Derivatives concept:
Equation of the secant line and tangent to a curve.
Let the function [tex]f(x)=2x^{2}+1[/tex] and its graph be:
(In both graphs (activity A and B) all the corresponding development must be carried out to arrive at the requested equation)
![Derivatives Concept:Equation Of The Secant Line And Tangent To A Curve.Let The Function [tex]f(x)=2x^{2}+1[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/EoaVcKCunuUW2JCmopONoSrx0mEzAwKj.jpeg)
![Derivatives Concept:Equation Of The Secant Line And Tangent To A Curve.Let The Function [tex]f(x)=2x^{2}+1[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/bbdgBZZBBEvVvFlSnixsjQSGpBzGlutJ.jpeg)
Answers
9514 1404 393
Answer:
A. y = -2x +13
B. y = 8x -7
Step-by-step explanation:
A. We can read the y-intercept of the secant line from the graph. It is 13.
The slope can also be read from the graph, but we choose to use the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (19 -9)/(-3 -2) = 10/-5 = -2
Then the slope-intercept formula for the line is ...
y = mx + b . . . . . . line of slope m and y-intercept b
y = -2x +13
__
B. The vertex of the given parabola is (0, 1). We notice that when x=1 (1 unit right of the vertex), y = 3 (2 units up from the vertex). This tells us the vertical scale factor of the parabola is 2. That means the vertex form equation is ...
y = a(x -h)^2 +k . . . . . . . . vertex (h, k), scale factor 'a'
y = 2(x-0)^2 +1 . . . . . . . use known values for (h, k)
y = 2x^2 +1
The derivative of this is ...
y' = 4x
So, at x=2, the given point A, the slope of the tangent line is ...
m = y' = 4(2) = 8
We have a point and the slope, so we can write the point-slope form of the equation for the tangent line:
y -9 = 8(x -2)
Rearranging to slope-intercept form, this is ...
y = 8x -7
__
Additional comment
You can also read the slope of the tangent line from the graph. The line also goes through the point (1, 1), so has a rise of 8 for a run of 1. The y-intercept can be found from ...
b = y -mx = 9 -8(2) = -7
This lets you write the equation of the tangent line directly from the graph.
That is, the parameters of both lines can be read from the graph, so there is very little "development" required.
Related Questions
A publisher reports that 54% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 200 found that 44% of the readers owned a personal computer. Is there sufficient evidence at the 0.10 level to support the executive's claim
Answers
The null and alternate hypotheses are
H0 : u = 0.44 vs Ha: u > 0.44
Null hypothesis: 44% of readers own a personal computer.
Alternate Hypothesis : greater than 44% of readers own a personal computer.
This is one tailed test and the critical region for this one tailed test for the significance level 0.1 is Z > ±1.28
The given values are
p1= 0.54 , p2= 0.44 ; q2= 1-p2= 0.56
Using z test
Z = p1-p2/√p2(1-p2)/n
Z= 0.54-0.44/ √0.44*0.56/200
z= =0.1/ 0.03509
z= 2.849
Since the calculated value of Z= 2.849 is greater than Z= 1.28 reject the null hypothesis therefore there is sufficient evidence to support the executive's claim.
Null hypothesis is rejected
There is sufficient evidence to support the executive's claim at 0.10 significance level.
https://brainly.com/question/2642983
The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.)
Answers
Answer:
a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c) the required probability is 0.2000
Step-by-step explanation:
Given the data in the question;
During a specific ten-hour period, one defective circuit board was found.
Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.
Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.
f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex]; ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]
= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
Now,
a) the probability that it was produced during the first hour of operation during that period;
P( Y < 1 ) = [tex]\int\limits^1_0 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^1_0[/tex]
= [tex]\frac{1}{10} [ 1 - 0 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) The probability that it was produced during the last hour of operation during that period.
