Find the values of θ at which there are horizontal tangent lines on the graph of r = 1 + cos θ.
Answers
Answer:
θ = π/3 and 5π/3
Step-by-step explanation:
x = r cos θ and y = r sin θ. Therefore:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dx = (r cos θ + r' sin θ) / (-r sin θ + r' cos θ)
In this case, r = 1 + cos θ and r' = -sin θ.
dy/dx = ((1 + cos θ) cos θ + (-sin θ) sin θ) / (-(1 + cos θ) sin θ + (-sin θ) cos θ)
dy/dx = (cos θ + cos²θ − sin²θ) / (-sin θ − sin θ cos θ − sin θ cos θ)
dy/dx = (cos θ + cos²θ − (1 − cos²θ)) / (-sin θ (1 + 2 cos θ))
dy/dx = (cos θ + 2 cos²θ − 1) / (-sin θ (1 + 2 cos θ))
The tangent line is horizontal when the numerator of dy/dx is 0 and the denominator of dy/dx is not 0.
0 = 2 cos²θ + cos θ − 1
0 = (cos θ + 1) (2 cos θ − 1)
cos θ = -1 or 1/2
θ = π/3, π, 5π/3
0 = -sin θ (1 + 2 cos θ)
sin θ = 0 or cos θ = -1/2
θ = 0, 2π/3, π, 4π/3
Therefore, the answer is θ = π/3 and 5π/3.
Related Questions
A cylinder has a height of 14 inches and a radius of 5 inches. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
Answer:
1099 inches
Step-by-step explanation:
We know that formula for volume of a cylinder is:
[tex]V=\pi r^2h[/tex]
[tex]V=\pi 5^2*14[/tex]
[tex]V=\pi 25*14[/tex]
[tex]V=\pi 350[/tex]
[tex]V=3.14*350[/tex]
[tex]V=1099[/tex]
Answer:
1099
Step-by-step explanation:
If the length of a rectangular television screen is 20 inches and its height is 15 inches, what is the length of its
diagonal
Answers
Answer:
25 inches
Step-by-step explanation:
Using the Pythagorean theorem;
20^2 + 15^2 = C^2
C= 25
Answer:
its 25
Step-by-step explanation:
there right
See the question above.
A) 96 ft2
B) 24 ft2
C) 48 ft2
D) 38 ft2
Answers
Answer:
C. 48 [tex]ft^2[/tex]
Step-by-step explanation:
The formula for finding the area of a triangle is:
[tex]\frac{1}{2}bh[/tex]
The "[tex]b[/tex]," is the base (10), and the "[tex]h[/tex]," is the height (9.6), so plug it in:
[tex]\frac{1}{2} (10)(9.6)\\[/tex]
[tex]\frac{1}{2} (96)[/tex]
48 [tex]ft^2[/tex]
A function g(x) has x-intercepts at (5,0) and (6, 0). Which could be g(x)?
g(x) = 2(x + 1)(x + 6)
g(x) = (x + 6) (2x - 1)
g(x) = 2(x-2)(x-6)
g(x) = (x + 6) (x + 2)
Answers
Answer:
g(x) = a(x-5) ( x-6)
Step-by-step explanation:
A function g(x) has x-intercepts at (5,0) and (6, 0)
g(x) = a(x-5) ( x-6)
If you mistyped and the x intercepts are at 2 and 6
g(x) = 2(x-2)(x-6)
15 POINTS! will be selecting Brainliest!
How do I do this? Please give step-by-step answers + "work"- will be selecting Brainliest!
Answers
What is the distance between (-3, 4) and (-3, 10)?
Answers
Answer:
6 is the the distance between the points
The required distance between coordinates (-3, 4) and (-3, 10) is 6 units.
Given that,
The distance between the coordinates (-3, 4) and (-3, 10) is to be determined.
Coordinate, is represented as the values on x - axis and y - axis of the graph. where the values of the x-coordinate are called abscissa and the values of y coordinate are called ordinate.
Let the distance between two points be C.
