Will mark brainliest
Find an equation of the tangent line to the function
y = 3x2
at the point P(1, 3).
Solution
We will be able to find an equation of the tangent line ℓ as soon as we know its slope m. The difficulty is that we know only one point, P, on ℓ, whereas we need two points to compute the slope. But observe that we can compute an approximation to m by choosing a nearby point
Q(x, 3x2)
on the parabola (as in the figure below) and computing the slope mPQ of the secant line PQ. [A secant line, from the Latin word secans, meaning cutting, is a line that cuts (intersects) a curve more than once.]
Answers
The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.
How to determine the equation of a line tangent to a quadratic equation by algebraic methods
Herein we must determine a line tangent to the quadratic equation y = 3 · x² at the point P(x, y) = (1, 3) by algebraic means. The slope of the line can be found by using the secant line formula and simplify the resulting expression:
m = [3 · (x + Δx)² - 3 · x²] / [(x + Δx) - x]
m = 3 · [(x + Δx)² - x²] / Δx
m = 3 · (x² + 2 · x · Δx + Δx ² - x²) / Δx
m = 3 · (2 · x + Δ x)
If Δx = 0, then the equation of the slope of the tangent line is:
m = 6 · x
If we know that x = 1, then the slope of the tangent line is:
m = 6 · 1
m = 6
Lastly, we find the intercept of the equation of the line: (x, y) = (1, 3), m = 6
b = y - m · x
b = 3 - 6 · 1
b = - 3
The equation of the tangent line to the quadratic function y = 3 · x² at the point (x, y) = (1, 3) is y = 6 · x - 3.
To learn more on tangent lines: https://brainly.com/question/23265136
#SPJ1
Related Questions
How does Mathematics differ from language to language across the world
Answers
The answer is explained below.
In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.
Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.
Learn more about mathematics click;
https://brainly.com/question/27235369
#SPJ1
Troys toy box is 4 ft x 3ft x 5 ft. What is the Volume of his toy box?
Answers
Answer:
60 ft^2
Step-by-step explanation:
To get the total volume we will need to multiply all the lengths. This means we will have to do 4 x 3x 5.
4 x 3 x 5 = 15x 4 = 60
Answer:
60 ft³
Step-by-step explanation:
V = 4 ft × 3 ft × 5 ft
V = 12 ft² × 5 ft
V = 60 ft³
#CMIIWwhat do you add to get the pattern 1, 8, 15, 22, 29 36, 43
Answers
Answer:
7
Step-by-step explanation:
Finding the common difference of an arithmetic sequence is easy peasy lemon squeezy. All you have to do is take any term and subtract it from the next one. For instance, if you take 1 and subtract it from 8, you get 7. If you take 8 and subtract it from 15, you get 7 again. You can do this for any pair of terms and you will always get 7. That's the common difference of the sequence 1, 8, 15, 22, 29, 36, 43. It means that you just add 7 to each term to get the next one. Isn't that neat?
A student has scores of 63, 65, and 73 on his first three tests. He needs an average of at least 70 to earn a grade of C in the class.
What is the minimum score that the student needs on the fourth test to ensure a C?
Answers
Answer: 79
Step-by-step explanation:
63+65+73+×/4=79
multiply by 4 on both sides
201+x=280
subtract 201 from both sides
x= 79
Tommy and Ruth are cycling to meet each other. Tommy cycles twice as fast as Ruth and they both set off at the same time. At which coordinate will they meet?
Answers
Tommy and Ruth will meet at a coordinate that is 0.5x km away from Ruth's starting point.
In this problem, Tommy and Ruth are cycling towards each other. We are given that Tommy cycles twice as fast as Ruth and they both start cycling at the same time. Our goal is to determine at which coordinate they will meet.
To solve this problem, we need to use the concept of distance, speed, and time. Let's assume that Ruth cycles at a speed of "x" km/hr. Since Tommy cycles twice as fast as Ruth, his speed will be "2x" km/hr.
