Mathematics College

Really need to someone to break this down so I can understand it
(a) Find the slope of the curve y= x^2 - 2x - 3 at the point ​P(2,​ -3​) by finding the limit of the secant slopes through point P.
(b) Find an equation of the tangent line to the curve at P(2, -3)

Answers

Answer 1

Answer:

Part A)

The slope is two.

Part B)

[tex]\displaystyle y = 2x - 7[/tex]

Step-by-step explanation:

Part A)

We want to find the slope of the curve:

[tex]\displaystyle y = x^2 - 2x - 3[/tex]

At the point P(2, -3) by using the limit of the secant slopes through point P.

To find the limit of the secant slopes, we can use the difference quotient. Recall that:

[tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex]

Since we want to find the slope of the curve at P(2, -3), x = 2.

Substitute:

[tex]\displaystyle f'(2) = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}[/tex]

Simplify. Note that f(2) = -3. Hence:

[tex]\displaystyle \begin{aligned} f'(2) &= \lim_{h\to 0} \frac{\left[(2+h)^2 - 2(2+h) - 3\right] - \left[-3\right]}{h} \\ \\ &=\lim_{h \to 0}\frac{(4 + 4h + h^2)+(-4-2h)+(0)}{h} \\ \\ &= \lim_{h\to 0} \frac{h^2+2h}{h}\\ \\&=\lim_{h\to 0} h + 2 \\ \\ &= (0) + 2 \\ &= 2\end{aligned}[/tex]

(Note: I evaluated the limit using direct substitution.)

Hence, the slope of the curve at the point P(2, -3) is two.

Part B)

Since the slope of the curve at point P is two, the slope of the tangent line is also two.

And since we know it passes through the point (2, -3), we can consider using the point-slope form:

[tex]\displaystyle y - y_1 = m(x-x_1)[/tex]

Substitute. m = 2. Therefore, our equation is:

[tex]\displaystyle y + 3 = 2(x-2)[/tex]

We can rewrite this into slope-intercept if desired:

[tex]\displaystyle y = 2x - 7[/tex]

We can verify this by graphing. This is shown below:

Really Need To Someone To Break This Down So I Can Understand It(a) Find The Slope Of The Curve Y= X^2

Related Questions

Using rational numbers how do you solve -37 + (-64)

Answers

Answer:

-101

Step-by-step explanation:

An addition sign in front of the negative number means to subtract that number.

Another way to write -37 + (-64) is:

-37 - 64

-37 - 64 = -101

can 0.462 be written as a fraction and is it a terminating or repeating decimal

Answers

Answer: 462/1000

Step-by-step explanation:

-3(4x+3)+4(6x+1)43
please solve the problem fully

Answers

Answer and Step-by-step explanation:

First, distribute the numbers outside of the parenthesis to the numbers on the inside.

-12x - 9 + 24x + 4 = 43

Combine like terms.

12x - 5 = 43

Add 5 to both sides.

12x = 48

Divide by 12 on both sides of the equation.

x = 3 <- This is the answer.

#teamtrees #PAW (Plant And Water)

Leave any questions you have, put it in the comments below :)

Name 10 different rays. Then name 2 pairs of opposite rays.

I simply need to check answers!

Answers

Answer:

Rays are.

DA,CB,AB,EA,CA,CD,EB,BC, rest I don't know

a line passes through the points 3, 0 and 4, 1. what is the y-intercept of the line
​

Answers

9514 1404 393

Answer:

  (0, -3)

Step-by-step explanation:

The slope is the same for any segment of the line. The slope from (0, y) to (3, 0) is the same as from (4, 1) to (3, 0).

  Δy/Δx = (y -0)/(0 -3) = (1 -0)/(4 -3)

  y = -3(1/1) = -3 . . . . . multiply by -3

The y-intercept is (0, -3).