P( Y > 9 ) = [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^{10}_9[/tex]
= [tex]\frac{1}{10} [ 10 - 9 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c)
no defective circuit boards were produced during the first five hours of operation.
probability that the defective board was manufactured during the sixth hour will be;
P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )
= P( 5 < Y < 6 ) / P( Y > 5 )
we substitute
[tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]
[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]
= ( 6-5 ) / ( 10 - 5 )
= 0.2000
Therefore, the required probability is 0.2000
a film lasts 45 minutes what fraction of the film is left after 15 minutes and 25 minutes ?
Answers
Answer: i) [tex]\frac{1}{3}[/tex]
ii) [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Total length of film = 45 mins
Fraction of time left after 15 mins = [tex]\frac{15}{45}[/tex]
= [tex]\frac{1}{3}[/tex]
Fraction of time left after 25 mins = [tex]\frac{25}{45}[/tex]
= [tex]\frac{5}{9}[/tex]
Find the slope of the graphed line
Answers
Answer:
4
Step-by-step explanation:
Pick two points on the line
(0,-5) and (1,-1)
We can find the slope using
m = (y2-y1)/(x2-x1)
= ( -1 - -5)/(1 - 0)
(-1+5)/(1-0)
4/1
= 4
Write an equation and solve it to answer each question. A pile of 55 coins consisting of nickels and dimes is worth $3.90. Find the number of each. I only need the equation plz. WILL MARK BRAINLIEST.
Answers
Answer:
0.05x + 0.1(55 - x) = 3.9
Step-by-step explanation:
There are 55 coins.
Let x = number of nickels.
The number of dimes is 55 - x.
The value of a nickel is $0.05, and the value of a dime is $0.10.
The value of x nickels is 0.05x
The value of 55 - x dimes is 0.1(55 - x)
The total value of the coins is 0.05x + 0.1(55 - x)
The total value of the coins is $3.90
0.05x + 0.1(55 - x) = 3.9
Last year at a certain high school, there were 56 boys on the honor roll and 150 girls on the honor roll. This year, the number of boys on the honor roll decreased by 25% and the number of girls on the honor roll decreased by 12%. By what percentage did the total number of students on the honor roll decrease?
Answers
Answer:
15.534% decrease
Step-by-step explanation:
Find the new number of boys and girls on the honor roll:
56(0.75) = 42 boys
150(0.88) = 132 girls
Find the new total number of students on the honor roll:
42 + 132 = 174
Find the percent decrease by dividing the difference in the number of students by the original number.
There were originally 206 total students on the honor roll. Find the difference:
206 - 174 = 32
Divide this by the original amount:
32/206
= 0.15534
So, the number of students on the honor roll decreased by approximately 15.534%
Whats the volume of this aquarium?
PLZ HELP!!
Answers
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope:
3/2
ordered pair: (3, 1)
Answers
Answer:
y = 3/2x-2
Step-by-step explanation:
slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = 3/2x+b
Substitute the point in for x and y
1 = 3/2(2)+b
1 = 3+b
1-3 =b
-2=b
y = 3/2x-2
The family trip to Grandma's consisted of both a train ride and a car ride. The average speed of the train ride was 72 miles per hour, and the average speed of the car ride was 62 miles per hour. The entire trip lasted 6 hours.
Let x be the number of hours the train ride lasted. Write an expression for the total distance of the trip, in miles.
Answers
Answer:
432
Step-by-step explanation:
x=1hr (6x)=6hours x= 72 hours through train so (6x)=72x6=432
Let x be the number of hours the train ride lasted. Write an expression for the total distance of the trip, in miles.
Answer-432
Factor completely 12a^3d^2 – 6ad^3
Answers
Answer:
[tex]12a^3d^2-6ad^3[/tex]
To factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5
In the end, the number of times each prime divides the original integer becomes its exponent.
Prime number 2 to the power of 2 equals 4 .
Prime number 3 to the power of 1 equals 3 .