Let's say that Tommy and Ruth meet at a distance of "d" km from Ruth's starting point. Now, let's calculate the time taken by both Tommy and Ruth to reach this point.
Time taken by Ruth = Distance/Speed = d/x
Time taken by Tommy = Distance/Speed = d/2x
Since they both start cycling at the same time, we can set these two equations equal to each other:
d/x = d/2x
We can then simplify this equation by multiplying both sides by 2x:
2d/x = d
Now we can solve for "d" by multiplying both sides by "x":
2d = dx
d = 0.5x
This means that Tommy and Ruth will meet at a coordinate that is 0.5x km away from Ruth's starting point. To determine the exact coordinates, we need to know where Ruth started cycling from and in which direction they are cycling. If we assume that Ruth started cycling from the origin (0,0) and they are cycling towards each other on a straight path, then they will meet at the coordinate (0.5x, 0).
To know more about Coordinate here
https://brainly.com/question/27749090
#SPJ1
Gavin is working two summer jobs making $14 per hour tutoring and $13 per hour landscaping. Last week Gavin worked a total of 10 hours and earned a total of $137. Determine the number of hours Gavin worked tutoring last week and the number of hours he worked landscaping last week.
Answers
Answer:
3 landscaping, 3 tutoring
Step-by-step explanation:
This is a system of equations.
Let T = number hours tutoring and L = number hours landscaping.
T + L = 10
137 = 14T + 13L
Now solve the system of equations.
We can rearrange the first equation so that T = 10-L. Substitute that in the 2nd equation.
137=14(10-L) + 13L
137 = 140-14L + 13L
-3=-L
3=L
He worked 3 Landscaping Hours. Substitute back into the original equation to solve for T (tutoring hours).
T+L = 10
T+3 = 10
T = 7.
We worked 7 tutoring hours.
Now double check with the earnings equation.
137 = 14T + 13L
137 = 14*7+ 13*3
137 = 98 + 39
137=137
Which factor of 24 can help you solve 24 divided by 4?
Answers
Answer:
im an expert
Step-by-step explanation:
The figure below shows the distance between two cities on a map. The scale of the map is 1 }8 inch to 12 miles.
Answers
The actual distance between the two cities is 432 miles.
The figure shows a map of two cities, with a distance between them measured at 4.5 inches.
The scale of the map is given as 1/8 inch to 12 miles.
This means that 1/8 inch on the map represents a distance of 12 miles in real life.
To determine the actual distance between the two cities, we can use the scale provided.
1/8 inch on the map represents 12 miles in real life.
A proportion to find the actual distance between the cities:
1/8 inch on map = 12 miles in real life
4.5 inches on map = x miles in real life
To solve for x, we can cross-multiply and simplify:
1/8 × x = 12 × 4.5
x = 12 × 4.5 × 8
x = 432 miles
Maps with scales can be useful for determining distances, sizes, and proportions of objects in real life.
It allows us to visually represent complex spatial relationships and make measurements without physically being present at the location.
Remember to use the correct scale and make sure to convert units properly in order to accurately determine real-life measurements.
For similar questions on Actual Distance
https://brainly.com/question/29363431
#SPJ11
1459 divided by 6 with remainder as fraction
Answers
Answer:
6 1/243
Step-by-step explanation:
6 goes into 1459, 243 times
243*6=1458
1459-1458=1
So there is a remainder of 1
So the answer would be 6 1/243
This as a fraction is also 1459/6.
This with a remainder is 1459 R1
Hope this helps :D
The Nut Shack sells cashews for $6.80 per pound and Brazil nuts for $4.70 per pound. How much of
each type should be used to make a 37 pound mixture that sells for $5.78 per pound?
Round answers to the nearest pound.
pounds of cashews
pounds of Brazil nuts
> Next Question
Answers
Answer:
Step-by-step explanation:
$6.80 x 19 pounds = $129.2
$4.70 x 18 pounds = $84.6
+___________________
37 pounds = $213.8
$213.8 divided by 37 pounds = 5.77837......
