The given curve has equation
r(θ) = 9 + 8 cos(θ)
and its derivative is
dr/dθ = -8 sin(θ)
When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.
Differentiate these with respect to θ :
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
In polar coordinates, we have
y(θ) = r(θ) sin(θ)
x(θ) = r(θ) cos(θ)
and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.
The slope of the tangent line to the curve is dy/dx. By the chain rule,
dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)
dy/dx = (dr/dθ sin(θ) + r(θ) cos(θ)) / (dr/dθ cos(θ) - r(θ) sin(θ))
When θ = π/3, the slope is
dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))
dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))
dy/dx = - 1/(17√3)
So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is
y - 13√3/2 = -1/(17√3) (x - 13/2)
y = -(x - 338)/(17√3)
What is the value of t?
Answer:
32°
Step-by-step explanation:
1) the sum of the angles is 180°. According to this rule the sum can be written:
t+(t+1)+[180-(t+33)]=180;
2) if to solve this equation, then
t=32°
Find the perimeter of the figure below. Notice that one side length is not given.
Step-by-step explanation:
Perimeter of the quadrilateral = sum of the length of all the four sides. Note: Missing side of the quadrilateral = Perimeter of the quadrilateral - Sum of the length of three sides.
find the average rate of change of f(x)=5x^2-3 from 3 to 9
9514 1404 393
Answer:
60
Step-by-step explanation:
The average rate of change on the interval is ...
(f(9) -f(3))/(9 -3) = ((5·9² -3) -(5·3² -3))/(9 -3) = (402 -42)/6 = 60
A sports marketing company interviewed 250 Supersport United fans and has found that the average fan spends R101 on non-ticket purchases at the stadium when he/she attends a home match. This includes money spent on food, drinks and merchandise. Assume that the standard deviation is R39.
Find the lower and upper limits for the average amount spent on non-ticket purchases per match by Supersport United fans. Use a confidence level of 90%. Round off your answers to 2 decimal places (4)
The 90% confidence interval is between R96.94 and R105.06
The confidence (C) = 90% = 0.9, Mean (μ) = 101, standard deviation (σ) = 39, sample size (n) = 250
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1 / 2 = 0.05
The z score of α/2 corresponds with the z score of 0.45 (0.5 - 0.05) which is equal to 1.645
The margin of error (E) is given by:
[tex]E=Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.645 *\frac{39}{\sqrt{250} } =4.06[/tex]
The confidence interval = μ ± E = 101 ± 4.06 = (96.94, 105.06)
Therefore the 90% confidence interval is between R96.94 and R105.06
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X= $25,000
1,500+.2(x-10,000)
Answer:
x-525000+0
Step-by-step explanation:
Help please? I’m not too sure what to do?
A student has scores of 66.75, 66, and 72.25 on his first three tests. He needs an average of at least 70 to earn a grade of C. What is the minimum score that the student needs on the fourth test to ensure a C?
Answer:
75
Step-by-step explanation:
Average needed to get grade C = 70
Average = Total Amount / No of Items.
No of items = 4
therefore Total needed = 70 x 4 = 280
current total score = 66.75 + 66 + 72.25 = 205
the fourth test minimum score = 280 - 205 = 75
Answer: i thank it is 75
Step-by-step explanation:
hope i help
Do you think the difference of 1.4-0.95 is less than one or greater than one? Explain.
Answer:
The answer would be , less than one .
The difference of 1.4 - 0.95 is less than one as per the concept of subtraction.
To determine this, we can simply subtract the two values:
1.4 - 0.95 = 0.45
Since the result of the subtraction is 0.45, which is less than one, we can conclude that the difference of 1.4 - 0.95 is indeed less than one.
In numerical terms, the difference is 0.45, which is 45 hundredths or less than half of one whole unit.
When comparing the two original values, 0.95 is almost half of 1.4, making the difference smaller than one.
In summary, the difference of 1.4 - 0.95 is less than one, specifically 0.45. It is essential to pay attention to the decimal values and their magnitudes when determining the difference between two numbers.
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Use the given information to determine which lines, if any, are parallel. Justify each conclusion with a theorem or postulate.
