(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:
Step-by-step explanation:
P=(2,-3)
Q=(a,a²-2a-3)
[tex]\Delta y=a^2-2a-3-(-3)=a^2-2a\\\Delta x=a-2\\\\\displaystyle \lim_{a \to 2} \dfrac{a^2-2a-3-(-3)}{a-2} \\\\=\lim_{a \to 2} \dfrac{a^2-2a}{a-2} \\\\=\lim_{a \to 2} \dfrac{a(a-2)}{a-2} \\\\=\lim_{a \to 2} \dfrac{a}{1} \\\\=\lim_{a \to 2} a \\\\=2\\[/tex]
Proof:
y'=(x²-2x-3)'=2x-2
y'(2)=2*2-2=2
Related Questions
Points A, B, and C are collinear. Point B is between A and C. Find the length indicated.
Answers
Answer:
AB=1
Step-by-step explanation:
Colinear means all points are on the same line. We need to find the measure of AB.
Using the segment addition postulate,
ab+bc=ac
Subsitue this for our known values
[tex]2x + 15 + 9 = x + 17[/tex]
Solve for x
[tex]2x + 24 = x + 17[/tex]
[tex]x + 24 = 17[/tex]
[tex]x = - 7[/tex]
Plug this in for AB
[tex]2( - 7) + 15 = 1[/tex]
(3x+2)(x^2-4x-2) simplify the expression to a polynomial in standard form
Answers
(3x+2)(x²-4x-2)
(3x) (x²-4x-2) + (2) (x²-4x-2)
= 3x³ – 10x² – 14x – 4
I hope I helped you^_^
Two kids at a summer camp, Amelia and Jennifer, are competing in a potato sack race. Amelia is younger, so she is given a head start of 3 yards. When the race starts, Amelia hops at a rate of 3 yards per second, and Jennifer hops 4 yards per second. Eventually, Jennifer will overtake Amelia. How far will Jennifer have to hop? How long will that take?
Answers
Can anyone explain how to do this pleaseee
-2+y/10=-6
Answers
Answer:
y = -58
Step-by-step explanation:
You have to isolate the y:
-2+y/10 = -6
First step, multiply both sides by 10:
-2+y = -60
Second step, add 2 on both sides:
y = -58
It's done!
Answer:
-2=-40/10=-6
Step-by-step explanation:
-2/10 alone is -0.2.
Using PEMDAS your problem should look more like, (-2)+((y)÷10)=
Using this new formula let's start plugging in numbers.
(-2)+((0)÷10)= -2
(-2)+((-1)÷10)= -2.1
(-2)+((-2)÷10)= -2.2
Now there is a pattern, you can calculate or just keep moving up the latter until you reach the desired sum.
After finding the plug-in use PEMDAS to solve.
(-2)+((-40)÷10)=
((-40)÷10)= -4
-4+-2=-6.
So (-2)+((-40)÷10)= -6
Can someone Help me please
Answers
Step-by-step explanation:
what do you need to do ? draw the line ? or find some intercepts on the x- or y-axis ? or ?
in any case it is important to bring this into the typical line equation form :
y = ax + b
so,
-4x = -1 + y
we leave y alone on one side
y = -4x + 1
to draw the line you need 2 points.
so, let's find some.
one typical choice is x = 0.
then y = -4×0 + 1 = 1
so, P1 = (0, 1)
and then e.g. let's pick x = 1
then y = -4×1 + 1 = -4 + 1 = -3
so, P2 = (1, -3)
there you have it
mark the two points on the coordinate graph, then take a ruler and draw the line all the way from top left to bottom right so that it goes through the two points.
Evaluate 2/11 + 1/17 + 2/3
Answers
Answer:
509/561
Alternate form is 0.9073
Step-by-step explanation:
The L.C.M is 561.
561/11 × 2 is 102.
561/17 × 1 is 33
561/3 ×2 is 374
102/561 + 33/561 + 374 /561
= 509/561
Alternate form is 0.9073
help I will give brainly!!!!!!!!
Answers
Write the rules for determining the sign of the product when multiplying integers. Then, write (4 points)
the rules for determining the sign of the quotient when dividing integers. Use your own words
and use complete sentences. Make sure you answer both questions presented in this problem.
