Equation of the tangent to the curve at point (-1,1) is: y=2x+3
Given,
x=cos(t)+cos(2t)
y=sin(t)+sin(2t)
P(-1,1)
For the point(-1,1), the value of t satisfy the equations x=cos(t)+cos(2t) and y=sin(t)+sin(2t) is pi/2.
To find an equation of the tangent to the curve at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2, we need to first find the slope of the tangent line at this point. To do this, we need to take the derivative of the x and y functions with respect to t:
dx/dt = -sin(t) + 2sin(2t)
dy/dt = cos(t) - 2cos(2t)
Now we can use this information to find the slope of the tangent line at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2:
slope = dy/dx = (cos(t) - 2cos(2t)) / (-sin(t) + 2sin(2t)) evaluated at t = pi/2
slope = (cos(pi/2) - 2cos(2pi/2))/(-sin(pi/2) + 2sin(2pi/2)) = 0 - (-2)/0 + 0 = 2
Now, we can use this slope to find the equation of tangent using:
(y-y1)= m(x-x1)
=> y-1=2(x+1)
=>y=2x+3
Read more about Tangent and Normal:
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What is the result when g+ + 2 is subtracted from 32 - 41
?
10
100
3
03
10
1 3
o
10
7 9
10
9
-3-3 +1
10
0 3 2 - 1
Answer:
6
Step-by-step explanation:
6 is the correct answer because-3-3+1
An airplane on autopilo 7 hours to travel 4,998 kilometers. What is the unit rate for kilometers per hour?
18. The stock bar chart below shows price and volume information for Medco Health
Solutions (MHS) on January 12. What was the opening price?
Answer:b $41.60
Step-by-step explanation:
You have a data set with a Gas Price variable. It lists the price of a gallon of regular gasoline at a randomly selected 100 gas stations around the country in a particular week. You calculate a 95% confidence interval for the mean of Gas Price, and it turns out to be $2.43 plus or minus $0.16. Which of the following most closely reflects what you can conclude? a. If your sample size had been 400, and you had observed the same sample mean but a sample standard deviation twice as large as in your original sample, the 95% confidence interval would have been approximately $2.43 plus or minus $0.08. b. If your sample size had been 400 and you had obtained the same sample mean and sample standard deviation as in your original sample, the 95% confidence interval would have been approximately $2.43 plus or minus $0.08. c. If you had observed the same sample mean and sample size, but a sample standard deviation twice as large as the one you observed, the 95% confidence interval would have been approximately $2.43 plus or minus $0.24. d. If you had observed the same sample mean and sample size, but a sample standard deviation half as large as the one you observed, the 95% confidence interval would have been approximately $2.43 plus or minus $0.04.
Answer:
b. If your sample size had been 400 and you had obtained the same sample mean and sample standard deviation as in your original sample, the 95% confidence interval would have been approximately $2.43 plus or minus $0.08.
Step-by-step explanation:
Confidence interval:
A confidence interval is given by the sample mean plus minus the margin of error.
Margin of error:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which M is the margin of error, z is related to the confidence level(the higher the confidence level, the higher the value of Z), [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
This is important to note that the margin of error is inversely proportional to the square root of the size of the sample.
In this question, we have that:
95% confidence interval for the mean of Gas Price is of $2.43 plus or minus $0.16, with a sample of 100.
Option A:
Sample size of 400, which is four times the original, while the standard deviation is twice the original.
This means that the margin of error would be the same, as it would be multiplied by 2 in the numerator and divided by the square root of 4, that is, 2 in the denominator. So the interval would still be of $2.43 plus or minus $0.16, which means that option a. is wrong.
Option B:
Sample size of 400, which is four times the original, while the rest is the same.
The margin of error would be divided by the square root of 4, that is, 2, which means that it would be half of the original, and the interval would be $2.43 plus or minus $0.08, which means that option b. is correct.
Option C:
In this case, the margin of error will be doubled, since the standard deviation is double the original. So the confidence interval would be of $2.43 plus or minus $0.32, which means that option c. is wrong.
Option D:
In this case, the margin of error will be halved, since the standard deviation is half the original. So the confidence interval would be of $2.43 plus or minus $0.08, which means that option d. is wrong.
Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Suppose the outcomes are equally likely. Compute the probability of the event E = {1,4,7,9).
P(E)= ____?
(Type an integer or a decimal. Do not round.)
