

- I was taught whatever you do at the bottom you have to do on top so multiply the 1 by 4 and now you have 4/12

- plug in 4/12 to the equation

- 4/12 -  1/12 = 3/12 or the simplified version is 1/4

Evaluate the expression 4y - 11 when y = 14

Answers

Answer:

The answer is 45 because 4 times 14 is 56 if you subtract 11 you get 45

The answer to the problem is 45.

Write the slope-intercept form of the equation of the line through the given points. through: (2, 1) and (4,3)​

Answers

Answer:

Slope is 1, in slope intercept form it will be y=1x+b

Step-by-step explanation:

You will use

y2-y1/x2-x1

What does 95% Confindent interval mean? at least 3 sentences with your own words.

Answers

Answer:

1.A 95% confidence interval is a set of numbers about which you may be 95% certain.

2.The genuine population mean is 95 percent guaranteed to be present.

3.A 95 percent confidence interval (CI) of the mean is a range computed from a sample having an upper and lower value. Because the real population mean is uncertain, this range denotes the range of probable mean values.

Step-by-step explanation:  

use quill bot to paraphrase sentences from online :3

Would a scale that is used to weigh food be the best tool to weigh concrete blocks?Explain

Answers

Answer:

A scale with a suitable range for weighing small items such as food in the home, would not be suitable for weighing large, heavy items, such as concrete blocks.  A scale for concrete blocks wouldn't be sensitive enough for food.

PLEASE HELP PLEASE PLEASE PLEASE PLZZZZZZZZZZZ

Answers

The answer is B bc 1/2 = 4/8 and then 4/8 + 3/8 = 7/8

Subtract-7-^2+1 from -2x^2-4

Answers

Answer:

- 5 x ^ 2 + 1 - 4 x

Step-by-step explanation:

First step is simplifying your answer.

− 7 x ^ 2 + 1 + 2 x ^ 2 − 4 x

Second step you will combine like terms.

( − 7 x ^ 2 + 2 x ^ 2 ) + 1 - 4 x

Third step is simplifying this is your answer.

- 5 x ^ 2 + 1 - 4 x

There were 45 girls and 24
At the
boys on the school bus. At the
last bus stop, four boys got on
and three girls got off. What is
the ratio of boys to girls?
A) 15:8

B) 8:15

C) 3:4

D) 3:2

E) 2:3

Answers

15:8 i belive if not then its 8:15 but i think its a

The table shows the altitude, in feet, of an airplane at certain times during its flight from Baltimore to Orlando since its departure at 11:00am. Find the equation for the curve of the best fit, then predict the altitude of the plane at 1:00 pm.

Answers

Answer:

around 8,000

Step-by-step explanation:

its because we can see that it roughly increases and decreases by 2000, its my guess, tell me how u get on

please help asap!!!!​

Answers

Answer:

-12

Step-by-step explanation:

Apply the radical rule :  [tex]\sqrt[n]{-a} =-\sqrt[n]{a}[/tex]

Therefore, [tex]\sqrt[3]{-1728} =-\sqrt[3]{1728}[/tex]

Factorise 1728:   [tex]1728=12^3[/tex]

Therefore, [tex]\sqrt[3]{-1728} =-\sqrt[3]{12^3}[/tex]

Apply the radical rule:  [tex]\sqrt[n]{a^n} =a, \ \ \ \ a\geq 0[/tex]

Therefore, [tex]-\sqrt[3]{12^3}=-12[/tex]

A restaurant bill for 4 people is $120. The group leaves a tip of $18. What percent tip is that?

Answers

Answer:

18÷120(100)

=0.15

=15%

so the answer is 15%

Percentage of tip compare to total bill is equals to 15%.

What is percentage?

"Percentage of a number is defined as it is a part which is equals to hundredth part of a given number."

Formula used

Percentage = [( part of a number) / ( whole number) ] × 100

According to the question,

Total bill paid by 4 people = $120

Amount of tip = $18

Substitute the value in the formula we get,

Percentage of tip = [(18) / (120)] × 100

                             =  0.15 × 100

                             = 15%

Hence, percentage of tip compare to total bill is equals to 15%.

Learn more about percentage here

https://brainly.com/question/14979505

#SPJ2

29. What is the slope of the line?(1 point)
A.-2
B.0
C.2
D. undefined

Answers

Answer:

A. -2

Step-by-step explanation:

You will always find the slope of the line on the y-axis, in thus question here it shows the line on the y-axis, on the -2. Therefore, your answer will be A. -2

On October 1, 2021, Oberley Corporation loans one of its employees $30,000 and accepts a 12-month, 8% note receivable. Calculate the amount of interest revenue Oberley will recognize in 2021 and 2022. x Answer Is complete but not entirely correct. Year 2021 Interest Revenue $ 60,000 $ 2,925 2022 < Prev 3 of 7 Next > 19​

Answers

Answer:

In order to calculate interest receivable and interest revenue for notes receivable, you can multiply the interest rate by the amount of notes receivable and then divide by 12 to capture the monthly rate.

What is 1/2 of some number?

(By the way this is translating to an algebraic expression)

Answers

Answer:

1/2(x)

Step-by-step explanation:

Let's break down the question.

1/2 = 1/2, of course

of = multiplied by

some number = x

Given the information above, we multiplying 1/2 by x. This can be algebraically written as 1/2(x).

Have a lovely rest of your day/night, and good luck with your assignments! ♡

A survey of 2,541 American households discovered that 53% of the households have children. What is the population?
a. Americans
b. Children
c. American Households
d. Households with Children

Answers

D i took thos test hope it helps

What is the solution to the system of equations using the graph

Answers

If it’s looking for a point then it would be (2, -4)
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