(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
Which linear inequality is represented by the graph?
Oys-x-1
O yzx-1
O y<3x-1
Oy> 3x - 1
Answers
Answer:
The fourth answer choice is correct.
y>3x-1
The linear inequality that is represented here is y> 3x - 1. The last option is correct.
What is a linear inequality?These are inequalities that shows linear functions. It is showing the data that is not equal in the graph that is presented.
We can see that the line cuts through 3 at the X axis and -1 at the y axis.
Read more on linear inequalities here:
https://brainly.com/question/17152894?referrer=searchResults
Find the value of this expression if x - -7.
x2 - 1
x+4
Enter the correct answer
Answers
a. -15
b. -3
hey please help i’ll give brain
Answers
Answer:
First, the dropdown is 9. Second, put in 9. The answer is 81.
Step-by-step explanation:
10* what equals 90? Well, let's do 90/10, our answer is 9. Then We are given 1 nine or 9 to put on the second slot. Our answer would be 90-9, or 81. Khan Academy is teaching you how to multiply.
Answer:
[tex]9 \times 9 = 10nines - 1nine \\ 9 \times 9 = 90 - 9 \\ 9 \times 9 = 81 \\ than \: you[/tex]
7x-5y<-15 graph and shade
Answers
Answer:
Slope: 7/5
y intercept: (0,3)
Step-by-step explanation:
find the GCF of 3,14,5?
Answers
Factors for 3: 1 and 3
Factors for 5: 1 and 5
Factors for 14: 1, 2, 7, and 14
Answer:
1
Step-by-step explanation:
Factors for 3: 1 and 3
Factors for 5: 1 and 5
Factors for 14: 1, 2, 7, and 14
Since 1 is the greatest common factor in 3,5,14 ,
GCF = 1
Mrs. Richards had a coupon for one-third off her total bill at the local
grocery store. She bought 2 boxes of cereal for $3.49 each, three cartons
of ice-cream for $2.99 each, and a six pack of soda for $1.99. How much
was her bill with the discount?
Answers
Answer: The bill with a discount is $18.59
Step-by-step explanation:
Given information
2 boxes of $3.49 cereal
3 cartons of $2.99 ice-cream
6 packs of $1.99 soda
1/3 discount off total bill
Given expression
Bill = (1 - 1/3) (2 × 3.49 + 3 × 2.99 + 6 × 1.99)
Simplify values in parentheses
Bill = (2/3) (6.98 + 8.97 + 11.94)
Simplify by addition
Bill = (2/3) (27.89)
Simplify by multiplication
Bill = $18.59 (Rounded to the nearest hundredth because the usual money ends in nearest cent)
Hope this helps!! :)
Please let me know if you have any questions
A rectangle has a width of 3 units. The rectangle's length is 5 times its width.
What is the area of the rectangle?
Answers
Answer:
Answer= 45 units
Step-by-step explanation:
lengths = 3 units
width = 3x5= 15 units
area= length times width= 3x15= 45 units!
Hope this helps :)
What is the sum of all positive intergers from √8 to √42
Answers
√8 < √9 = 3
and
√42 > √36 = 6
which means the positive integers between √8 and √42 are 3, 4, 5, and 6, and their sum is 18.
Joe was driving on the highway a car ahead of him was driving far below the speed limit so he decided to pass. In the first second he gained(gained means to get nearer to something you are chasing) 5m on the car and as he accelerated he gained 1.5 times as much distance in each second as he had the second before. If there was 30 m between joe and the car he was passing then how long did it take him to pass
Answers
Answer:
537/100s.
Step-by-step explanation:
The midpoint of AB is M(3,-2). If the coordinates of A are (1, -3),
what are the coordinates of B?
Answers
Answer:
23 just took the test
Step-by-step explanation:
Answer:
B(5,-1)
Step-by-step explanation:
The formula for finding the midpoint of any line is: [ (x1+x2) / 2 ] , [ (y1+y2) / 2 ] .So, x1=1 and x2=x. And y1=-3 and y2=y.
So,
(1+x)/2=3, then manipulating it gives x=5.
And,
(-3+y)/2=-2, then manipulating the equation gives y=-1.