Answer:
Step-by-step explanation:
With replacement
(1/10)^4
1/10000
0.0001
Without replacement
(1/10)(1/9)(1/8)(1/7)
1/5040
0.00019841269
write down the 3 integers, all the less than 25, whose range is 10 and
mean is 13
The three integers are
Enter the rational number as a decimal. Then tell whether the decimal is a terminating or a repeating decimal.
3
5
=
The decimal is
(select)
.
Answer:
3
Step-by-step explanation:
the answer is 3, you can also search up the answers on the internet or use an online calculator
Answer: Decimals are of different types based on the numbers that come after the decimal point. These types are terminating decimal numbers, non-terminating repeating decimals, recurring decimal numbers, and non-recurring decimal Numbers. The answer is 3, you can also search up the answers on the internet or use a calculator.
Encontrar la media, mediana, moda y rango de los siguiente valores:
84,91, 72,68,87, 78,65,87,79.
Answer:
La mediana es 79 la moda es 87 la media 87 y él rango es 26
Step-by-step explanation:
Espero te ayude ;)
The mode, median and the range are 87, 79 and 26 respectively
Given the data 84,91, 72,68,87, 78,65,87,79., we are to get the median, mode, and range of the data.
The mode is the number that occurs the most from the given data. Since 87 occurs twice, hence the mode is 87The median is the number in the middle after arrangement. On arranging, we will have:
65, 68, 72, 78), 79, (84, 87, 87, 91
From the data, we can see that the median value is 79Range = Highest - lowest
Range = 91 - 65
Range = 26
Hence the range of the data is 26Learn more on measure of central tendency here: https://brainly.com/question/17726154
Simplify the expression below.
12a−8−5a+12
Step-by-step explanation:
Given
12a - 8 - 5a + 12
= 7a + 4
Hope it will help :)
Answer:
7a + 4
Step-by-step explanation:
First, let's rewrite this expression to combine like terms:
12a – 8 – 5a + 12 — I bolded the constants and underlined the expressions with variables
12a – 5a – 8 + 12 — it looks a little easier regrouped, doesn't it?
The last two terms are easy, right?
12 – 8 = 4 — simplify with subtraction
We'll focus on the first two terms now. Let's rewrite the terms with variables attached to make the subtraction easier:
a(12 – 5) = a(7) = 7a
We could also think of it this way: multiplication is just repeated addition.
12a = a + a + a + a + a + a + a + a + a + a + a + a (we just add a to itself 12 times)
5a = a + a + a + a + a (we just add a to itself 5 times)
Subtracting this expression would then look like this:
a + a + a + a + a + a + a + a + a + a + a + a – (a + a + a + a + a)
a + a + a + a + a + a + a + a + a + a + a + a – a – a – a – a – a
Five of the a values will cancel out, and to show this, we can rewrite the expression once more, like this:
a – a + a – a + a – a + a – a + a – a + a + a + a + a + a + a + a
The five a values cancel out and leave us with this:
a + a + a + a + a + a + a
How many a values are added together now? Seven of them, right? We add a to itself 7 times. We can then rewrite that expression as 7a.
Using the [12 – 8 = 4] expression from above, we add the 4 to the 7a to find our final answer: 7a + 4
I hope this helps increase your understanding of the concept! Have a great day!
Which expression is equivalent to 4f/3÷1/4f
What is the acronym used to help remind you of the order
used to simplify expressions?
Answer:
I think it's PEMDAS, but I'm not sure- sorry if it's wrong.
Step-by-step explanation:
Kaliq and Maria ench improved their yards by planting grass sod and shrubs. They bought their supplied from the same store. Kali spent $119 on 14ft^2 of grass sod and 3 shrubs. Mana spent 398 on 7ft^2 of grass sod and 7 shrubs. Find the cost of one ft^2 of grass sod and the cost of one shrub
Answer:
i dont get it
Step-by-step explanation:
On a trip, a family travels 180 km in 2.5 h on the first day, 220 km in 4.4 h on the second day, and 88 km in 2.2 h on the third day. What was the average speed, in kilometers per hour, for the total trip?
Answer:
Step-by-step explanation:
180+220+88 = 488 km
2.5+4.4+2.2 = 9.1 h
(488 km )/(9.1 h) = (488/9.1 km)/h ≈ 53.6 km per hour
The speed of the current in the river is 4 mph about travel 17 miles downstream with the current in the this river in the same time that it travels 9 miles upstream against the current find the speed of the boat in the Stillwater
Answer:
Step-by-step explanation:
b = speed of boat in still water
traveling downstream, the boat goes (b+4 miles)/hour.
traveling upstream the boat goes (b-4 miles)/hour.
