*F7 Consider the curve y = 2x sin(x). Find the equation of the tangent line at the point 71 when I 2
Answers
The equation of the tangent line at the point (71, -142) is y = -39.80x + 2842.
To find the equation of the tangent line at the point (71, -142), we need to find the slope of the tangent line at that point.
First, we can find the derivative of y with respect to x using the product rule:
y' = 2x cos(x) + 2sin(x)
Now, we can substitute x = 71 into y' to get the slope of the tangent line at the point (71, -142):
y'(71) = 2(71)cos(71) + 2sin(71) ≈ -39.80
So the slope of the tangent line at the point (71, -142) is approximately -39.80.
Next, we can use the point-slope form of the equation of a line to find the equation of the tangent line:
y - y1 = m(x - x1)
where m is the slope we just found, and (x1, y1) is the point we're using, which is (71, -142).
Plugging in the values, we get:
y - (-142) = -39.80(x - 71)
Simplifying, we get:
y = -39.80x + 2842.2
So the equation of the tangent line at the point (71, -142) is y = -39.80x + 2842.2.
To learn more about tangent line, refer below:
https://brainly.com/question/31326507
#SPJ11
Related Questions
Find the product. 526 x 9
Answers
Answer:
526 X 9= 4734 is the answer.
On a standard dice, the sum of the numbers of dots on opposite faces is always 7. Four standard dice are glued together, as shown. What is the minimum number of dots that could lie on the whole surface?
Answers
The minimum number of dots that could lie on the whole surface of four standard dice glued together is 56.
This can be achieved by placing the faces with 1 dot opposite the faces with 6 dots, the faces with 2 dots opposite the faces with 5 dots, and the faces with 3 dots opposite the faces with 4 dots on all four dice. Since the sum of the numbers on opposite faces of each individual die is always 7, the sum of the numbers on opposite faces of the four glued-together dice is also always 7. Therefore, the minimum number of dots on the whole surface is 7 times the number of faces, which is 7 x 8 = 56.
More on dice: https://brainly.com/question/20693691
#SPJ11
the figure above shows the graph of the twice-differentiable function g and the line tangent to the graph of g at the point (0,3). the value of limx→0g(x)e−x−3x2−2x is
Answers
Using L'Hopital's rule, we can find that the limit is equal to (g(0) - 3)/2.
Since the line tangent to g at (0,3) has slope 2, we know that g(0) - 3 = 2(0) = 0. Therefore, the limit is 0/2 = 0. Based on the given information, we have a twice-differentiable function g(x) and its tangent line at the point (0,3). To find the value of the limit as x approaches 0 for g(x)e^(-x) - 3x^2 - 2x, we can use L'Hopital's rule since it involves indeterminate forms of the type 0/0 or ∞/∞. Apply L'Hopital's rule twice on the given expression. Then, evaluate the resulting expression at x=0. This will give you the value of the limit for the given expression. Make sure to check if the conditions for using L'Hopital's rule are met before applying it.
To know more about tangent visit:
https://brainly.com/question/10053881
#SPJ11
K(x) = 2x^2 + 7
What is k(4)
Answers
Answer:maybe this helps
Step-by-step explanation: k*(x)-(2*x^2+7)=0
STEP
1
:
Equation at the end of step 1
kx - (2x2 + 7) = 0
STEP
2
:
Trying to factor a multi variable polynomial
2.1 Factoring kx - 2x2 - 7
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Equation at the end of step
2
:
kx - 2x2 - 7 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve kx-2x2-7 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
So the market is selling guns and their $100.50 but their half off what is the amount to buy a gun.
Answers
Answer:
50.25
Step-by-step explanation:
100.50/2=50.25
Answer:
50.25
explanation:
44 < 5x6 and 5x - 6 ≤ 54
Answers
Answer:
5x - 6 ≤ 54
5x-6+6 ≤ 54+6
5x ≤ 60
divide by 5
x ≤ 12
Step-by-step explanation:
eathan answer 80% correctly on his history test he correctly answers 32 enter the amount of questions on his test
Answers
Answer:
40 questions.
Step-by-step explanation:
By proportion:
80 % is equivalent to 32 questions
So 100% .. .. .. .. .. .. (32/80) * 100
= 32 * 5/4
= 160/4
= 40
Answer:
40
Step-by-step explanation:
80/100=32/x
You can also set this up with a diagram.
x=40
The length of a rectangle is 3x +2 and the width of the rectangle is 6x-1. Express the
perimeter of the rectangle in terms of x.
Answers
Answer:
2(3x+2+6x-1)
=2(9x+1)
=18x+2
Which point lies on the line with a slope of m = ⅔ that passes through the point (-3, -2)?