Hence B(5,-1)
Find the value of unknown side
Answers
Answer:
hope this helps you
have a great day
Hakim and Aziz had some savings in the ratio 3 : 5. Hakim saved another $82 and Aziz spent $110. Both have the same amount of money now. How much do each of them have now?
Answers
===========================================================
Explanation:
Hakim and Aziz have savings in the ratio 3:5. This means that Hakim has 3x dollars while Aziz has 5x dollars. The x is some positive real number.
We're then told that Hakim saved another $82, which means it goes from 3x to 3x+82
At the same time, Aziz spent $110 which means the 5x decreases to 5x-110
At this point, the two people have the same amount of money. Set the expressions we found equal to one another and solve for x.
3x+82 = 5x-110
3x-5x = -110-82
-2x = -192
x = -192/(-2)
x = 96
Then use this x value to compute each expression like so
3x+82 = 3*96+82 = 3705x-110 = 5*96-110 = 370Both have $370 after Hakim saved that additional $82 and after Aziz spent that $110.
------------------
Extra info:
If we rewind things a bit, Hakim would have 3*x = 3*96 = 288 dollars while Aziz would have 5x = 5*96 = 480 dollars. This is before any additional saving or spending.
Then note how the ratio 288:480 fully reduces to 3:5 after dividing both parts by the GCF 96.
How do I solve this
Answers
Answer:
it's 67
Step-by-step explanation:
Step-by-step explanation:
the base is already same.
-9 + (-8) - (-7) = -10
= m^-10
Which expression has the same value as -5, + (-4)?
Submit Answer
0 -5 8 3 - 4 2 3
O 4; -(-5%)
O 5+(-4)
O-52-(-41)
Answers
-9+__ =-3 find the missing value
Answers
Answer:
6
Step-by-step explanation:
-9+6=-3
The sum of a number and it's absolute value is negative.
Answers
Answer:
False; the scenario is not possible.
Step-by-step explanation:
This scenario is not possible. I will demonstrate it by representing a number by [tex]x[/tex]. There are two possibilities: [tex]x[/tex] and [tex]-x[/tex]. Let's try both:
[tex]x + |x|[/tex]
[tex]x + x[/tex]
[tex]2x[/tex]
The sum for positive [tex]x[/tex] and its absolute value is not negative. Let's try with the negative value of [tex]x[/tex] now:
[tex]-x +|-x|[/tex]
[tex]-x + x[/tex]
[tex]0[/tex]
The sum for negative [tex]x[/tex] and its absolute value is not negative either, it is zero which is neither negative or positive. Therefor, we can safely say that the scenario described is not possible.
I need help guys like rn please someone!!
Answers
Answer:
B
Step-by-step explanation:
The correct answer is B, because you have -4 +(-6)+(-2) which is really just
-4-6-2 which is -12. Think of it as getting rid of the plus sign and just leaving the negative sign. Which this would make the answer to the equation be -12, but for the answer of the question, it would be B because it is accumulating the drops in temperatures making the numbers go down in temperature, therefore making them negative.
A is not the answer because although it is similar to letter B, the difference is the final sentence, "What was the overall change in temperature?" Since -4 is listed as the pre-existing temperature, that would make -6 - 2 be equal to negative eight (-8).
C is not the answer because it includes a temperature rising by 18 degrees.
D is not the answer either because it is saying the temperature rose, which is shouldn't have risen.
The only time C and D could be right, is if they included bigger number that equaled out to negative twelve (-12), like saying the temperature rose 18 degrees, but fell by 26 degrees by midnight, that would make the equation look like -4 + 18 - 26 = - 12
Even in that case, C and D would be wrong immediately because of the use of numbers outside of the expression given.
Hope this helps!
4. Complete the following explanation to show that the sum of two rational numbers a
rational number.
