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
Zachary and Heather are measuring the growth of a plant for a science experiment. They stopped recording the growth after week 6. Which of the following could be a reasonable estimate for the value of the plant height at week 10?
35 inches
47 inches
50 inches
43 inches
will mark brainliest
Answers
Answer:
43, it raises by 4 each time. good luck!
Step-by-step explanation:
pls help i feel like im doing it right but i wanna make sure
Answers
Answer:
-43
Step-by-step explanation:
1. -3 x -3 x -3 = -27
2. -27- 4 x 4
3. -27- 16 = -43
Misaki’s fish tank is half full of water because she is cleaning it. The tank is a right rectangular prism with a length of 8 inches, a width of 6 inches, and a height of 6 inches.
A prism has a length of 8 inches, width of 6 inches, and height of 6 inches.
What is the volume of water in the tank while Misaki is cleaning it?
O 10 Inches cubed
O 36 Inches cubed
O 144 Inches cubed
O 288 Inches cubed
Answers
Answer:
144 Inches cubed
Step-by-step explanation:
8 × 6 × 6 = 288.
288 / 2 = 144.
you multiply to get the original volume then divide by 2 because the tank is only half full.
Answer:
d
Step-by-step explanation:
i said
what is 64 (y7)7 2y3 mark branliest if right
Answers
Answer:
65
Step-by-step explanation:
hope this helps
Answer:
32256y^4
Step-by-step explanation:
hey can anyone help me in dis!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1. blue
2. blue because I measured both lines with a ruler.
3. this one was harder to decide because when I look at the picture both lines look the same length but since I measured both lines with a ruler I realized that the blue line was longer that the red line.
Step-by-step explanation:
I actually measured both lines with a ruler and the blue line is just barely bigger that the red line
You revived 1/4 pound of candy from your grandmother, 1/2 pound of candy from your sister, and 1/8 pound of candy from your best friend. How many pounds of candy did you receive?
Answers
Answer:
⅞ pound
Step-by-step explanation:
You received 1/4 pound of candy from your grandmother.
You received 1/2 pound of candy from your sister.
You received 1/8 pound of candy from your best friend.
The total amount of candy you received is given as the sum of all the candy that he received from your grandmother sister and best friend.
The total amount of candy is therefore:
¼ + ½ + ⅛ = ⅞ pound
You received ⅞ pound of candy in total.
A student used the point-slope form to write the equation of a line that has a slope of Three-fourths and passes through the point (3, –2). The student’s work is shown to the left. Examine the steps to determine whether the student made an error. The student made .
Answers
Answer:
The student made an error in step 3
Step-by-step explanation:
Answer:
The student made an error on C. Or step 3.
Step-by-step explanation:
easy geometric shapes question #6 help please!
Answers
Answer:
it will gemetry and get 15
laura goes shopping she spends one fourth of her money on a pair of shorts and one third of her remaining money on a belt if laura has $42 dollars left after these two purchases how much money did she have when she started shopping?
Answers
Answer:
84 dollars
Step-by-step explanation:
use x to represent the amount of money Laura had when she started shopping.
use y to represent the amount of money she had left after buying a pair of shorts.
You can create these two equations:
3/4x=y
2/3x=42
now, subsitute the value of y into the second equation.
2/3(3/4x)=42
1/2x=42
x=84
If a taxi ride is m miles, which expression can be used to find the total charge of the ride
Answers
Answer:
d. 0.85m + 2.50
Step-by-step explanation:
In the figure attached, the complete question is shown.
We can see in the table that $2.50 is a fixed charge, that is, it is not modified by any variable. On the other hand, for each travelled mile, the cost of the travel increases $0.85 ($0.75 by mileage charge + $0.1 by city gas tax). Then, if m miles are travelled, the cost of the travel increases 0.85*m
what is the equation of the linear function?
Answers
Answer: [tex]y=-\frac{1}{2} x+3[/tex]
Step-by-step explanation:
use the formula y=mx+b
m = slope
b = y-intercept
slope is rice over run
rise 1 run -2 m= -1/2
y- intercept is the point where the line intercepts with the y-axis
b=3
plug into equation
[tex]y=-\frac{1}{2} x+3[/tex]
Answer:
what she said
Step-by-step explanation:
Martin dennis brought a wide screen television for $1720. He made a down payment of 15% and paid the balance over 18 months. The fiance charge was 4% of the amount financed. Find the down payment and the installment price of the televison and the monthly payment
Answers
Answer:
Down payment is $258
Installment price is $1766.22
monthly payment is $83.79
Step-by-step explanation:
Down payment is 15% of $1,720 which is $258 (15%*$1720)
Monthly payment can be computed using pmt formula in excel
=pmt(rate,nper,-pv,fv)
rate is the interest rate per month which 4%/12=0.33%
nper is the number of months of payments that is 18
pv is the finance amount which is the price minus down payment i.e $1462 *($1720-$258)
fv is the total finance amount plus interest which is unknown i.e 0
=pmt(0.33%,18,-1462,0)=$ 83.79
installment price =down payment +total repayment
=$258+($83.79*18)=$1766.22
The number of customers rose from 118 on monday to 205 on tuesday. What is the percent increase to the nearest tenth of a percent
Answers
Answer:8
Step-by-step explanation:$4
Solve algebraically
x-4y=-10
x+y=5
Answers
Answer:
if x+y=5, then x=5-y
so x-4y=-10
5-y-4y=-10
5-5y=-10
-5y=-15
y=3
x=5-y
x=5-3
x=2
x=2; y=3
What is the slope of the line ?