= $5.78 per pound
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.
What is the domain of the relation?
{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}
Answers
The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.
How to determine domain relation?The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.
Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.
Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.
Hence, the correct option is {−4, −2, 0, 3, 5}.
Find out more on domain here: https://brainly.com/question/26098895
#SPJ1
X/5-y = m-1 resolver para y
Answers
Okay, let's solve this step-by-step:
X/5-y = m-1
Add y to both sides:
X/5 = m
Multiply both sides by 5:
X = 5m
So in this equation, X = 5m.
To find y, we subtract m-1 from both sides of the original equation:
X/5 = 5m
X/5 - (m-1) = 5m - (m-1)
X/5 - m + 1 = 4m
(X - 5m) / 5 = m - 1
X - 5m = 5(m - 1)
X = 20m - 5
So if we let m = any value, we can calculate y. For example:
If m = 3, then:
X = 20*3 - 5
= 55 - 5 = 50
50/X = 5(m - 1) = 5*2 = 10
y = 10
Does this make sense? Let me know if you have any other questions!
513.4497 rounded to the hundredths place
Answers
Answer:
513.45
Step-by-step explanation:
use intelligence
A natural food company produces and sells organic almond milk for $9.00 per gallon. This company
estimates its fixed costs to be 1121 dollars per month and the variable cost to produce each gallon of
almond milk is $7.50.
What is the margin of profit if 1494 gallons of almond milk are produced and sold each month?
A Select an answer of $
Answers
Okay, here are the steps to solve this problem:
Fixed costs per month: $1121
Variable cost per gallon: $7.50
Selling price per gallon: $9.00
Monthly sales (gallons): 1494
Cost of goods sold = Variable cost per gallon * Monthly sales
= $7.50 * 1494 gallons
= $11,105
Gross margin = Revenue - Cost of goods sold
= $9 * 1494 gallons
= $13,446
- $11,105 (Cost of goods sold)
= $2,341
Margin of profit = Gross margin - Fixed costs
= $2,341 - $1121
= $1,220
So the margin of profit if 1494 gallons are produced and sold each month is $1,220.
The answer is:
B $1,220
Carlos is a door to door vacuum salesman. His weekly salary, S, is $400 plus $35 for each vacuum he sells.
This can be written as S = 400+35v , where v is the number of vacuums sold.
If Carlos earns $1590 for a week's work, how many vacuums did he sell?
Answers
Answer:
34
Step-by-step explanation:
1. Plug in the week's salary into the formula
S=400+35v
1590=400+35v
2. Solve for v.
1590=400+35v
Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.
1190=35v
Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.
34=v
If ARSU-AVST, then the triangles are
similar by:
Answers
Answer:
AA sim post
Step-by-step explanation:
They DO have equal (similar) angles.....but they do not have equal sides
Out of 1000 students who appeared in an examination,60% passed the examination.60% of the failing students failed in mathematics and 50% of the failing students failed in English.If the students failed in English and Mathematics only, find the number of students who failed in both subjects.
Answers
The value of number of students who failed in both mathematics and English is 40.
Since, Given that;
60% of the 1000 students passed the examination,
Hence, we can calculate the number of students who passed the exam as follows:
60/100 x 1000 = 600
So, 600 students passed the examination.
Now, let's find the number of students who failed the examination.
Since 60% of the students passed, the remaining 40% must have failed. Therefore, the number of students who failed the examination is:
40/100 x 1000 = 400
Of the 400 failing students, we know that 60% failed in mathematics.
So, the number of students who failed in mathematics is:
60/100 x 400 = 240
Similarly, we know that 50% of the failing students failed in English.
So, the number of students who failed in English is:
50/100 x 400 = 200
Now, we need to find the number of students who failed in both subjects.
We can use the formula:
Total = A + B - Both
Where A is the number of students who failed in mathematics, B is the number of students who failed in English, and Both is the number of students who failed in both subjects.
Substituting the values we have, we get:
400 = 240 + 200 - Both
Solving for Both, we get:
Both = 240 + 200 - 400
Both = 40
Therefore, the number of students who failed in both mathematics and English is 40.
Learn more about the subtraction visit:
https://brainly.com/question/17301989
#SPJ1
Round 73,609 to the nearest thousand
Answers
Answer:
74,000
Step-by-step explanation:
use intelligence
help me please!! I’m not quite sure how to solve this so explanations for this will be appreciated
Answers
The solution is:
the area of this figure is 21.9 ft².
Here, we have,
To find the area of this figure, we must find the area of the 6 x 6 square and subtract the area of a semi-circle with a diameter of 6.
Area square:
6 x 6
36
Area semi-circe:
A = 1/2(πr²)
A = 1/2(6/2)²π
A = 1/2(9π)
A = 14.1
Area shape:
36 - 14.1
21.9
The units are ft², so the answer is 21.9 ft².
To learn more on Area click:
brainly.com/question/20693059
#SPJ1
An object in the shape of a rectangular prism has a length of 9 inches, a width of 5 inches, and a height of 4 inches. The object's density is 11.1 grams per cubic centimeter. Find the mass of the object to the nearest gram.
Answers
Answer:
32.741 kg---------------------------
Mass is the product of the volume and density and the volume of the rectangular prism is the product of its three dimensions.
Find the volume first:
V = 9*5*4 = 180 in³Convert volume to cm³, taking 2.54 cm per in:
180*(2.54)³ = 2949.67152 cm³Find the mass:
Mass = 11.1*2949.67152 = 32741.353872 g ≈ 32.741 kg (rounded)A bag contains 40 marbles. 12 of the marbles are red. What is the percent of red marbles in the bag?
Answers
Answer:
the percentage of red marbles in the bag is 30%.
Step-by-step explanation:
To find the percentage of red marbles in the bag, we need to divide the number of red marbles by the total number of marbles and then multiply by 100:
Percentage of red marbles = (Number of red marbles / Total number of marbles) x 100
Number of red marbles = 12
Total number of marbles = 40
Percentage of red marbles = (12/40) x 100
= 0.3 x 100
= 30%
Therefore, the percentage of red marbles in the bag is 30%.
There are 5,144 blocks to be placed
evenly into 8 storage containers. How
many blocks are in each storage
container?
Answers
Divide the total number of blocks by the total number of storage containers.
5144/8 = 643 blocks in each storage container.
ABCD is a rectangle. If AC is 20 inches, what is DE?
B
Al
E
C
D
Answers
The measurement of DE is 10 inches.
If we know that E is the point where the diagonals of the rectangle intersect, then we know that DE is equal to half the length of the diagonal BD.
Using the Pythagorean theorem, we can relate the length of the diagonal BD to the sides of the rectangle.
Let's assume that the length of the rectangle is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:
BD = √(L^2 + W^2)
Since we know that the diagonals of a rectangle are equal, we have:
AC = BD
BD = 20
Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.
Learn more about rectangles here:
https://brainly.com/question/29147156
#SPJ1
The dosage the pharmacy carries in stock (on hand), is different than the prescribers order. Use ratio and proportion to calculate the total quantity of tablets to dispense for each of the prescriptions below: Order: Zocor 40 mg po qd for 60 days On hand: 20 mg tabs How many 20 mg tabs should be given? Give:
Answers
Using ratios and proportions, the number of 20 mg tabs that should be given in place of 40 mg po qd for 60 days is 120 tabs.
How the number is determined:Using ratios and proportions, the number of tabs of 20 mg that should be given in place of 40 mg qd for 60 days is determined as follows:
Order: Zocor 40 mg po qd for 60 days
= 60 tabs since it is once per day (qd)
Total mg = 2,400 mg (40 mg x 60 tabs)
On hand: 20 mg tabs
Proportionately, 20 mg = 120 tabs (2 x 60) since 40 mg is for 60 tabs
Total mg = 2,400 mg (20 mg x 120 tabs)
Learn more about ratios and proportions at https://brainly.com/question/29774220.