Answers
Answer:
Step-by-step explanation: you would use point form slope in the equation and plug it in like this
y+2= 2/3(x+3)
y+2=2/3x+2
y= 2/3x
and whatever point goes through this line is your answer
Remember the y-intercept is 0!
Serenity and her children went into a restaurant and will buy hamburgers and tacos. Each hamburger costs $5.50 and each taco costs $2. Serenity has a total of $45 to spend on hamburgers and tacos. Write an inequality that would represent the possible values for the number of hamburgers purchased, ℎ h, and the number of tacos purchased, � . t.
Answers
Answer: Less than or equal to 45
Step-by-step explanation:
Let's use algebra to write the inequality.
Let h be the number of hamburgers purchased and t be the number of tacos purchased.
Each hamburger costs $5.50 and each taco costs $2, so the total cost of h hamburgers and t tacos is:
5.5h + 2t
Serenity has a total of $45 to spend, so we can write:
5.5h + 2t ≤ 45
This is the inequality that represents the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t.
Note that the inequality is less than or equal to 45, since Serenity cannot spend more than $45.
To represent the possible values for the number of hamburgers and tacos purchased, an Inequality can be written as 5.5x + 2y ≤ 45.
To write an inequality to represent the possible values for the number of hamburgers purchased (h) and the number of tacos purchased (t), we need to consider the cost of each item and the total amount Serenity has to spend.
Let's assume Serenity buys x hamburgers and y tacos. Each hamburger costs $5.50, so the total cost of hamburgers purchased would be 5.5x. Each taco costs $2, so the total cost of tacos purchased would be 2y.
The total amount Serenity has to spend is $45. Therefore, the inequality that represents the possible values for h and t is: 5.5x + 2y ≤ 45.
Learn more about Inequality here:https://brainly.com/question/30231017
#SPJ2
How many times larger is the area of Polygon DDD than the area Polygon CCC?
Answers
Answer: You simply square the linear scale factor 6 and we get 6^2 = 6*6 = 36
You can think of a square with sides of 2 by 2, so the area is 4 If you multiply each dimension by 6, then the square is now 12 by 12 and the new area is 144.
Step-by-step explanation:
help me please :) 2(2 - x) = -3(x + 1)
Answers
Explanation:
I need more assistance :D Instructions: Using the image, find the distance between the points given on the graph.
Answers
Answer:
I usually explain even in the answer.
So we use som\(\sqrt{x}\)ething called distance formula which is branched of Pythagorean theorem.
But we dont need to as it just makes it more complicated. We need to find split into 2 vectors, one vertical, and horizontal. The horizontal is 5 long.
The vertical is 1, you can find them by calculating how long is it and how tall.
Use pythogorean theorem from the formula and do 5^2+1^2 = c^2
25+1 = 26, so the answer is √26
I am pretty sure answer is right. Always take abolute value
√26
Exponents - help me pls
Answers
PLEASE HELP!!!!!!!!!!!!!!!!!!!! ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
729
Step-by-step explanation:
I have not done this in some time so the terms may be a bit unconventional, but they work. The key to this is multiplying by -3.
1*(-3) = -3
-3*(-3) = 9
And so on.
1, -3, 9, -27, 81, -243, 729
The volume of a cone is 36piin to the power of 3. What is the volume of a cylinder with the same base and height as the cone?
Answers
Answer:
108πin³
Step-by-step explanation:
The volume of a cone = ⅓ of the volume of a cylinder
Thus, volume of cylinder = 2πr²h
Where, r = radius, h = height of cylinder.
Volume of cone = ⅓×πr²h
So therefore, the volume of a cone given = ⅓ of the volume of a cylinder with the same height and and base of the cone
Thus,
If Volume of cone = 36πin³ , volume of cylinder would be 3 × 36πin³
Volume of cylinder = 108πin³
the burning times of scented candles, in minutes, are normally distributed with a mean of 249 minutes and a standard deviation of 20 minutes. find the number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles. use excel, and round your answer to two decimal places.
Answers
The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.
When the distribution is normal, we use the z-score formula.
In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:
Z = (X – µ) / σ
What is Z-score?The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
So, in this case, given that:
µ = 249, σ = 20
The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:
100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.
Now, put all the values into the formula:
Z = (X – µ) / σ
–0.253 = (X – 249) / 20
X – 249 = –0.253 * 20
X = 244
Hence, the candle burns for 244 minutes.
Learn more about z-score at: https://brainly.com/question/15016913
#SPJ4
It took the race car 22 minutes to travel 114. 4 kilometers. At what rate did the car travel? Use the formula r = StartFraction d Over t EndFraction, where r is the rate, d is the distance, and t is the time. Round your answer to the nearest tenth. 0. 2 kilometers per minute 5. 2 kilometers per minute 92. 4 kilometers per minute 2,516. 8 kilometers per minute.