Answers
Answer:
-3
Step-by-step explanation:
1. Express as a unit rate
a) Serena walks 4 km in 1 h.
Answers
Answer:
Step-by-step explanation:
Serena walks 4 km in 1 h.
That means:
1) She walks 4 km per hour.
2) She spends 1/4 = 0.25 hour per mile.
Have a good day.
We can write this as:
4 kilometers/1 hour
The unit rate is already simplified so there is nothing else to do.
Answer: 4km/1hr
Best of Luck!
Lightning strikes Earth 1000 times in 10 seconds. a. How many times does lightning strike in 12 seconds? Lightning strikes times in 12 seconds. Question 2 b. How many seconds does it take for lightning to strike 7250 times? It takes seconds for lightning to strike 7250 times.
Answers
Answer:
1000/10x12= answer
Step-by-step explanation:
Part A:
Divide the number of lightning strikes to the number of seconds to find the average rate.
1000 / 10 = 100 strikes per second
Now, multiply by 12 to find the number of strikes that occurred.
100 * 12 = 1200 strikes in 12 seconds
Part B:
Divide the number of seconds to the number of lightning strikes to find the average rate.
10 / 1000 = 0.1 seconds per strike
Now, multiply by 7250 to find the number of seconds that passed.
0.1 * 7250 = 72.5 seconds in 7250 strikes
Best of Luck!
Brennan measured a boarding school and made a scale drawing. A building at the school is 21 centimeters long in the drawing. The actual building is 147 meters long. What is the scale of the drawing?
Answers
Answer:
Check the explanation
Step-by-step explanation:
1 centimetre is = 0.01 meter
therefore the scale in Brennan drawing is 1 centimetre is used to represent 7 metres
Answer:
1 cm:7 meters
Step-by-step explanation:
The scale drawing shows the length in the drawing, then a colon and the actual lenght of the object. The actual building is 147 meters long and the drawing is 21 centimeters long. From this, we have:
21 cm:147 meters
As both numbers can be divided by 21, you can simplify and you would have that the scale of the drawing is:
1 cm:7 meters
Which property of equality could be used to solve -3x = 348? A. addition property B. subtraction property C. division property D. multiplication property
Answers
Answer:
B:subtraction property
Step-by-step explanation:
Area of a Circle
10 POINTS+BRAINLIEST
Answers
Answer:
Circle 1 = 24 pi in² = 452.2 in²
Circle 2 = 706.5 in²
Circle 3 = 271.6 in²
Step-by-step explanation:
In order to find the Diameter of a circle, you have to multiply the radius by 2. According to circle 1, 12in (radius) multiplied by 2 gets you 24 pi in².
In order to find the area, you multiply the radius² and then multiply it by pi or 3.14.
Is green the circumference or the diameter??? Had a little bit of confusion in that part, but I gave you the area only for Circle 2 and 3. For circle 1 I found the diameter (24 pi in²) and the area.
set f(y)=x and solve for y
Answers
Answer:
f = 1
y = 0
Solved for y
Step-by-step explanation:
Step 1 :
Pulling out like terms/ factors.
Step 2 :
Theory - Roots of a product .
Step 3 solving a Single Variable Equation.
Answers:
f = 1
y = 0
Hope this helps.