[tex]2^{2} \times 3\times a^{3} \times b^{2} -(2\times3)ad^{3}[/tex]
Result:- [tex]6ad^2\left(2a^2-d\right)[/tex]
OAmalOHopeO
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answers
Answer:
2x-1=3
2x=3+1
2x=4
x=2
[tex]\huge\boxed{\underline{\bf \: Answer}}[/tex]
(a) Let's try with x = - 1
[tex] \sf \: 2x - 1 = 3 \\\sf 2( - 1) - 1 = 3 \\ \sf- 2 - 1 = 3 \\ \\ \boxed{\bf- 3 \: \bcancel= \: 3}[/tex]
So, x = - 1 is not the solution to the given equation.
______________
(b) Now, try with x = 2
[tex]\sf2x - 1 = 3 \\ \sf2(2) - 1 = 3 \\ \sf4 - 1 = 3 \\ \\ \boxed{\bf3 = 3}[/tex]
Yes, we can see that x = 2 is the correct solution for the equation.
______________
Hope it helps.
RainbowSalt2222
The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 28 ft^2. Find the dimensions of the rectangle.
Answers
Answer:
7 x 4
Step-by-step explanation:
Let the width be x, length will be 3x-5. ATQ, x(3x-5)=28. x=4 and x=-7/3, since length isn't negative, x=4. Width=4 and length=7
Find the sum : (i) 23123, 11001 and 21302 (iii) 21031, 12301 and 32211 (v) 21003, 12346 and 21220 (ii) 32101, 12301 and 1032 (iv) 301242, 123310 and 10002
Answers
Answer:
(i) 23123 + 11001 + 21302 = 55426(ii) 32101 + 12301 + 1032 = 45434(iii) 21031 + 12301 + 32211 = 65543(iv) 301242 + 123310 + 10002 = 434554(v) 21003 + 12346 + 21220 = 545691:-
[tex]\\ \sf\longmapsto 23123+11001+21302[/tex]
[tex]\\ \sf\longmapsto 55426[/tex]
2:-
[tex]\\ \sf\longmapsto 21031+12301+32211[/tex]
[tex]\\ \sf\longmapsto 65543[/tex]
3:-
[tex]\\ \sf\longmapsto 21003+12346+21220[/tex]
[tex]\\ \sf\longmapsto 54569[/tex]
4:-
[tex]\\ \sf\longmapsto 32101+12301+1032[/tex]
[tex]\\ \sf\longmapsto 45434[/tex]
5:-
[tex]\\ \sf\longmapsto 301242+123310+10002[/tex]
[tex]\\ \sf\longmapsto 434554[/tex]
Rachael needs to rent a car while on vacation. The rental company charges $17.95, plus 19 cents for each
mile driven. If Rachael only has $40 to spend on the car rental, what is the maximum number of miles she
can drive?
Answers
Answer:
116 miles
Step-by-step explanation:
We can solve this by first writing an equation for the cost of the car rental. To begin, the base cost is $17.95, so any further costs must be added to that. Next, the car costs 19 cents (0.19 dollars) for each mile driven, so for each mile, we add 19 cents. This can be written as 0.19 *x if x represents the amount of miles driven. Therefore, we can add the two input costs of the car (the base cost and cost per mile) to get
17.95 + 0.19 * x = total cost.
After that, we want to maximize x/the number of miles with only 40 dollars. We can do this by setting this equal to the total cost, as going over the total cost is impossible and going under would be limiting the amount of miles (this because we are adding money for each mile, so more money means more miles). Therefore, we have
17.95 + 0.19 * x = 40
subtract 17.95 from both sides to isolate the x and its coefficient
22.05 = 0.19 * x
divide both sides by 0.19 to isolate x
22.05/0.19 = x = 116.05
The question asked us to round down, and 116.05 rounded down is 116 for our answer
what is 3/16 of 200 written as a percentage?
Answers
Answer:
Step-by-step explanation:
3/16 = 0.1875
As a % this is 18.75%
18.75/100 * 200 = 37.5
I'm not sure from the question, exactly what you want. 18.75% of 200 is one possibility.
3/16 of 200 as a percentage is 3750%
The question can be represented as:
[tex]\frac{3}{16} * 200[/tex]
Rewrite as:
[tex]\frac{3}{16} * 200 =\frac{3* 200}{16}[/tex]
Multiply the numerator
[tex]\frac{3}{16} * 200 =\frac{600}{16}[/tex]
[tex]\frac{3}{16} * 200 =37.5[/tex]
Multiply by 100% to represent it as a percentage
[tex]\frac{3}{16} * 200 =37.5 * 100\%[/tex]
[tex]\frac{3}{16} * 200 =3750\%[/tex]
Read more at:
https://brainly.com/question/19994306
If anyone knows answer with steps that will be greatly appreciated :)
Answers
Answer:
The area formula is= 1/2(a+b)×height
1/2×20×6=60metres squared
Step-by-step explanation:
kindly correct me if am wrong
A tank filled with water begins draining. The number of minutes t since the water began draining from the tank is a function of the number of gallons of water in the tank, v. We will call this function f so that f(t) = v.
Required:
a. Using function notation, represent the of gallons of water in me tank 4 minutes after the water darning from the Ink.
b. Suppose that f(4) = 7, what does this mean in the context of the problem?
Answers
Answer:
[tex](a)\ f(4) = v[/tex]
(b) There are 7 gallons left in the tank after 4 minuted
Step-by-step explanation:
Given
[tex]f(t) = v[/tex]
[tex]t \to[/tex] time since water began draining
[tex]v \to[/tex] gallons in the tank
Solving (a): Notation for gallons remaining at 4 minutes
This means that [tex]t=4[/tex]
[tex]f(t) = v[/tex] becomes
[tex]f(4) = v[/tex]
Solving (b): Interpret f(4) = 7
We have:
[tex]f(t) = v[/tex]
[tex]t \to[/tex] time since water began draining
[tex]v \to[/tex] gallons in the tank
This means that:
[tex]t =4[/tex]
[tex]v =7[/tex]
It can be interpreted as:
There are 7 gallons left in the tank after 4 minuted
What’s v=(324pie)(3)
Answers
Fixed costs are $2000, and the cost of producing each pair of skies is $100. The selling price is $220 (per pair). How many pairs should be sold to make a profit of $29200?
Answers
260 pairs
Step-by-step explanation:
220-100= 120
(29200+2000)÷120= 260
For what value of x is the parallelogram a rhombus.
Answers
Answer:
Step-by-step explanation:
2 × ( 3x + 6 )° + ( 16x + 14 )° = 180°
22x + 26 = 180
22x = 154
x = 7
Can you please me with the word problem thank you so much
Answers
Answer:
4. 53
5. 66
6. 89
7. 31
Step-by-step explanation:
4. 14 + 18 + 21
^ ^
33 + 21
53
5. 86 - 20
66
6. 34 + 55
89
7. 14 + 11 + 6
^ ^
25 + 6
31
Please help me to find this answer
Answers
Step-by-step explanation:
question 1
angle DBA=90°, meaning to find m<D you have to add 90+38 then subtract by 180, because ABD is a triangle
90+18+m<D=180
108+m<D=180
m<D=180-108
=72°
question 2
m<D again in this case angle ABD is also 90
m<D=180-(90+48)
=180-138
=42°
I hope this helps
Evaluate: 2-4
1
O A.
loo
O B.-8
O c.