What's (9+9i)(-1-5i) using foil method

Answers

Answer:

36-54i

Step-by-step explanation:

(9+9i)(-1-5i)

v

-9-9×5i-9i-9i×5i

v

-9-45i-9i-45i^2

v

-9-45i-9i-45×(-1)

v

(-9)-45i-9i+(45)

v

36(-45i)(-9i)

v

36-54i

cho hàm số y= x^{3} +3x^{2} -1 .viết phương trình tiếp tuyến tại điểm có hoành độ bằng -1

Answers

hope you do not mind expressing this on in English ‍♂️

Write this as an algebraic expression:

You have $100 and make $25 a day

Answers

Answer:

25d + 100

Step-by-step explanation:

I will call "d" the days passed

25d + 100

A worker earns the same amount for each
hour. If he earned $48.00 in 3 hours, how
much would he earn in 8? In 40?

Answers

Answer: 8 hours= $128      40 hours= $640

Step-by-step explanation:

$48.00 divided by 3 = $16.00 an hour. so 16x8=128 and 16x40=640

Find the missing angle.

Answers

Answer:

Angel V = 74

I hope it's helps you

The missing angle is 74 degrees. Triangles add up to 180° so do 180 minus the angles given to get 74.

The area of this shape is 24 square units. Which of these statements is true about the area ?​

Answers

D.

Because the area of an object is number of square units or square grids inside the shape.

Answer:

D.

Step-by-step explanation:

What is the quotient of 7.584 x 10^9 and 7.9 x 10^ 2 expressed in scientific notation?

Answers

Answer:

9.6 × 10  6

Step-by-step explanation:

(7.584 × ) ÷ (7.9 × 10²)

This gives;

×    = 0.96 ×

Simplifying further gives;

9.6 ×  = 9.6 ×

Solve the following equation.
X - (-6) = 15

Answers

X = 9, good luck, Chuck.

Answer:  x=9

Step-by-step explanation:

x-(-6)=15

first the subtraction sign and the negative sign becomes a plus sign

x+6=15

  -6  -6

Next you subtract 6 from both sides of the equation. And that leaves you with

x=9

Simplify show all steps thirty POINTS!

Answers

6a + 3
Hope it helped
I think it’s 2a+3
Since you have to divide 6a AND 9 by 3 :)

HELP PLS IM BEGGING YOU PLS HELP, its due todayyy pls. Angle CBD is the only one i got right and the rest is wrong. I dont know how to answer it anymore.

Answers

Answer:

try It would be number 81

Step-by-step explanation:

Abc= 110

ceo=70

dbe=110 or 120

and abe= 60 70 or 81

Answer:

ABC=112 degrees

DBE=112 degrees

ABE=68 degrees

Step-by-step explanation:

CBD=ABE

ABE=68 degrees

First let's take these as X,

ABC=DBE=X(Vertically opposite angles)

ABC+DBE+CBD+ABE=360(angles around a point)

   x  + x     +68   +68  =360

      2x        +136        =360

                       2x       =360-136

                       2x       =  224

                             x    =112 degrees

therefore;

   ABC=112 degrees

   DBE=112 degrees

can someone help me with this one again bc I didn't show the decimal Decimal: 0.44​

Answers

Step-by-step explanation:

The answer is 10 times

=> 4 hundredths x 10 = 4 tenths

=> 0.04 x 10 = 0.4, which is correct

Hope that helps

solve for y
-10x + 2y =4

Answers

Answer:

y = 5x + 2

Step-by-step explanation:

Add 10x to both sides

2y = 10x + 4

Divide both sides by 2

y = 5x + 2

find the midpoint of R(5,3) and S(-4,6) PLEASEEE

Answers

Answer:

(0.5, 4.5)

Step-by-step explanation:

midpoint formula:

((sum of the two x values)/2, (sum of the two y values)/2)

= ((5+(-4))/2 , (6+3)/2)

= (0.5, 4.5)


If a >b, then A must be positive number.

Answers

Step-by-step explanation:

NO,IT DEPENDS UPON SITUATIONS

IF B IS -5 THEN A CAN BE -2,-4,-3 OR 1 ,2,3,4,......

If a function is defined by the equation y = 1/2x -3/2 , which equation defines the inverse of this function?