#SPJ1
please help fast i don’t feel like typing
Answers
Answer:
he should have subtracted 17 from both sides of the equation
Step-by-step explanation:
x+ 17 = 22
subtract 17 from both sides
X + 17 = 22
-17 -17
x = 5
Find surface area without mistaking the lateral height.
Answers
The total "surface-area" of cone having "slant-height" as 10, and base-radius as 6, is 301.44 square units.
The total surface area of a cone can be calculated by adding the area of the base to the lateral surface area.
Let us first calculate the lateral surface area of the cone:
Lateral surface area = πrl; where r is radius , and 'l" = slant-height,
The radius of base = 6 units and slant height is = 10 units.
So, we have:
Lateral surface area = π × 6 × 10
Lateral surface area = 60π square units
Next, Area of the base = πr²;
Area of the base = π × 6²,
Area of the base = 36π square units,
Total surface area = Lateral surface area + Area of the base
Total surface area = 60π + 36π
Total surface area = 96×3.14 = 301.44 square units.
Therefore, the total surface area of cone is 301.44 square units.
Learn more about Surface Area here
https://brainly.com/question/29147652
#SPJ1
6% pay increases 62,900 thanks i look forward to the additional _ per month
Answers
Answer:
Step-by-step explanation:
$314.50
The pay increase is 6% of $62,900, which is:
0.06 x $62,900 = $3,774
Therefore, the additional pay per month is:
$3,774 / 12 = $314.50
So, Ciara can look forward to an additional $314.50 per month.
Scores on a final exam in a large class were normally distributed with a mean of 75 and a standard deviation of 8. What percent of the students scored above an 83?
Answers
Using z - score, the percentage of students above 83 is 15.9%
What is the percentage of students that scored above 83?To find the number of students that scored above 83 can be calculated using z - score formula.
This is given as
z = x - μ / σ
μ = meanσ = standard deviationx = scoreSubstituting the values into the formula;
z = 83 - 75 / 8
z = 1
The z-score is 1
Let's find the percentage of z -score under the score
p(x > 83) = 1 - P(x < 83) = 0.15866
p = 15.9%
Learn more on z-score here;
https://brainly.com/question/29367643
#SPJ1
A study of religious practices among college students interviewed a sample of 125
students; 105
of the students said that they prayed at least once in a while. What is the sample proportion who said they pray?
0.84
1.19
105
84
Answers
The sample proportion who said they pray is approximately 0.84, or 84%.
How to solve for the sample proportionThe sample proportion of college students who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).
Sample proportion = Number of students who said they pray / Total number of students in the sample
Sample proportion = 105 / 125
Sample proportion = 0.84
Therefore, the sample proportion who said they pray is approximately 0.84, or 84%.
Read more on sample proportion here:https://brainly.com/question/24232216
#SPJ1
A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 13.2 inches and standard deviation of 2.3 inches. If a sample of 37 items are chosen at random, what is the probability the sample's mean length is greater than 12.1 inches? Round answer to four decimal places.
Answers
The probability that the sample's mean length is greater than 6.3 inches is0.8446.
Here, we have,
Given mean of 6.5 inches, standard deviation of 0.5 inches and sample size of 46.
We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.
Probability is the likeliness of happening an event.
It lies between 0 and 1.
Probability is the number of items divided by the total number of items.
We have to use z statistic in this question because the sample size is greater than 30.
μ=6.5
σ=0.5
n=46
z=X-μ/σ
where μ is mean and
σ is standard deviation.
First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.
z=6.3-6.5/0.5
=-0.2/0.5
=-0.4
p value from z table is 0.3446
Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.
Hence the probability that the mean length is greater than 6.3 inches is 0.8446.
Learn more about probability at
brainly.com/question/24756209
#SPJ1