Tio determined the distance between two points [tex](x_1, y_1)[/tex] and ([tex]x_2,y_2[/tex]) is given by the distance formula
C = √(x_1-x_2)^2(y_1-y_2)^2}
Putting the given coordinate in the above formula.
C = (-3+3)^2+(4 -10)^2}
C = {(0)^2+(6)^2}
C = √36
C = 6
The required distance between points is 6 units.
Thus, the required distance between coordinates (-3, 4) and (-3, 10) is 6 units.
Learn more about coordinate here:
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1/4 (8x - 20) - 16 = 10x + 51
Answers
Answer:
The answer is -9 (If your looking for x)
Step-by-step explanation: I would suggest using the app Photomap for this kind of stuff. You take a picture of an equation and it gives you a step by step explanation and the answer. Glad I could help!
find the value of c that creates a perfect square trinomial
Answers
Answer:
C equals 64
Step-by-step explanation:
To find the missing value you have to take B divide it by two and then square it. So 16/2 ----> 8 -----> 8 squared =64. Hope this helped
Which set of angles can form a triangle?
A: 2 acute and 1 right
B: 1 acute and 2 obtuse
C: 1 acute and 2 right
D: 1 acute, 1 right and 1 obtuse
Answers
Answer:
A: 2 acute and 1 right
Step-by-step explanation:
A triangle is a polygon that has 3 sides as well as three angles
Triangles can be can be classified based on their three sides as well as their three angles.
Based on their sides, we have 3 types of triangles.
1. Equilateral triangle: This means they have 3 equal sides.
2. Isoceles triangle: They have only 2 equal sides.
3. Scalene triangle: The 3 sides are not equal
Based on their angles, we have 3 triangles.
a. Acute triangle
b. Obtuse triangle
c. Right angle triangle.
One of the way by which we can form a triangle, is by forming it with 2 acute angles and 1 right angle.
Answer:
The correct option is;
A: 2 acute and 1 right
Step-by-step explanation:
Here we have the definitions of the angles as follows;
The sum of angles in a triangle = 180°
An acute angle is an angle less than 90°
An obtuse angle is an angle more 90 ° but less 180°
A right angle triangle is an angle equal to 90°
∴ A right angle triangle is an angle = 90°
Therefore, we compare each of the options
A: 2 acute and 1 right = <90 +<90 +90 < 180 =180 or >180 Possible
B: 1 acute and 2 obtuse = 1<90 + > 90 +>90 > 180°
C: 1 acute and 2 right = <90 + 90 + 90 > 180
D: 1 acute + 1 right + 1 obtuse = <90 + 90 + >90 > 180
Therefore, the only possible correct option is A.
Amy has 2 crayons. Cameron gives her 5 more crayons. How many crayons does Amy have now?
Answers
Answer:
Amy now has 7 crayons.
Step-by-step explanation:
2 crayons + 5 crayons = 7 crayons.
Answer:
Amy has 7 crayons now
Step-by-step explanation:
2+5=7
You are jumping off the 12-foot diving board at the municipal pool. You bounce up at 6 feet per second and drop to the water. Your height (h) in feet above the water in terms of (t) seconds is given by h = -16t^2 + 6t + 12. What is the first step in determining the maximum height that you reach during your dive?
Answers
Answer:
h_max = 12.56 units
(the exercise does no specify the units)
Step-by-step explanation:
You have the following function:
[tex]h(t)=-16t^2+6t+12[/tex] (1)
To calculate the maximum height reach by you, you first derivative the function h(t) respect to t:
[tex]\frac{dh(t)}{dt}=-32t+6[/tex]
Next, you equal the result of the derivative to zero and you obtain t:
[tex]-32t+6=0\\\\t=\frac{6}{32}=\frac{3}{16}[/tex]
Then, you replace this value of t in the equation (1) and you obtain the maximum height:
[tex]h(t)=-16(\frac{3}{16})^2+6(\frac{3}{16})+12[/tex]
[tex]h(t)=12.56[/tex]
hence, the maximum height is 12.56 units
Mabel is the costume manager for a large theater company. She has 20 different hats,
including 4 pork pie hats.
What is the probability that a randomly chosen hat from Mabel's inventory will be a pork pie
hat?