I
Answers
Answer:
hahaaaaaaaaaaaaaaaaa
Step-by-step explanation:
Answer:
IF the signs ARE same the result is a POSITIVE, if the signs are NOT the same the result is NEGATIVE
Step-by-step explanation:
1. Which of the following is a true statement?
a. To square a number, multiply the number
by 2.
b. The inverse of squaring a number is to
divide the number by 2.
c. To square a number, multiply the number
by itself.
d. A perfect square is a number whose
square root is an even number.
SHOW PROOF
Answers
Answer:
C
Step-by-step explanation:
Squaring is multiplying a number by itself
Examples:
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
etc.
please help me quickly
Answers
Answer:
A. step 1
Step-by-step explanation:
I think its A , because a negative plus a negative is a postive
Answer:
step 2 is the incorrect step
help!!! hurry......-_-
Answers
Replace x and y’all with the point and solve the equations
1. 2(0.5)+ 4(-6.75) = 1 + -27 = -26
This is true so is an answer.
2. Y = 0.5-7.5 = -7, -7 is not -6.75 so this is not true.
3. 2(-6.75) = 0.5 + 13
13.5 = 13.5
This is true so is also an answer.
4. -6.75 = 0.5(0.5) -7
-6.75 = 0.25-7
This is true so also an answer.
Answers are 1, 3 and 4
Answer:
Equation 1 and 4
Step-by-step explanation:
Point = (x,y) = (0.5,-6.75)
Hence,
x = 0.5 , y = -6.75
Equation 1:
2(0.5) + 4(-6.75) = -26
1 - 27 = -26
-26 = -26
This equation is true for the given point.
Equation 2:
-6.75 = 0.5 - 7.5
-6.75 ≠ -7
The equation is not true for the given point.
Equation 3:
2 (-6.75) = 0.5 + 13
-13.5 ≠ 13.5
The equation is not true for the given point.
Equation 4:
-6.75 = 0.5(0.5) - 7
-6.75 = 0.25 - 7
-6.75 = -6.75
This equation is true for the given point.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!Does a rhombus have perpendicular line segments
Answers
Answer:
A rhombus is a geometric figure that lies in a plane. It is defined as a quadrilateral all of whose sides are congruent. It is a special type of parallelogram, and its properties (aside from those properties of parallelograms) include:
Its diagonals divide the figure into 4 congruent triangles.
Its diagonals are perpendicular bisectors of eachother.
If all of a rhombus' angles are right angles, then the rhombus is a square.
Answer:yes it does have perpendicular lines
Step-by-step explanation:
Please no links because they dont work :).
Answers
Answer:
C. x + 9
Step-by-step explanation:
[tex]x-\frac{5}{5}+10\\\\x-1+10\\\\x+9[/tex]
hey please help i’ll give brain
Answers
Answer:
The answer is 2. It is the commutative property of addition. This states that the order of numbers does not matter in addition or multiplication. As long as all the numbers are there, it will give the same answer :)
Step-by-step explanation:
d/3 =13 what is d and explain why its d.
Answers
Answer: d = 39
Solve:
Given
d / 3 = 13
In order to get the value of d, we need to isolate d, which means we should multiply 3 on both sides to delete the 3 on the left-hand side
d / 3 × 3 = 13 × 3
d = 39
Check:
Left-hand side = d / 3 = 39 / 3 = 13
Right-hand side = 13
13 = 13
Hope this helps!! :)
Please let me know if you have any questions
Answer:
39
Step-by-step explanation
so d ÷ 3 = 13
first we want to change these numbers into a fraction so
d ÷ 3 = [tex]\frac{d}3}[/tex]
13 is whole but we can still display it as 13÷1 =[tex]\frac{13}{1}[/tex]
line these up like this
[tex]\frac{d}{3} \frac{13}{1}[/tex]
now cross multiply the numbers that always line up diagonally so 13 and 3
13x3=39
next divide that answer by the number diagonal to the unknwon so 39÷1 = 39
that means d = 39
solve for A. W = a/3
PLEASEEEE
Answers
Answer:
3w
Step-by-step explanation:
[tex]w=\frac{a}{3} \\3w=a\\[/tex]
13 Points Plz Help Me
Answers
Step-by-step explanation:
y+x-2-6x = y-5x-2
2x+3-x-4 = x-1
5xy+4x-5xy-3 = x
PLEASE HELPP MEEE I NEED THE ANDWER QUICKKK
20.00$ - a=8.45$
Answers
Answer:
a= 11.55
Step-by-step explanation:
If the answer is 8.45, then the variable equals the difference of 20 minus the answer, 8.45
Hope this helps!