1. angle 2 is supplementary to angle 3
2. Angle 1 is congruent to angle 3
3. Angle 6 is supplementary to angle 7
Angle 9 is congruent to angle 12
[tex]\lim_{x \to \ 7} \frac{2x^2-11x-21}{x^2-9x+14}[/tex]
Answer:
[tex] \frac{17}{5} [/tex]
I hope this helps you...
Convert 150 degrees to radians.
Answer:
Option 2
Step-by-step explanation:
Radians = 150 × π/180
=5π/6
will mark as brainliest
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros of -1, 2, and -3i. Show all work.
Please help me this a important test and I’m not good at math please explain step by step so I can learn the formula for once
Answer: You"ll earn $884 because we know that 707.20 divided by 32 equals 22.1 and 22.1x40 = $884. Therefore, you"ll make $884 for 40 hours.
Drag the numbers to order them from least to greatest.
0.9
2.4
0.8
1.6
0.2
Answer:
0.2
0.8
0.9
1.6
2.4
Step-by-step explanation:
I hope this helps!
the area of 1.25 and 0.8
Answer:
2.05
Step-by-step explanation:
1.25 + 0.8= 2.05 but if your doing multiplication then it would be 1 just 1.
Javier reads 40 pages every hour, how many pages does Javier reads in 2.25 hours?
Answer:
Javier reads 90 pages in 2.25 hours.
Step-by-step explanation:
# of pages read every hour: 40 pages.
# of hours in total: 2.25 hours.
Multiply the number of pages he can reads every hour (40 pages) by the number of hours in total.
40 x 2.25 = ?
The Product is your answer;
? = 90
Hope this helps :)
An isosceles triangle has two sides of equal lenght. The length of the third side is 1 ft less than twice the length of one of the equal sides find the length of each side when the perimeter is 23 ft, answer as a comma separated list
Answer: An isosceles triangle has two sides of equal length. The length of one of the equal sides is two more than 3 times the length of the third side. If the perimeter is 46m, find the length of each side.
Step-by-step explanation:
Hope this helps!
Answer:
Step-by-step explanation:
The perimeter is equal to the lengths of all the sides.
Let x equal the two sides that are equal to each other.
Then the 3rd side is 2x - 1 which is 2 times the length of the equal side minus 1.
So the perimeter 23 = x + x + (2x-1)
Now solve for x
23 = x + x + 2x - 1
add 1 to both sides
24 = x + x + 2x
24 = 4x
x = 6
The two equal sides would be 6 feet each
The other side would be 2(6) - 1 = 11
The perimeter is 6 + 6 + 11 = 23
2/3 cup water 1/2 cup oil what's the ratio of water to oil?
Answer:
4:3
Step-by-step explanation:
ratio of H20 to Oil = (Amount of H20) / (Amount of Oil) = (2/3 cup)/(1/2 cup) =
(2/3) / (1/2) = (2/3) * (2/1) = 4/3 = 4:3
Hey ! Can anyone help me with this question please ? Thank you
Answer:
7
Step-by-step explanation:
4x-13 = x + 8
3x = 21
x = 7
enjoy
Pls give me an answer with step by step explanation
Please help me as soon as possible!
Answer:
9.53 AU
Step-by-step explanation:
Find the missing dimension of the prism.
Answer:
10
Step-by-step explanation:
To find volume you have to multiply all 3 sides 7*8*x=560 = 56*x=560 we divide it by 56 and get x=10
The height of a building is 1383 feet. How long would it take for an object to fall from the top?
Answer:hope this helps
Step-by-step explanation:
Me.Ramirez divid 12 frogs
Answer: my last names Ramirez!
Step-by-step explanation:
Look at the screen shot teach me how to do this thank you.
Answer:
Slope intercept form (y = mx + b) = [tex]y = \frac{2}{3} x + \frac{7}{3}[/tex]
X intercept (slope): [tex](-\frac{7}{2} , 0)[/tex]
Y Intercept: [tex](0, \frac{7}{3} )[/tex]
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x.
To find the y-intercept, substitute in 0 for x and solve for y.