Write your answer as a fraction or whole number.
P(pork pie hat) =
Submit
Answers
Answer:
4/20 or 1/5 being simplified
Step-by-step explanation:
Find the area of the composite figure.
a.) 364 sq ft
b.) 796 sq ft
c.) 800 sq ft
d.) 980 sq ft
Answers
Answer:
B. 796 sq ft
Step-by-step explanation:
All of these shapes are rectangles.
The formula for the area of a triangle is length x width.
Dining Room
26 x 14 = 364
Bedroom
14 x 8 = 112
Enclosed Porch
20 x 16 = 320
Then you add all of the products.
364 + 112 = 476
476 + 320 = 796
This is the last one!!!
Answers
Answer:
B
Step-by-step explanation:
the mean goes up more than the median
cha cha cha reallllllllllllll smooth what the answer?
Answers
Answer:
d=12
Step-by-step explanation:
7d-28=56
Add 28 to both sides
7d=84
Divide both sides by 7
d=12
Cha Cha Real Smooth indeed! :3
Answer:
d=12
Step-by-step explanation:
first step is to add 28 to both sides and get 7d=84
then divide 84 by 7
d=12
good luck :D
Use the graph to find the relationship between variable
Answers
Where is the picture at?
How much water will it take to fill the aquarium?
Please anawer this question. Will put as brainliest if i get an answer
Answers
Answer:
4096
Step-by-step explanation:
You multiply 32 in. by 8 in. by 8 in.
Answer:
4096
Step-by-step explanation:
to find volume you can just multiply length, width, and height together :) Hope this helps!!! ❤
Mark wanted to find out which types of movies students in his grade at school preferred. He divided the list of student names in his grade into boys and girls and then from each group, drew names from a hat so that the number in each group was proportional to the total number of boys and girls in his grade. Will this sample represent the population, and if so, which type of sampling method did Mark use? A. Yes, simple random sampling. B. Yes, systematic random sampling. C. Yes, stratified random sampling. D. No, this was not a random sample.
NOT"C"
Answers
Answer:
the answer is not b
Step-by-step explanation:
The random sampling used is stratified random sampling
What is simple random sampling ( SRS )?The most accurate type of probability sampling is random sampling. Each person in a population has an equal probability of getting selected for the sample thanks to this method of sampling.
This kind of sampling is perfect for highly controlled investigations where it is unacceptable to have human bias in the selection of the sample.
Each sampling unit in a population has an equal probability of being included in the sample when using simple random sampling (SRS). As a result, each potential sample has an equal probability of being chosen.
Given data ,
Mark used a stratified random sampling method by dividing the list of students into boys and girls and drawing from each group in proportion to their numbers in the population. This method helps ensure that the sample is representative of the population in terms of gender.
Hence , the sample is likely to represent the population. Answer: C. Yes, stratified random sampling.
To learn more about simple random sampling click :
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2) On average, 75% of the planes leave on time. If 120 planes left on time
yesterday, how many total planes were there?
Answers
Answer:
Step-by-step explanation:160
Find the distance between point a and point b
Answers
Answer:
5 units
Since they both have the same y value, just subtract the a value's x from the b's x value
If I have 21 cone shaped hats with a diameter of 16in and height of 9in. How much paper do I need to cover the hats?
Answers
Answer:
10584 inches of paper
Step-by-step explanation:
to find the surface area of a cone the formula you use is A= πr(r+h2+r2) *you need to divide 16 by two to find the radius 16 is the diameter*
and this subsituted is π8(8+9(2)+8(2)) and this equals 504 inches and you then multiply by 21 to get enough paper to cover all 21 cones and that equals 10584 inches
Solve the following inequality for hh. Write your answer in simplest form.
h-8>4h+5
Answers
Answer:
h<-13/3
Steps:
Move variable to the left side and change its sign
h-4h-8>5
Move constant to right and change its sign
h-4h>5+8
Collect like terms
-3h>5+8
Add the numbers
-3h>13
Divide both sides of the inequality by -3 and flip the inequality sign
h<-13/3
25POINTS!!!