Is the graph a linear function, nonlinear function, or relation?
Answers
Answer:
Non-linear
Step-by-step explanation:
just did it
Answer:
Nonlinear function
Step-by-step explanation:
Because it's along the x-axis but isn't a straight line if it was a straight line it would be considered a "Linear Function".
Please help. I’m not sure what the answer is
Answers
Answer:
A
Step-by-step explanation:
Slope=-7, through (-3,2)
Answers
Answer:
Final equation: y = -7x -19
Step-by-step explanation:
You are looking for slope intercept correct?
Formula: y = mx + B
Y = y-value of point ( coordinates )
M = slope
X = x - value of point ( coordinates )
B = Y - intercept
Equation:
2 = -7(-3) + B
2 = 21 + B
-21 = -21 = B
------------------
-19 = B
Final equation: y = -7x -19
Unless if it asks you to plug back the numbers for anything else then you do that but this is how you get slope intercept.
A 3m ribbon is cut into two pieces.The shorter length measures 0.75m.Write the ratio of the shorter length to the longer length in the simplest form a:b,where a and b are both integers.
Answers
Answer:
1:3
Step-by-step explanation:
3 m - .75 m = 2.25 m Find the length of the longer piece.
.75:2.25 Ratio in un-simplified form
[tex]\frac{.75}{2.25}[/tex] Write it as a fraction.
[tex]\frac{75}{225}[/tex] Multiply the numerator and denominator by 100 to remove the decimal.
[tex]\frac{3}{9}[/tex] Divide the numerator and denominator by 25.
[tex]\frac{1}{3}[/tex] Simplify further by dividing the numerator and denominator by 3.
1:3 Convert back to ratio form.
If a = 6 and b = 2, then what does ab equal?
Answers
Answer:
12
Step-by-step explanation:
ab
Let a = 6 and b = 2
6*2
12
The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?
Answers
Answer: 2 degrees + 3 degrees = 5 degrees
Step-by-step explanation: Though the times might be confusing, the problem itself is simple addition- if the temperature rises, or goes up, by a certain number, in this case three, you're just going to add that number to the initial number, two.
Find the possible subsets of A = {a,b}
Answers
Answer:
Step-by-step explanation:
Subset of A = { {} , {a} , {b}, {a.b} }
HELP PLEAASSEE ?? ANYONE ???
The diagram shows 3 identical circles inside a rectangle.
Each circle touches the other two circles and the sides of a rectangle, as shown in the diagram.
The radius of each circle is 2 mm.
Work out the exact area of the rectangle. Give your answer in the form
[tex]a \sqrt{3} + b[/tex]
where a and b are integers.
Answers
Answer:
as the diagram is not provided by you
Step-by-step explanation:
proper an answer cannot be written if the three circles touch Each Other as well as the the sides of the rectangle it means that rectangles length and breadth are made by attaching to circles together which means that length and breadth of the rectangle are equal therefore length is equal to diameter of one circle into two that is 8 therefore length and breadth of the rectangle are 8 each other for exact area of rectangle is 8 x 8 = 64
Answer:
apparently 4root3 + 8
Step-by-step explanation:
Josh sees that the ratio of boys to girls is 1/2, so he says that half of the students are boys?
Answers
Answer:
no.
Step-by-step explanation:
The ratio is 1/2. That means that if there is one boy, there are 2 girls. Altogether, there are 3 people.
The answer is no. Boys would be one-third and girls are two-thirds.
If this helped, please mark me as brainliest. Thank you! ;)
(50 POINTS!!!!!) I NEED THE CORRECT ANSWER... FAST!
Answers
Answer:
don't know sorry forgive me
i dont know if im right or not
Answers
Answer:
You are right
Step-by-step explanation:
80% of a number is always going to be less than 100% of a number. Assuming the numbers positive, which it said
Answer: its >
Step-by-step explanation: beacuse80% x .01 =0.008 and 0.008= 0.8%
HELPPPPPPPPPPPPPPPPPPPPPPP
(jus take the points dont really need help)
Answers
Answer:
Alright- if you want any help just reply to this