Hope this helps! :D
Step-by-step explanation:
solve for y
[tex]3y - 7 = 2x[/tex]
isolate the y variable to one side
let's first add 7 to both sides of the equation
[tex]3y - 7 + 7 = 2x + 7[/tex]
sevens on the left side of the equation cancel so we get
[tex]3y = 2x + 7[/tex]
Now let's divide everything in the equation by 3 to further isolate the y variable
[tex] \frac{3y}{3} = \frac{2x}{3} + \frac{7}{3} [/tex]
The threes on the left hand side of the equation cancel
[tex] y = \frac{2}{3}x + \frac{7}{3} [/tex]
The ratio of pigs to cows on a farm is 4:3.
a) If there are 36 cows, how many pigs are there?
b) If there are 70 pigs and cows all together, how many are cows?
Step-by-step explanation:
#ap : c
4 : 3 = x : 36
3x = 4 × 36
3x = 144
x = 48
#bp + c = 70
c = 3/7 × 70
c = 3 × 10
c = 30
SOMEONE HELP ME AND EXPLAIN HOW ITS THE ANSWER PLZ!!!
Answer:
20 guests
Step-by-step explanation:
20 (20) + 400 = 400 + 400 = 800
10 (20) + 600 = 200 + 600 = 800
answer B = 20 guests
Answer:
For 20 persons the price would be same.
Step-by-step explanation:
y=y
20x+400=10x+600
20x-10x=600-400
10x=200
x=20
Therefore, for 20 persons the price would be same.
Help please don’t know what to do???!
Answer:
81.75
Step-by-step explanation:
First, find the median of all the answers.
78.25, 77.75, and 84 = 80 (median)
now that we know 80 is the median, we will add it to our solution.
And still, there is no OTHER TEST in to make this stay 80.
78.25, 77.75, 84, and 80 = 79.125
since this is incorrect, we go higher.
78.25, 77.75, 84 and 81 = 79.625
since this is also incorrect, we go higher.
78.25, 77.75, 84 and 82 = 80.125
since this is higher and incorrect, we will go lower to 81.5.
78.25, 77.75, 84 and 81.5 = 79.875
since this is lower AND 82 is not the correct solution, we will go up by 0.25.
78.25, 77.75, 84 and 81.75 = 80
To check, we will do the problem again.
78.25, 77.75, 84 and 81.75 = 80
So, the solution is 81.75
Write the equation of the line parallel to the line and passing through the point.
Chapter Reference
d
y=x+5, (8, 1)
Answer:
y = x - 7
Step-by-step explanation:
Parallel lines have the same gradient in this case 1 is the gradient.
Using the point (8,1) we can form our own equation.
1 will be y, 1 will be m, 8 will be x
All we have to do is find C in order to form the equation y=mx+c
1 = 1(8) + c
1 = 8 + c
C = - 7
Therefore;
y = x - 7
The list shows the thicknesses of several different types of art paper.
Thickness
(cm)
0.004
0.007
0.011
0.011
0.012
0.020
0.200
0.214
What is the range of this set of data?
O A. 0.055
OB. 0.210
OC. 0.214
OD. 0.218
O E. 0.498
Y
Answer:
B. 0.210
Step-by-step explanation:
Range is the minimum value subtracted from the maximum value. In this case 0.004 is the smallest value and 0.214 is the largest.
Range = 0.214 - 0.004 = 0.210 = B
The range set of the given data is 0.21.
The given data sets are,
0.004
0.007
0.011
0.011
0.012
0.020
0.200
0.214
We know that,
In statistics, the range is the difference between the highest and lowest values for a given data collection.
For instance,
if the given data set is 2,5,8,10,3, the range is 10 - 2 = 8.
As a result, the range can also be defined as the difference between the highest and lowest observations.
The range of observation is the name given to the outcome. In statistics, the range indicates the dispersion of observations.
Now to find the range set pf the given data,
Subtract minimum value to maximum value
Since maximum value = 0.214
And minimum value = 0.004
Then range set = 0.214 - 0.004
= 0.21
Thus, range of set ⇒ 0.21
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Simplify, the solve.
Answer:
1/64
Step-by-step explanation:
4x4^3/4^7
4^-3
1/4^3
1/64