In ΔFGH, h = 7.1 cm, f = 6.7 cm and ∠G=103°. Find the length of g, to the nearest 10th of a centimeter.
Answers
Answer:
10.8 cm
Step-by-step explanation:
Using cosine law
g² = 7.1² + 6.7² - 2(7.1)(6.7)cos(103)
g² = 116.7018433
g = 10.80286274
Answer:
10.8
Step-by-step explanation:
deltamath
Jasmine and her brother Nat are saving to buy a digital camera that costs $135. Jasmine earns $15 per week for babysitting and spends $5 of it. Nat earns $18 per week for walking dogs and spends $7 of it. Which expression can be used to find how many weeks it will take to save for the digital camera?
Answers
Answer:
7 weeks
Step-by-step explanation:
Jasmine=$10
Nat=$11
10+11=$22 each week
135/22=6.14
at least 7 weeks
You and two friends go to eat pizza there are two deals 10% off of 1 pizza or 30% off of 3 pizzas. Do you want to each pay separately and get 10% off of your bill or do you want to spl it the bill 3 wa
Answers
Answer:
Step-by-step explanation:
Assuming the price of 1 pizza is $x. Total number of pizzas is 3.
Considering the first deal,
10% off your pizza is 10/100 × x = 0.1x. The amount that you will pay is x - 0.1x = 0.9x
The cost of the remaining two pizzas is 2 × x = 2x
The total amount to be paid is
2x + 0.9x = $2.9x
Considering the second deal, 30% off the bill would be
30/100 × 3x = 0.9x
The amount to be paid is
3x - 0.9x = $2.1x
Therefore, I prefer the second deal
What is the solution to
2x-y=1
Зу + 3 = 6x
Using system of equations
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
Reduce the second equation by dividing all three terms by 3: y + 1 = 2x. Then compare this result to the first equation 2x - y = 1. Noe that these two equations are identical. Thus, the two lines coincide. There are "infinitely many solutions."
I need help immediately with middle school
Answers
Answer:
5*7=35 square units
Step-by-step explanation:
area of parrelogram =B×h
plzz mark me brainliest
a system of equations is shown.
Answers
Answer:
x=4 , y=1
Step-by-step explanation:
y = 2x-7
y = -x +5
Set them equal to each other
2x-7 = -x+5
add x to each side
2x+x-7 = -x+x+5
3x-7 = 5
Add 7 to each side
3x-7+7 = 5+7
3x = 12
Divide by 3
3x/3 = 12/3
x=4
Now find y
y = -x+5
y = -4 +5
y = 1
Use your ruler to draw a rectangle that measures
by 4 1/2 by 2 3/4 inches, and find its area.
Answers
Answer:
Area of rectangle, [tex]A=\dfrac{99}{8}\ \text{inch}^2[/tex]
Step-by-step explanation:
We have,
A rectangle that measures [tex]4\dfrac{1}{2}\times 2\dfrac{3}{4}[/tex].
It is required to find the area of the rectangle
The product of length and breadth of a rectangle is called its area. It can be calculated as :
[tex]A=4\dfrac{1}{2}\times 2\dfrac{3}{4}\\\\A=\dfrac{9}{2}\times \dfrac{11}{4}\\\\A=\dfrac{99}{8}\ \text{inch}^2[/tex]
So, the area of the rectangle is [tex]\dfrac{99}{8}\ \text{inch}^2[/tex].
Find the sum: 4√3+11√12
15√15
15√3
26√3
48√3
Answers
Answer:
26√3
Step-by-step explanation:
4√3+11√12
We know that sqrt(ab) = sqrt(a) sqrt(b)
4√3+11[tex]\sqrt{4} \sqrt{3}[/tex]
4√3+11*[tex]2 \sqrt{3}[/tex]
4√3+22 [tex]\sqrt{3}[/tex]
Combine like terms
26√3
Answer:
[tex]26\sqrt{3}[/tex]
Step-by-step explanation:
Simplify them:
[tex]11\sqrt{12} = 22\sqrt{3}[/tex]
[tex]22\sqrt{3}+4\sqrt{3}=26\sqrt{3}[/tex]