Let a,b,c and d be integers. Let x and y be rational numbers. Consider the following
expression:
* = and y =
The above expressions represent the
If x + y = y + x
represents the
then, we can use the
to show that x +y = 3+. Using the rule for addition of
fractions to write an equivalent expression for x + y = 4+we obtain
The product of two integers results in an integer, so bd, ad and cb are all integers. Also.
since the sum of two integers results in an integer, ad + cb is an integer. Therefore,
xty is
Answers
Five times the sum of a number and 7 is 8
Answers
Answer:
5(n+7) = 8
Step-by-step explanation:
this is the equation you are look for if its the value of n it would be -27/5
Answer:
Step-by-step explanation:
5(x + 7) = 8
x + 7 = 8/5
x = 8/5 - 7 = -27/5 = -5.4
can someone help me with this question
Answers
Answer: The guage block height is 4.98 m
The base of the right triangle that is formed is 7.3784 m
The last angle in the triangle is 56 degrees
Step-by-step explanation:
Redraw the triangle formed in the picture and use H for the hypotenuse, O for the block height, and A for the base. Now we can use trig (SOHCAHTOA) to find the answaers.
Using sine, we can first find the gauge block height, O (Opposite). Given the Hypotenuse (H) is 8.9 m, we can use the definition of the sine of an angle to find the height, O.
Sine(34) = Opposite/Hypotenuse (O/H), or O = H*Sine(34)
O = (8.9)*(0.5592)
O = 4.98 m, the height of the gauge block,
The base of the triangle, A, can be determined with cosine.
Cosine(34) = A/O, or A = Cosine(34)*O
A = (0.82904)*(8.9)
A = 7.3784 m
The sum of all angles in a triangle is 180 degrees.
180 = X + 34 + 90
X = 56 degrees
A motorcycle can travel 48 miles for every gallon of gas used
Use the unit rate to complete the table for the miles traveled by motorcycle
Answers
Answer:
A-96
B-144
C-192
:) have a nice rest of your day!
Step-by-step explanation:
AAAAAAAAAAHHHHHHHHHHHH
Answers
Answer:
[tex] \sqrt{45 {x}^{2} } + \sqrt{5 {x}^{2} } + 4x \sqrt{5} \\ = 3 \sqrt{5} x + \sqrt{5} x + 4x \sqrt{5} \\ = 8x \sqrt{5} \\ thank \: you[/tex]
A popular amusement park has had199,792,458 visitors since it opened. Which
number, written in scientific notation, is the
best approximation of the number of visitors?
a) 0.2 x 107 visitors
b) 0.2 x 108 visitors
c) 2.0 x 107 visitors
d) 2.0 x 108 visitors
Answers
Answer:
d) 2.0 * 10⁸
Step-by-step explanation:
199,792,458 ≈ 200,000,000 = 2.0* 10⁸
The total surface area of a hemisphere is 300cm2. What is the surface area of the sphere having equal radius to the hemisphere.
Answers
Answer:
400cm²
Step-by-step explanation:
the surface area of the sphere =
4/3 x The total surface area of a hemisphere
=> 4/3 x 300 = 400cm²
I NEED HELP ASAP!!! #32!!
Answers
Answer:
If it's parallel, then it has the same slope.
Find the slope from the two coordinates and compare the slope to see which ones are right.
You should get a slope of like 2/3 from the two points, so the only equation with the same slope is B.
Your answer is B.
Simplify: 2(a-4)+15=13
Answers
Answer:
a = 3
Step-by-step explanation:
2(a−4)+15=132
a−8+15=132
a=13−15+82
a=6
a=6/2
a=3
the expression x - 0.10 X gives the cost of an item that is discounted 10% write this expression in the other way
Answers
Answer:
Step-by-step explanation:
Take out a common factor (x)
x ( 1 - 0.10 )
Now do the subtraction
0.90x
giải phương trình :
-4x-8x>0
Answers
Answer:
[tex]x < 0[/tex]
Step-by-step explanation:
[tex] - 4x - 8x > 0[/tex]
➡️ [tex] - 12x > 0[/tex]
➡️ [tex]x < 0[/tex]
A mobile device that normally sells for $99.90 is
marked down 10%. What's the discount price?
$99.00
$89.99
$89.91
$89.90
Answers
Answer:
89.90 is the answerrrrrrrrrrr
Answer:
89.91
Step-by-step explanation:
You can do this with a calculator 99.90-10%
please help easy maths
Answers
Answer:
A
Step-by-step explanation:
Answer:
Step-by-step explanation:
The y intercept occurs when x = 0.
All you have to do is read the table until you come to x = 0.
When you do, read down to get the y value.
The answer is A (0,2)