What is the measure of STR
Answers
Answer:
Str (Texture aspect ratio) Str is a measure of uniformity of the surface texture
Step-by-step explanation:
The sound of thunder from a bolt of lightning was heard 2.6 seconds after the lightning hit,from 895 meter away.What was the speed of sound to the nearest tenth of a meter of a meter per person
Answers
Answer:
344.2m/s
Step-by-step explanation:
The parameters given are:
Distance=895meter
Time=2.6seconds
Therefore the speed of sound is:
Speed of sound= distance/time taken
= 895/2.6
=344.23
=344.2m/s ( to the nearest tenth)
Answer:
d 344.2 meters per second
Step-by-step explanation:
edge 2021
1. The speed of a motorcycle increases from 10 km/hr to 50 km/hr in 9
seconds. What is its acceleration?*
Answers
Answer:
The acceleration is 4.4 km/sec/sec
Step-by-step explanation:
Acceleration of motorcycle is 4.44 km/sec²
Given that;Starting velocity = 10 km/hr
Final velocity = 50 km/hr
Time taken = 9 second
Find:Acceleration of motorcycle
Computation:Acceleration of motorcycle = [Final velocity - Initial velocity] / Time taken
Acceleration of motorcycle = [50 - 10] / 9
Acceleration of motorcycle = [40] / 9
Acceleration of motorcycle = 4.44 km/sec²
Learn more:https://brainly.com/question/12550364?referrer=searchResults
Aretha is driving her car 325 miles to get to her vacation home. She travels the first 195 miles in 3 hours. At this rate, how long will it take her to make the complete trip
Answers
Answer:
For this case we know that the total distance to travel is 325 mi. And we know that Aretha travels at the following velocity:
[tex] V = \frac{X}{t} = \frac{195 mi}{3 hr}= 65 \frac{mi}{hr}[/tex]
Then we can use the following definition:
[tex] D = Vt[/tex]
Where D is the distance and V the velocity. And solving for t we got:
[tex] t = \frac{D}{V}[/tex]
And replacing we got:
[tex] t = \frac{325 mi}{65 \frac{mi}{hr}}= 5[/tex]
So then we can conclude that after 5 hours at this rate Aretha will arrive to home
Step-by-step explanation:
For this case we know that the total distance to travel is 325 mi. And we know that Aretha travels at the following velocity:
[tex] V = \frac{X}{t} = \frac{195 mi}{3 hr}= 65 \frac{mi}{hr}[/tex]
Then we can use the following definition:
[tex] D = Vt[/tex]
Where D is the distance and V the velocity. And solving for t we got:
[tex] t = \frac{D}{V}[/tex]
And replacing we got:
[tex] t = \frac{325 mi}{65 \frac{mi}{hr}}= 5[/tex]
So then we can conclude that after 5 hours at this rate Aretha will arrive to home
Answer: 5 hours
Step-by-step explanation:
An easy way to find the answer is to make an equation.
[tex]\frac{195}{3} =\frac{325}{x}[/tex]
Make a diagonal oval with the two known numbers. So for this equation, it is 325×3. After multiplying, you will get a product of 975. Then divide this by the 3rd known number, which in our case is 195. 975÷195=5.
I hope you learned from this and don't hesitate to ask if you have any questions.
in a certain algebra class of 26 students, 16 of them play basketball and 9 of them play baseball. there are 5 students who play both sports. what is the probability that a student chosen randomly plays basketball or baseball
Answers
Answer:
3/26 students or 11%
Step-by-step explanation:
Answer:
8/9
Step-by-step explanation:
24/27 = 8/9
Please can people help??!!
Photo below
Answers
i think this is the method for solving it
The Waves swim team has a ratio of 14 boy: 12 girls. If there are 39 athletes,How many girls are there?
If 7 more boys join the Waves team, how many girls should be added to the team to maintain the same ratio of boys and girls.
Answers
Answer:
1. 18 girls
2. 5 girls will be added to maintain the same ratio of boys and girls
Step-by-step explanation:
1. Boys : Girls = 14 : 12
14 + 12 = 26, 39/26 = 1.5
Boys: 14 x 1.5 = 21
Girls: 12 x 1.5 = 18
21 + 18 = 39 athletes, there are 18 girls on the 39 athletes.
2. Boys : Girls = 14 : 12
14 : 12
7 : ?
14 - 7 = 12 - ?
7 = 12 - ?
12 - 7
= 5
If there is any wrong, Please correct me or reply to me!
Of the last 12 contestants on a game show, 9 qualified for the next round.
What is the experimental probability that the next contestant will qualify for the next round?
Answers
Answer:
0.75
Step-by-step explanation:
Given:
Of the last 12 contestants on a game show, 9 qualified for the next round.
To find:
The experimental probability that the next contestant will qualify for the next round.
Solution:
Probability refers to the chances of occurrence of some event.
Probability = Number of favourable outcomes/Total number of outcomes
Number of contestants who qualify for the next round = 9
Total number of contestants = 12
So,
The experimental probability that the next contestant will qualify for the next round = [tex]\frac{9}{12}=\frac{3}{4}=0.75[/tex]
Can anyone help me fix the mistakes i made? I will give you brainiest if you do and the teacher tells me its correct.
Answers
Answers:
#1: infinite solutions; #2: no solutions
Step-by-step explanations:
Steps for #1
3(2x+7)=13+4(x+2)+2x
6x+21=13+4x+8+2x
6x+21=21+6x
6x=6x
x=x
After completing the steps to find the value of x using Order of Operations, we see that in the end, the answer we have is x=x. We can easily conclude that x is equal to any number because the final answer in this exercise is always whatever the value of x is. For example, if x=4, our final answer would be 4.
Steps for #2
5(6x+8)=9x-10+21x
30x+40=30x-10
40=-10
Here, we see that once we've completed the steps using the Order of Operations, we come out with the answer 40=-10, which is not true on any terms. Therefore we can simply conclude that the answer for #2 is "no solutions."
If you have any trouble figuring out how I got my answers, please refer back to the steps I used to get the answers.
Thank you!
