Answers
=========================================================
Explanation:
Let's say that point A is at (0,0) and B is somewhere else on the parabola.
I'll make point B go to the right of point A.
For now, let's say B is at (4,16).
If we compute the slope of line AB, then we find the average rate of change (AROC). The AROC in this case is (y2-y1)/(x2-x1) = (16-0)/(4-0) = 16/4 = 4. Because point A is at (0,0), we're really just computing y/x where the x,y values come directly from point B.
--------------
Now let's move B to (3,9). If we used the slope formula again, we would get the slope of 3. Note how y/x = 9/3 = 3.
Then let's move B to (2,4). The AROC is now y/x = 4/2 = 2
As B gets closer to A, the AROC is decreasing. The AROC is slowly approaching the IROC (instantaneous rate of change).
--------------
Point B is generally located at (x,x^2) for any real number x. Keeping A always fixed at the origin, the slope of line AB is y/x = (x^2)/x = x.
What does this all mean? It means that if x = 0, then the IROC is 0. You might be quick to notice that we cannot divide by zero. So instead of letting x be zero itself, we'll just get closer and closer to it. This is where the concept of limits come into use. This is what calculus is based on (both integral and differential calculus).
Anyway, when calculating the IROC, we're really calculating the slope of the tangent line to the f(x) curve. Refer to the diagram below.
----------------
In short, the slope of the tangent line at x = 0 is m = 0. We have a flat horizontal line that touches the parabola at (0,0).
Related Questions
The sum of the angles of a triangle is
Select one:
a. 360
b. 180
c. 90
d. 60
Answers
Answer: b. 180
Step-by-step explanation:
The sum of the angles of a triangle is 180°.
Step-by-step explanation: The sum of all the interior angles is always180°
What is the volume of the cone? Use 3.14 for π
Answers
Answer:
What is the height, radius or diameter of the cone?????
Celeste is planning to buy a new bedroom set. Because sales tax rates can vary from town to town,
Celeste wants to compare the sales tax rates at two retail locations before making the purchase.
The price of the new bedroom set that Celeste wants to buy is $2,734. The sales tax rates in the
two cities at the time of purchase are given in the table.
Answers
9514 1404 393
Answer:
$13.67, Valdosta, Tallahassee
Step-by-step explanation:
The total sales tax rate in Valdosta is 4% +3% = 7%.
The total sales tax rate in Tallahassee is 6% +1.5% = 7.5%, which is 0.5% higher than in Valdosta. That percentage makes a difference in the final price of ...
0.5% × $2734 = 0.005×$2734 = $13.67
Celeste will save $13.67 in sales tax if she makes her purchase in Valdosta rather than Tallahassee .
What is an
equation of the line that passes through the points (0, -1) and (6, 1)?
Answers
Answer:
y = 1/3x -1
Step-by-step explanation:
The slope is y2 - y1 / x2 - x1
y2 is 1
y1 is -1
x2 is 6
x1 is 0
So it is 1 - (-1) / 6 - 0, or 2/6, or 1/3
The slope is 1/3.
The y-intercept is the place where x is 0. It shows the y-intercept here as
(0, -1), The y-intercept is -1
Slope form is y = mx + b. m is the slope, 1/3, and b is the y-intercept, -1
So the equation is: y = 1/3x -1
Select the correct answer.
Given: ΔABC
Prove: The sum of the interior angle measures of ΔABC is 180°.
Answers
Answer:
C
Step-by-step explanation:
When ever a problem gives information about parallel lines, look for Alternate Interior angles.
Answer:
A
Step-by-step explanation:
Seema is travelling to Guernsey. She travels a distance of 3,800 km by plane to London and then another 400 km to Guernsey. Both planes fly at an average speed of 900 kmh-1.
What is her total flight time in hours and minutes, to the nearest minute?
Answers
9514 1404 393
Answer:
4 hours 40 minutes
Step-by-step explanation:
The appropriate relation is ...
time = distance/speed
time = (3800 km)/(900 km/h) +(400 km)/(900 km/h) = (38+4)/9 h
= 14/3 h = 4 2/3 h
Seema's flight time is 4 hours 40 minutes.