1
16
O D.-16
Answers
Answer:
c is the answer
[tex] \frac{1}{16} [/tex]
It is claimed that the average child has no time to go to school. For the child spends 8 hours per day,or one third of his/her time sleeping. Based on a 365 day year, that’s 121.67days sleeping. Also the child spends three hours per day eating. That’s a total of 45 days in the year spent eating. Also the child spends 90 days taking summer vacation. Also the child spends 21 days on Christmas and Easter holiday. Finally, the child has each Saturday and Sunday off. That’s a total of 104 days. In short, we (rounding to whole days accounted for 122+45+90+21+104=382 days of the year taken up by ordinary child inlike activities. This is already more than the 365 days that are known to comprise a year. We conclude that there is certainly no time for the child to attend school. What is wrong with this reasoning?
Answers
Answer:
See below.
Step-by-step explanation:
Sleeping:
8/24 * 365 = 121.76 days
Eating:
3/24 * 365 = 45.63 days
Total sleeping and eating: 167 days
Summer Vacation & Holidays:
90 + 21 = 111 days
Saturdays and Sundays: 52 + 52 = 104 days
Vacation + Holidays Saturdays + Sundays = 111 + 104 = 215 days
It may be true that all days of vacation, holiday, Saturdays, and Sundays combined are a total of 215 days, but these 215 days cannot be added to the 167 days above because these 215 days include time for sleeping and eating which was already included in the sleeping and eating times for the entire year. The mistake in the reasoning is counting twice the time of sleeping and eating on the 215 days in which there is no school.
Which values of a and b make this system of equations have infinitely many solutions?
2y + 16 = 6x
y = ax + b
a = -3, b = 8
a = -3, b = -8
a = 3, b = -8
a = 3, b = 8
Answers
9514 1404 393
Answer:
a = 3, b = -8
Step-by-step explanation:
Solving the first equation for y, we get ...
2y +16 = 6x . . . . . given
y = 8 +3x . . . . . . . divide by 2
y = 3x -8 . . . . . . . subtract 8
In order for the system of equations to have infinitely many solutions, the second equation must be the same as this:
y = ax +b
a = 3, b = -8
write your answer in simplest radical form
Answers
Answer:
a = 3√6 in
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 60°
Adjacent = 3√2 in
Opposite = a =?
The value of 'a' can be obtained by using the tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 60 = a / 3√2
√3 = a / 3√2
Cross multiply
a = √3 × 3√2
Recall:
c√d × n√m = (c×n) √(d×m)
Thus,
√3 × 3√2 = (1×3)√(3×2)
√3 × 3√2 = 3√6
a = 3√6 in
find the value of n . 80×π×n=1100000
Answers
Answer:
110000/8π
Step-by-step explanation:
Divide 1100000 by 80 and cancel 0. Then divide pi
If sin x = –0.1 and 270° < x < 360°, what is the value of x to the nearest degree?
Answers
Answer:
354°15'38.99''
Step-by-step explanation:
The diameter of a cone is 34 ft. the height is 16 ft what is the volume in cubic ft?
Answers
Answer:
4842.24 cubic feet
Step-by-step explanation:
Use the formula for the volume of a cone, V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
The diameter of the cone is 34 ft, so the radius is 17 ft.
Plug in the radius and height into the formula, and solve for the volume:
V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
V = [tex]\pi[/tex](17)²[tex]\frac{16}{3}[/tex]
V = [tex]\pi[/tex](289)[tex]\frac{16}{3}[/tex]
V = 4842.24
So, the volume of the cone is 4842.24 cubic feet
Answer:
4,841.32 ft³.
Step-by-step explanation:
Let’s assume that this is a right circular cone and that the radius of the cone is r.
For our problem, r = (1/2)d = (1/2)34 = 17.
The volume of the cone is:
V = (1/3)pi r^2 h, where r is the radius and h is the height.
So, V = (1/3)pi(17^2)16 = 4,841.32 ft³.
Cho hình thang ABCD vuông tại A và D biết AB=AD=3cm, BC=6cm. Tính góc C và D
Answers
Answer:
C=6cm
D=3cm
Step-by-step explanation:
C=6×6cm
36cm
D=3×3cm
=9cm