Time to travel 17 miles downstream = 17 miles × (1 hour)/(b+4 miles)
Time to travel 9 miles upstream = 9 miles × (1 hour)/(b-4 miles)
17 miles × (1 hour)/(b+4 miles) = 9 miles × (1 hour)/(b-4 miles)
17/(b+4) = 9/(b-4)
cross-multiply denominators:
17(b-4) = 9(b+4)
17b - 68 = 9b + 36
8b = 104
b = 13 miles per hour
Three yellow balls, two red balls and five orange balls are placed in a bag. Mark draws a ball out, and replaces it. He then picks another ball.
What is the probability that he gets at least one yellow ball?
Answer:
45
Step-by-step explanation:
because of me and I can send you a picture when
What is the slope of the line shown below?
Answer:
you've gotta show us the slope so that we can help u
The average diameter of a tree is measured over time. The equation y=3/5x, where x is the time in years and y is the diameter in inches, models the relationship. What is the predicted diameter, in inches, of the three after 12 years?
Find the unit rate is 120 apples are in 6 baskets. (Follow this example 3 bananas/ 1 bunch)need help with my homework 10 points
Answer:
120/6 = 20 apples unit rate
Step-by-step explanation:
please explain what else the question wants
Find the slope of the line represented in the table.
x
Answer:
The slope is -3
Step-by-step explanation:
Use the slope formula to find the slope.
The formula is .... ⏬
Hello, I need help!!!!?
Someone help me it's due right now help please helpppppppp
Answer:
The answer is c
the line needs to start at $5 then go up in increments of $2 each hour after. Time is in 2 hour blocks, meaning each block should increase by $4
Write an equation of a line in slope-intercept form given the slope (m) and the y-intercept (b).
Slope, m =-
y-intercept, b =7
7
Step-by-step explanation:
y = mx + b
y = -7x + 7
this assumes m = - 7 , it got chopped off, otherwise what ever slope is change the first 7 for that number.
Can u help me answer this?
Thanks!
Answer:
190 trees
Step-by-step explanation:
38% of the plantings in the garden are trees. There are 500 plantings.
So we are looking for 38% of 500.
To find the percentage of a number, convert the percentage to a decimal and multiply:
38%=0.38
500*0.38=190
Knowing that 6 × 7 = 42, we know that 42 ÷ 7 = ___
Answer:
Knowing that 6 × 7 = 42, we know that 42 ÷ 7 = 6
Step-by-step explanation:
Sorry but its very simple question you need to try to do it by yourself
Answer:
6
Step-by-step explanation:
By understanding the relationship between multiplication and division we can positively say that since 6 × 7 = 42, we know that 42 ÷ 7 = 6.
When converted to speeds, which list is in order from slowest to fastest?
17 miles in 2 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes;
60 miles in 8 minutes
17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
33 miles in 6 minutes;
26 miles in 4 minutes;
60 miles in 8 minutes;
17 miles in 2 minutes
60 miles in 8 minutes;
33 miles in 6 minutes;
26 miles in 4 minutes;
17 miles in 2 minutes
Which playwright has only seven surviving plays, and many people consider his Oedipus Rex the greatest Greek tragedy?
Aeschylus
Sophocles
Euripides
Aristophanes
Answer:
its b Sophocles
Step-by-step explanation:
got it right
A + 1.05 = 3.7 plz help
Answer:
a=2.65
You just bring over the 1.05 to the 3.7, and just go on from there!
Hope this helps!
brainleist
which algebraic expression will Alex want to use to determine the total amount of food (f) a dolphin will eat over a 5-year period, if x equals pounds per year?
A. F = 5 + x
B. F = 5x
C. F = 5/x
D. F = x/5
Answer:
A.) F=5+x
Step-by-step explanation:
I think A is the answer because 5 year period is fixed. The x equals pounds per year is what we don't know .
Bir okuldaki öğrencilerin
erkektir. Okulda 90 kız öğrenci
olduğuna göre kaç erkek öğrenci vardır?
Answer:
Soru gözükmüyor. Okulda kaç öğrenci var? Bunu söylersen çözebilirim.☺️
Are there any supplementary, vertical, or complimentary angles? If so wich ones
Supplementary: N and M & N and I
Supplementary angles: A pair of angles whose sum is equal to 180°.
Vertical: M and I
Vertical angles: A pair of opposite angles that are made by two intersecting lines.
Complimentary: None
Complimentary angles: A pair of angles whose sum is equal to 90°.
Hope this helps! :D