__
2/3 of 60 minutes is 40 minutes
find <BDC. (no lines are parallel)
Answers
Answer:
35 degrees
Step-by-step explanation:
180-55-55=70
180-70=110
180-110=70
70/2=35
Property: All straight lines from the centre of a circle are the same length, hence the triangles are isoceles.
======================================================
Explanation:
Inscribed angle ABC = 55 subtends the minor arc AC which is 110 degrees (use the inscribed angle theorem).
The inscribed angle BDC subtends the minor arc CB, which we'll call x for now.
The two minor arcs (AC and CB) combine to form the arc ACB. Note how this is a semicircle since AB is a diameter. For any semicircle, the arc measure is 180 degrees.
So,
(arc AC) + (arc CB) = arc ACB
110 + x = 180
x = 180-110
x = 70
This cuts in half to 35 which is the inscribed angle BDC, again we're using the inscribed angle theorem here.
PLease Help!! will mark brainilest!!
Answers
Answer:
(x+4)(x+6)
Step-by-step explanation:
(x^2+4x)+(6x+24)
x(x+4) 6(x+4)
(x+4) (x+6)
Hãy giải giúp tôi câu tính giới hạn này
Answers
Answer:
Step-by-step explanation:
PLS HELP I WILL GIVE BRAINLIEST
Answers
Answer:
80°
Step-by-step explanation:
So as you can see, the givin angle is 100°. So that must mean that angle DBF is 80° because they are supplementary angles. (Together they equal 180°) And sense the pair of lines are parallel, and x is the smaller angle so it is 80°.
Which of the following best describes the use of the formula S = (n - 2)180°,
where n is the number of sides?
A. It is used to find the number of interior angles in a regular polygon.
B. It is used to find the sum of the interior angles in a regular
polygon.
O c. It is used to find the sum of the exterior angles in a regular
polygon
O D. It is used to find the number of exterior angles in a regular
polygon
SUBMIT
Answers
(») Evaluate the expression.
* * (4 + 8)
Answers
Answer:
6
Step-by-step explanation:
work out the brackets first....4+8=12
the multiply 1/2 by 12
1/2 x 12 = 6
What’s the range of the given function?
I marked that answer by accident btw
Answers
The range of the given function is - 2
Find the value of x.
Plz help :/
Answers
Answer:
10
Step-by-step explanat
ion:
y>2x y>3 orderd pair
Answers
[tex]y > 2x \: y \: > \: 3 \: \\ solve \: for \: x \\ x \: € \: ( \frac{3}{2y} \: \frac{1}{2} )\: y > \: 3 \\ solve \: for \: y \\ y \: > \: \frac{3}{2x} \: x \: > \: 0 \: and \: x \: < \: \frac{1}{2} [/tex]
HOPE IT HELPS!!!I NEED BRAINLIEST ✌️Which of the following is an example of data organization?
A. administering questionnaires
B. calculating a standard deviation
c. representing data with a histogram
D. declaring a statistically significant difference between groups
Answers
c) representing data with a histogram is an example of data organization
don’t understand this help please
Answers
Step-by-step explanation:
Since he sold $70,834 worth of cars, he earned an extra 5% commission on the sale. That means he got
0.05×($70,834) = $3,541.70
Therefore, his salary for the month m is
m = $2250 + 0.05s = $2,250 + $3,541.70 = $5,791.70
Determine the perimeter of the figure below
Answers
Answer:
39 feet
Step-by-step explanation:
p = 15 + 8 + 10 + 6
p = 39
39 feet
Of all the calls in the first quarter of year 5, how many were abandoned
Answers
I do not know what you mean, but ok.
The population of a rabbit colony triples each month.
The population started with 5 rabbits. How many
rabbits are there after 6 months?
Answers
Answer:
3645 rabbits after 6 months.
Step-by-step explanation:
The population of a rabbit colony triples each month.
This means that the population of the colony after t months is given by:
[tex]P(t) = P(0)(3)^t[/tex]
In which P(0) is the initial population.
The population started with 5 rabbits.
This means that [tex]P(0) = 5[/tex]
So
[tex]P(t) = 5(3)^t[/tex]
How many rabbits are there after 6 months?
This is P(6). So
[tex]P(6) = 5(3)^6 = 3645[/tex]
3645 rabbits after 6 months.
7) -4 = 2(b + 5)
please help!
Answers
Answer:
b = -7
Step-by-step explanation:
Let's solve your equation step-by-step.
−4 = 2(b + 5)
Step 1: Simplify both sides of the equation.
−4 = 2(b + 5)
−4 = (2)(b) + (2)(5)(Distribute)
−4 = 2b + 10
Step 2: Flip the equation.
2b + 10 = −4
Step 3: Subtract 10 from both sides.
2b + 10 − 10 = −4 − 10
2b = −14
Step 4: Divide both sides by 2.
[tex]\frac{2b}{2} = \frac{-14}{2}[/tex]
b = -7
Hope this helps, please mark brainliest if possible. Have a great day! :)
Which is shown by the map
Answers
Answer:
A
Step-by-step explanation:
Well I am not fully sure but I would say A
Un ganadero está reparando una mezcla de avena y harina de maíz para ganado. Cada onza de avena proporciona 4 gramos de proteína y 18 gramos de carbohidrato; una onza de harina de maíz proporciona 3 gramos de proteína y 24 gramos de carbohidratos.
¿Cuántas onzas de cada uno se pueden usar para satisfacer las metas nutricionales de 200 gramos de proteína y 1320 gramos de carbohidrato por ración?
Answers
Answer:i love you
Step-by-step explanation:
Given A = (-1 -2 3 4 8 -6 0 1 5) and B = (-5 -1 6 4 1 2 0 -3 2) What is X if B - X = A?
Answers
Answer:
5(-3)2-2(-3)+1. =5(9)+6+1. =45+7 ... 7x – 6= 0). (3x + 2)(x – 3)=0. =3x + 2 = 0; x – 3 = 0. _486x 5 – 7x. 1 1 8 1 6. uh this is hard..
Step-by-step explanation:
What is the solution of the equation x2 + 4x + 10 = 0?
Answers
Answer:
The answer for thid equation is x = -5/3
Answer Question Pls? I need Help!!
Answers
Answer:
option D
Step-by-step explanation:
Take the two through which the lines passes.
Let it be ( -5 , 0) and ( 0 , -3)
Step 1 : Find slope, m
[tex]Slope,m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
[tex]= \frac{-3-0}{0--5} = \frac{-3}{5}[/tex]
Step 2 : Find the equation
[tex](y - y_ 1) = m( x - x_1)\\\\( y - 0) = \frac{-3}{5} (x --5) \\\\y = -\frac{3}{5}( x + 5 ) \\\\y = -\frac{3}{5}x - 3[/tex]
at the present time, gerald is eight less than five times his nephews age. seven years ago gerald was 9 times his nephews age.
(A)if g represents geralds age now and n represents his nephews age today. use a system of equations that could be used to model this scenario?
(B)than use the equations to determine algebraically the ages of both Gerald and his nephew.
(C)than determine in how many years Gerald will be three times as old as his nephew?
Answers
What you know about rollin' down in the deep?
When your brain goes numb, you can call that mental freeze
When these people talk too much, put that sh*t in slow motion, yeah
I feel like an astronaut in the ocean, ayy
What you know about rollin' down in the deep?
When your brain goes numb, you can call that mental freeze
When these people talk too much, put that sh*t in slow motion, yeah
I feel like an astronaut in the ocean
Divide the following two complex numbers.
3+2i
5-3i
Answers
Step-by-step explanation & answer:
Conjugate = 5+3i
Multiply fraction by conjugate:
(15+9i+10i+6i^2) / (25-9i^2)
Simplify:
(15+19i+6i^2) / (25-9i^2)
i^2 is -1:
(15+19i-6) / (25+9)
So:
9+19i / 34
Into a +bi form:
9/34 + 19i/34
Selena Gomez is running the Gary Mintz Marathon. After 6 miles, Selena Gomez's clock reads 48 minutes. If Selena Gomez maintains her current pace, what will her clock read at 20 miles? You can use the table below to calculate her times.
A : 56
B: 160
C: 140
D: 96
Answers
Answer:
The answer would be C: 140.
How much will you have if : S900 invested at 6% compounded semiannually
for 5 years.
Answers
Answer:
Step-by-step explanation:
A = P(1+r/n)^nt
A = 900(1 + .06/2)^(5*2)
A = 900(1.03)^10
A=1209.52