Answers
Write a linear equation for a line that passes through point(2, 3) with a slope of 1/2
Answers
Answer:
y = 1/2x + 2
Step-by-step explanation:
y = 1/2x + b
3 = 1/2(2) + b
3 = 1 + b
2 = b
please help me answer this.
Answers
Answer:
-15
Step-by-step explanation:
f (10) = 10/2 = 5 . how to solve this problem
Answers
Answer:
f(10) means to input x = 10 into the function.
From inspection of the given function:
\(\sf f(10)=\dfrac{10}{2}=5\)
the "10" is the numerator of the fraction.
Therefore, swap the "10" for "x" to give the function in terms of x:
\(\sf f(x)=\dfrac{x}{2}\)
For a function
f(x)=yx is the input or domain
y is the output or range
Here
f(10)=10/2So
x=10
y=10/2
Hence the function is
f(x)=x/2Solve for x
Marking brainliest
Answers
Answer:
110°
Step-by-step explanation:
What is the percent rate of change in function y = (0. 98) ^ x? determine whether the function represents exponential growth or exponential decay
Answers
Answer:
rate of change: -2% per periodexponential decayStep-by-step explanation:
You want to know the rate of change represented by the function y = 0.98^x, and whether it is exponential growth or decay.
Growth factorThe base of the exponent in an exponential function is the "growth factor".
When it is less than 1, the function represents exponential decay.
When it is more than 1, the function represents exponential growth.
The growth factor of 0.98 is less than 1, so this is an exponential decay function.
Rate of changeThe growth factor is 1 added to the growth rate. This means we can subtract 1 from the growth factor to find the growth rate:
growth rate = 0.98 -1 = -0.02 = -2%
The rate of change in the given function is -2%. (The negative indicates exponential decay.)
how many four-digit integers greater than 5000 are there for which the thousands digit equals the sum of the other three digits?
Answers
21 percentage of four-digit integers above 5000 have a thousands digit that is equal to the sum of the other three digits.
Given that,
We have to find what percentage of four-digit integers above 5000 have a thousands digit that is equal to the sum of the other three digits.
We know that,
The other three numerals must add up to 5 because the first digit is 5.
The other two digits must add up to 5 if the second digit is 0, thus they
are 0+5, 1+4, or 2+3 or their reverses 5+0, 4+1, and 3+2, that 6
The last two numbers must add up to 4 if the second digit is 1, thus they
are 0+4, 1+3, or 2+2. There are five more since the first two are reversed.
The last two digits must add up to 3 if the second digit is 2, thus they
are 0+3 and 1+2, and their reverses, so that's 4 more.
If the second digit is 3, the last two digits must sum to 2, so they
are 0+2 and 1+1 and the reverse of the first, so that's 3 more.
The last two digits must add up to 1, so if the second digit is 4, they must.
are 0+1 and its reverse, so that's 2 more
If the second digit is 5, the last two digits must sum to 0, so they
are 0+0, so that's 1 more.
Total = 6+5+4+3+2+1 = 21.
Therefore, 21 percentage of four-digit integers above 5000 have a thousands digit that is equal to the sum of the other three digits.
To learn more about sum visit: https://brainly.com/question/13013054
#SPJ4
What's the answer to 13 times 12
Answers
\(13 \times 12 = 156\)
Please hurry!!!
At the same time, Min's little brother throws a
baseball from a height of 4 feet with an initial
vertical velocity of 20 feet per second. What
polynomial models the height of this ball, in feet?
- 16t²+ ?t +?
Answers
Answer:
20t+4
Step-by-step explanation:
20t=?t
4=?
Answer:
here
Step-by-step explanation:
c
3.18
What is the correct way to write the above number
as a rational number?
Answers
Answer:
1
Step-by-step explanation:
I NEED HELP ASAPPPPPPP
Answers
Answer:
B
Step-by-step explanation:
You can see that the only difference between the two graphs is that the red one is shifted up by 4 units. To accomplish this, simply add 4 to the parent function (which in this case is x²). Thus, the answer is just x²+4
A rectangle has a length that is 3 more than twice the width. Its perimeter is 96 inches.
Answers
Answer:
W=22.5inL=25.5inStep-by-step explanation:
given data
let the width be x
W=x
L=x+3
the perimeter= 96in
the expression for perimeter is
P=2L+2W
Step two:
substitute
96=2(x+3)+2(x)
solve for x
96=2x+6+2x
96=4x+6
96-6=4x
rearrange
4x=90
divide both sides by 4
x=90/4
x=22.5
The width W=22.5in
the length L=22.5+3
L=25.5in
What expression is equivalent to x^-1 • y^-2?
Answers
Answer:
1/(xy^2)
I hope it will be useful.
Answer:
1/x times 1/y squared
Step-by-step explanation: