The equations of the tangent and normal to f(x) at x = 2 are -
Tangent → y = 5x - 7
Normal → y = -1/2 x + 3.4
What is tangent and normal to a curve?A tangent is a line touching the curve at one distinct point, and this distinct point is called the point of contact.
The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent.
Given is a function f(x) and f(2) = 3 and f'(2) = 5.
We can find the tangent to the curve at x = 2 by finding the value of the derivative of f(x) at x = 2. The slope of the tangent at x = 2 is -
m[T] = (dy/dx) [at x = 2] = f'(2) = 5
Now. the equation of tangent can be written as -
(y - y₁) = m [T] (x - x₁)
and
f(2) = 3
At x = 2, y =3 →
y - 3 = 5 (x - 2)
y - 3 = 5x - 10
y = 5x - 10 + 3
y = 5x - 7
This is the equation of the tangent.
In order to find the slope of Normal at x = 2, use the following formula -
m [T] x m [N] = -1
m [T] = 5
Then -
m [N] = - 1/5
The equation of the normal is given by -
(y - y₁) = m [N] (x - x₁)
(y - 3) = -1/5 (x - 2)
y - 3 = -x/2 + 2/5
y = -x/2 + 2/5 + 3
y = -1/2 x + 3.4
This is the equation of Normal.
Therefore, the equations of the tangent and normal to f(x) at x = 2 are -
Tangent → y = 5x - 7
Normal → y = -1/2 x + 3.4
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Tell whether the sequence is arithmetic. If it is, what is the common difference?
A. -6,2,10,18, ...
B. 1,2,4,8, ...
simplify the expression r^-3 s^5 t^2/r^2 st^-2
write this 15 is 12 less than 2 times a number.
height of a table tennis net: 6 in. height of a tennis net: 3ft
Round each number to the nearest hundredth. What is the best estimate for the sum of 12.547 + 83.919?
That gives the equation Ax=C which is a vertical line, so the slope is undefined.For the equation Ax + By = C (where A, B, C are real numbers) what is the slope (in terms of the traditional y = mx+ b) and state any restrictions.
Help!!!
It costs $15 for a yearly membership to a movie club at a movie theater. A movie ticket costs $5 for club members and $8 for nonmembers.
The total cost of a movie ticket for club members is $20 ($15 membership fee + $5 ticket price) and for non-members it is $8.
Explanation:To find the total cost of a movie ticket for club members and non-members, we need to consider the membership fee and the ticket price. Let's break it down:
For club members:
Membership fee: $15 per yearTicket price: $5For non-members:
Ticket price: $8To calculate the total cost for club members, we add the membership fee to the ticket price: $15 + $5 = $20.
To find the total cost for non-members, we simply use the ticket price: $8.
The system of equations representing the total cost for a club member (y) and a nonmember (y) after viewing x movies is given by:
y = 15 + 5x
y = 8x
Explanation:Let's break down the system of equations. For a club member, the total cost (y) is the sum of the membership fee ($15) and the product of the ticket price $5 and the number of movies viewed (x). This relationship is represented by the equation y = 15 + 5x.
On the other hand, for a nonmember, the total cost (y) is solely the product of the ticket price for nonmembers $8 and the number of movies viewed (x), as there is no membership fee. This is expressed by the equation y = 8x.
To find the number of movies (x) after which the total cost (y) for a club member equals the cost for a nonmember, we set the two equations equal to each other:
15 + 5x = 8x
Now, solving for x, we can determine the point at which the total cost for a club member is the same as the cost for a nonmember. This helps in understanding the break-even point where joining the movie club becomes financially advantageous, factoring in the membership fee and the reduced ticket price for club members.
The complete question of the above answer is:
Certainly, here is the complete question:
It costs $15 for a yearly membership to a movie club at a movie theater. A movie ticket costs $5 for club members and $8 for nonmembers.
a. Write a system of equations that you can use to find the number x of movies viewed after which the total cost y for a club member, including the membership fee, is the same as the cost for a nonmember.
Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this class must be 5:12. What is Jeff’s error and how can he correct it?
Is this function linear or nonlinear? y=1x
A computer can sort x objects in t seconds, as modeled by the function below:
t=0.005x^2+0.002x
How long, in seconds, will it take the computer to sort 10 objects?
Round your answer to the nearest hundredth of a second. ...?
To determine the time it takes for the computer to sort 10 objects, substitute x with 10 in the given function, resulting in 0.52 seconds, rounded to the nearest hundredth.
The student's question involves determining how long it takes a computer to sort 10 objects, given the function t = 0.005x² + 0.002x, where x is the number of objects and t is the time in seconds. To find out the time it takes to sort 10 objects, we substitute x with 10 into the function.
So, we have:
t = 0.005(10)² + 0.002(10)
t = 0.005(100) + 0.002(10)
t = 0.50 + 0.02
t = 0.52 seconds
Therefore, it takes the computer approximately 0.52 seconds to sort 10 objects, when the result is rounded to the nearest hundredth of a second.
If a polygon has six sides, then it is called a hexagon.
Identify the contrapositive of the conditional statement.
A. If a polygon is not called a hexagon, then it does not have six sides.
B.If a polygon does not have six sides, then it is not called a hexagon.
C.If a polygon has six sides, then it is not called a hexagon.
D.If a polygon is called a hexagon, then it has six sides.
What is the value of x in the equation 1/5x – 2/3y = 30, when y = 15?
What are the sine, cosine, and tangent of Θ = 3 pi over 4 radians?
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = -1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = 1
sin Θ = square root 2 over 2; cos Θ = negative square root 2 over 2; tan Θ = 1
sin Θ = negative square root 2 over 2; cos Θ = square root 2 over 2; tan Θ = -1
What percentage of Anchor Global Insurance Full Time employees are employed in the US?
No. Of Employees
FULL TIME PART TIME
US:1,740 170
South East Asia:670 64
UK:300 30
Europe:250 24
China:380 32
Middle East:135 12
Total Cost (IN $ MILLIONS)
Full Time PART TIME
47.0 2.5
What is the exact value that is 47% of 2302??
Which statement is true about the result of a rigid transformation?
The image will be larger than the pre-image.
The pre-image will be larger than the image.
The pre-image will be congruent to the image.
Each one is unique; no general statement can be made about size.
Answer:
C The pre-image will be congruent to the image.
Step-by-step explanation:
Which of the following best represents the average speed of a fast runner?
10 meters per second
10 miles per minute
10 centimeters per hour
10 kilometers per second
the one above is incorrect the real answer is 10 meters per second and you don't really need an equation for this (it's pretty obvious ) :)
Solve sin2x + 2sinx = 0 for 0 ≤ x < 2π. ...?
What is 4.24 in simplified radical form? (:
I think it's 106/25 but I could be totally wrong.
The number 4.24 in its decimal form is already a simplified numerical value, it does not require conversion to a simplified radical form, unless it's interpreted as the square root of 4.24.
Explanation:The student is wanting to know the simplified radical form of 4.24. The student's proposed answer of 106/25 indicates that they are interpreting the number as a fraction. As the number 4.24 is already a decimal, which is a form of a simplified numerical expression, it does not need conversion to a simplified radical form or fraction. A number in radical form typically denotes the square root of a number, for which 4.24 does not have a simple whole number equivalent.
In summary, 4.24 in its decimal expression is already a simplified numerical value. Unless it is interpreted as the square root of 4.24, which represents an entirely different value and is not commonly presented in radical form when it's a decimal.
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The number 4.24 can be simplified to 106/25.
Explanation:No, actually, you're right! The decimal number 4.24 can be expressed as the simplified fraction 106/25.
Here is how:
1. First, express the number 4.24 as a fraction, understanding that the number after the decimal point stands for hundredths. Thus, we can write it as 424/100.
2. Next, we need to simplify the fraction. To do that, we find the greatest common divisor (GCD) of 424 and 100. The gcd of 424 and 100 is 4.
3. Now we divide both the numerator and the denominator by the gcd. So, 424 divided by 4 is 106, and 100 divided by 4 is 25.
4. Now we write the simplified fraction as 106/25.
However, it seems there's a misunderstanding in the question. The term 'radical form' usually refers to the square root of a number which we can only do in contrast to perfect square numbers (those whose square root is a whole number). However, the decimal number 4.24 doesn't have a perfect square root, so it can't be expressed in 'radical form'. But, as per your query, 106/25 is the simplified fractional form of 4.24.
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cos(x/5)sin(x/5)=1/2[sin(2x/5)]
A. True B. False ...?
Quotient of 296.16 ÷ 2.4
Answer:
The answer would be 123.4
Step-by-step explanation:
Resiprical
What is the probability of rolling a number less than or equal to 8 with two dice, given that at least one of the dice must show a 6?
Final answer:
The probability of rolling a number less than or equal to 8 with two dice, given at least one die shows a 6, is 5/36, considering all the valid dice combinations that meet the criteria.
Explanation:
The probability of rolling a number less than or equal to 8 with two dice, given at least one must be a 6, is calculated by considering the possible combinations of dice that adhere to these conditions. First, we determine how many outcomes include at least one 6:
If the first die is a 6, the other die can be 1, 2, or a 3 (since 6+4 is already 10, which is greater than 8).
If the second die is a 6, the first die can again be 1, 2, or 3.
Both dice can be 6, which adds one more outcome.
These are mutually exclusive events, therefore we add their probabilities. There are 5 outs of 36 possible rolls (3+3) when the numbers can sum up to less than or equal to 8 with at least one die showing a 6 (1+6, 2+6, 3+6, 6+1, 6+2, 6+3).
The probability of rolling a number less than or equal to 8, given that at least one die shows a 6, is 5/36.
The probability of rolling a number less than or equal to 8 with two dice, given that at least one die shows a 6, is [tex]\( \frac{10}{11} \).[/tex]
To find the probability of rolling a number less than or equal to 8 with two dice, given that at least one of the dice must show a 6, we can use conditional probability.
Let's consider the outcomes where at least one die shows a 6:
- (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
- (1, 6), (2, 6), (3, 6), (4, 6), (5, 6)
Out of these 11 outcomes, the ones where the sum of the two dice is less than or equal to 8 are:
- (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)
- (1, 6), (2, 6), (3, 6), (4, 6), (5, 6)
So, there are 10 favorable outcomes out of 11 possible outcomes when at least one die shows a 6.
Therefore, the probability of rolling a number less than or equal to 8 with two dice, given that at least one of the dice must show a 6, is [tex]\( \frac{10}{11} \).[/tex]
Write an equation ;
you have cable plan that costs $39 a month for a basic plan plus one movie channel . Your friend has the same basic plan plan plus two movies channels for $45.50 . What is the basic plan change that you both pay ?
can you determine the zeros of F(x)=x^2 +64 by using a graph?
explain why or why not
please help me out ...?
Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below:
Which statement is correct?
The two tiles are not similar because segment SP is to segment SR is 4 : 7 and segment MJ is to segment ML is 1 : 3.
The two tiles are similar because segment PQ is to segment QR is 4 : 3 and segment JK is to segment KL is also 4 : 3.
The two tiles are similar because segment SR is to segment ML is 7 : 4 and segment PQ is to segment JK is also 7 : 4.
The two tiles are not similar because segment PQ is to segment QR is 7 : 4 and segment JK is to segment KL is 4 : 3.
Answer:
D is the answer
Step-by-step explanation:
The ratios aren't the same, the ratios must be the same.
A company makes video games. The price of a video game is modeled by the function p(x) = 30x + 2, where x is the number of years since the company started producing games. The number of video games they sell is modeled by the function s(x) = 500x + 250. To find the total revenue from their video games, the company should use what operation on the polynomials?
Addition
Subtraction
Multiplication
It cannot be determined
The answer is option C "multiplication." You have the function p(x) = 30x + 2 and x equals the number of years since the company started producing games which has this equation also s(x) = 500x + 250 in order to find the revenue from their video games the company should use the multiplication on the polynomials.
Hope this helps!
How do i find the quotient of rational expressions???
Simplify √240
a.) 2√60
b.)10√24
c.)6√40
d.)4√15
Answer: the correct answer is D.
Step-by-step explanation:
A wooden beam 24 feet long leans against a wall and makes an angle of 71° with the ground. How high up the wall does the beam reach to the nearest foot?
The beam reaches approximately 23 feet up the wall.
Given that, a wooden beam is 24 feet in length and makes an angle of 71° with the ground.
We need to determine how high does it touches the wall,
To find the height up the wall reached by the wooden beam, we can use trigonometry.
Let's denote the height as "h".
In a right triangle formed by the wooden beam, the height "h" represents the opposite side, and the length of the beam (24 feet) represents the hypotenuse.
The angle between the ground and the beam is given as 71°.
We can use the sine function to solve for "h" since sine is defined as the ratio of the opposite side to the hypotenuse in a right triangle.
sin(71°) = h / 24
To find "h," we rearrange the equation:
h = sin(71°) × 24
Calculating this, we get:
h ≈ 0.9511 × 24 ≈ 22.8264
Rounding to the nearest foot, the beam reaches approximately 23 feet up the wall.
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Tanya is raising money to go on a field trip. She is selling stickers for $1 and rubber bracelets for $3. The cost of the field trip is $36. Write an equation to show how many stickers and bracelets she must sell to raise the money for the field trip