Answers

Answer:

B

Step-by-step explanation:

Rearrange the equation making x the subject

y = [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] ( multiply through by 2 to clear the fractions )

2y = x - 3 ( add 3 to both sides )

2y + 3 = x

Change y back into terms of x with x being the inverse function, that is

y = 2x + 3 → B

please solve this question i need help​

Answers

Answer:

4c/2a 60 degrees 3bf 2ad

Answer:

f=120

b=40

d=140

e=120

c=30

a=30

maths
class 8th
give answers
​

Answers

Answer:

8/9 + -8/9 = 0

[2^-1 + 3^-2 + 4^-3]^0 = 1

it takes a lady 26 minutes to travel 3 km by walking the first part at 6 km per hour and running the second part at 10 km per hour what distance does she walk​

Answers

Answer:

78 meter 360meters 600 meters

Is 4 or 3 bigger in a integer

Answers

Answer:

4 is bigger than 3

Step-by-step explanation:

4 is bigger than 3

But

-3 is bigger than - 4

278 kg to pounds, rounded off to the nearest pound.

Answers

Answer:

About 613 pounds

Step-by-step explanation:

1 : 2.20462262

278 : 612.885089

612.885089 --> 612.89 --> 612.9 --> 613

please help with math

Answers

1.) - sqrt. 2 (which, in decimal, is about -1.4142…) , 0, sqrt. 5 (which, in decimal, is about 2.2360…) , 13/4

2.) -1.5, 3/4 (which, in decimal, is 0.75) , 3, sqrt 10 (which, in decimal, is about 3.1622…)

3.) -3/2 (which, in decimal, is -1.5), -3/7 (which, in decimal, is about -0.4285…) , 0.75, 2

(-8, -2) and (1, 9) find the slope

Answers

Answer:

11/9

Step-by-step explanation:

To find the slope

m = ( y2-y1)/(x2-x1)

    = ( 9 - -2)/(1 - -8)

    = ( 9+2)/ (1+8)

    = 11/9

Write an equation in slope-intercept form for the line with slope -3/2 and y -intercept -3

Answers

Answer:

It is

[tex]{ \underline{ \sf{y = - \frac{3}{2}x - 3 }}}[/tex]

Step-by-step explanation:

General equation:

[tex]{ \sf{y = mx + c}}[/tex]

m is the slope

c is the y-intercept

[tex]y = - \frac{ 3}{2} x - 3[/tex]

Combine Like Terms
1. What is the simplest expression equivalent to 2 - 11 + 18 - 20.x ?
-7-21x
7-19x
7+21x
-7+19x

Answers

Answer:

-9x+20

Step-by-step explanation:

what passes through the points (-1/2 4) and (1/2 6). show your work​

Answers

Step-by-step explanation:

The equation of line which passes through these points is determined by:

p(x1,y1)=(-1/2,4) p(x2,y2)=(1/2,6)

[tex] \frac{y - y1}{y2 - y1} = \frac{x - x1}{x2 - x1} \\ \frac{y - 4}{6 - 4} = \frac{x + \frac{ 1}{2} }{ \frac{1}{2} + \frac{1}{2} } \\ \frac{y - 4}{2} = \frac{2x + 1}{2} \\ 2(2x + 1) = 2(y - 4) \\ 4x + 2 = 2y - 8 \\ 4x - 2y + 2 + 8 = 0 \\ 4x - 2y + 10 = 0[/tex]

Note:if you need to ask any question please let me know.

Other Questions
Plz help me this is due ASAP ! Help mee 25 points for this, anyone mind helping? Need help ASAP thank you round 6.7 to the nearest whole number. in the following sentence what word or words are adverbs first, i looked here, and then i looked there, i cant find them anywhere a. them b. first,then c. here, there,anywhere d. looked, find halp please??????????? What do you mean by sclupture ? The quotient c and -19 is 38 It was recommended that students drink 48 or more ounces of water.How could you use a histogram to easily display the number of studentswho drank the recommended amount? P- 24000 R-10% T-2 years find the sum What are viruses able to do: why jesus christ died in cross? Find the value of x,y and z I am confident in my ability to locate my classes and assignments on OMHS.strongly agreeagreeneutraldisagreestrongly disagree What, according to WHO, is the definition of health a virus can reproduce but only inside a host cellTrue or false? You are planning your holiday with your friend. Make a conversation to discuss: 1/ What you need to bring 2/ Where you decide to visit 3/ What you plan to do 4/ Arrange date and time to goNotes: Remember to start and end the conversation properly. Easy for smart people HELP PLS :( Which of the following is most likely the next step in the series? Name any FIVE diversity issues that affect the farm manufacturing