The slope of the line tangent to the polar curve [tex]\rm r =3sin\theta[/tex] is 1.79.
What is the slope?A surface on which one end or side is at a higher level than another; a rising or falling surface.
The slope of the line tangent to the polar curve;
[tex]\rm r =3sin\theta[/tex]
The slope of the tangent is given by the following formula;
[tex]\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ (\dfrac{dr}{d\theta}sin\theta + cos\theta)}{(\dfrac{dr}{d\theta}cos\theta-rsin\theta)}[/tex]
Differentiate the given polar curve
[tex]\rm r =3sin\theta\\\\\dfrac{dr}{d\theta}=3cos\theta\\\\[/tex]
Substitute all the values in the formula
[tex]\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ (\dfrac{dr}{d\theta}sin\theta + rcos\theta)}{(\dfrac{dr}{d\theta}cos\theta-rsin\theta)}\\\\\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ (3cos\theta \times sin\theta +3 sin \theta \times cos\theta)}{(3cos\theta \times cos\theta-3 sin \theta \times sin\theta)}\\\\\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{3 (cos\theta sin\theta + sin \theta cos\theta)}{3(cos\theta cos\theta- sin \theta sin\theta)}\\\\[/tex][tex]\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ 2sin\theta cos\theta}{(cos^2\theta -sin^2 \theta)}[/tex]
Substitute the value of [tex]\theta[/tex] in the equation
[tex]\rm \text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{ 2sin \dfrac{\pi }{6} cos\dfrac{\pi }{6} }{(cos^2\dfrac{\pi }{6} -sin^2 \dfrac{\pi }{6} )}\\\\\text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{2 \times 0.5 \times 0.86}{0.86^2 -0.5^2}\\\\\text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{0.86}{0.73- 0.25}\\\\\text{Slope of tangent line} = \dfrac{dy}{dx} =\dfrac{0.86}{0.48}\\\\\text{Slope of tangent line} = \dfrac{dy}{dx} =1.79[/tex]
Hence, the slope of the line tangent to the polar curve [tex]\rm r =3sin\theta[/tex] is 1.79.
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The cost of 4 sweatshirts and 10 pairs of shorts is $188. The cost of 9 sweatshirts and 12 pairs of shorts is $276.
Enter the cost of one sweatshirt and one pair of shorts in the response boxes
Answer: The cost of one sweatshirt is $12 and the cost of one short is $14
Step-by-step explanation:
x= sweat shirt cost
y= shorts cost
4x + 10y = 188
9x+2y=276
x= 12, y=14
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Answer:it should be b!
Step-by-step explanation:
I’m pretty sure I had the question before
The selling price of an item is $720. It is marked down by 30%, but this sale price is still marked up from the cost of $420. Find the markup from cost to sale price. Please help!
Answer:
20%
Step-by-step explanation:
old selling price = $720
new selling price = 720 x (1 - 30%) = 720 x 70% = $504
cost = $420
markup = (504 - 420)/ 420 = 84/420 = 20%
The coordinates of point R are (−3, 2), and the coordinates of point T are (4, 1). What is the length of RT?
Answer: [tex]d=\sqrt{50}, 5\sqrt{2}, \,\text{or about}\;7.1[/tex]
Step-by-step explanation:
We can use the distance formula to solve.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(4--3)^2 +(1-2)^2}[/tex]
[tex]\displaystyle d=\sqrt{(4+3)^2 +(1-2)^2}[/tex]
[tex]\displaystyle d=\sqrt{(7)^2 +(-1)^2}[/tex]
[tex]\displaystyle d=\sqrt{49+1}[/tex]
[tex]\displaystyle d=\sqrt{50}[/tex]
d ≈ 7.1
6 Three of the ten people in the Latin club are chosen at random to represent the club at a tournament. What is the probability that Joseph, Heidi, and Katy are chosen?
The probability that Joseph, Heidi, and Katy are chosen is 1/40 if three of the ten people in the Latin club are chosen at random to represent the club at a tournament option (G) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Total ways of choosing 3 out of 10 = C(10, 3) = 120
Total outcomes = 120
Total favorable outcomes = 3(Joseph, Heidi, and Katy)
Probability = 3/120 = 1/40
Thus, the probability that Joseph, Heidi, and Katy are chosen is 1/40 if three of the ten people in the Latin club are chosen at random to represent the club at a tournament option (G) is correct.
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the price of a video game was reduced from 65 to 45.50. by what percent was the price of the video games reduced
Find a factor pair of 80 that has a sum of 21.
Answer:
16 and 5
Step-by-step explanation:
Hope that helps! :)
Write 1/2 as a percent.use repeating decimals when necessary.
Answer:
50%
Step-by-step explanation:
1 / 2 = 0.5
to turn a decimal to a percent you multiply it by 100
0.5 x 100 = 50%
1. Reflect triangle A across the line x = 2.
2. Write a single rule that reflects triangle A across the line x = 2.
PLEASE HELP
I only have till tomorrow midnight to turn this in
Draw a perpendicular at x=2
Now reflect each coordinates across there
(2,2)
Will remain same as x=2 is on Q1 positive side(8,4)
x coordinate=2-8=-6y coordinate=4(same)New coordinate (-6,4)
(6,8)
x coordinate=2-6=-4 y coordinate is sameNew coordinate
(-4,8)Answer:
Rule: Reflect the figure across the y-axis then translate the reflected figure 4 units to the right.
Step-by-step explanation:
Part 1Points of Figure A:
(2, 2)
(8, 4)
(6, 8)
Draw a line at x = 2, then reflect each point across the line
(2, 2) → (2, 2)
(8, 4) → (-4, 4)
(6, 8) → (-2, 8)
Part 2Reflection in the y-axis: (x, y) → (-x, y)
As the y-values of our two figures have not changed, the first part of the rule is: reflect across the y-axis
If we reflect the figure across the y-axis, the points of the reflected figure are:
(-2, 2)
(-8, 4)
(-6, 8)
To bring the reflected figure back to where we want it (reflection in x = 2) we need to translate the figure 4 units to the right:
(-2 + 4, 2) = (2, 2)
(-8 + 4, 4) = (-4, 2)
(-6 + 4, 8) = (-2, 8)
So the final rule is:
Reflect the figure across the y-axis then translate the reflected figure 4 units to the right.
What is the area of a square with sides of length 2 1/2 cm?
The area of the square with the sides 2 1/2 cm will be A=6.25 square cm.
What is the area?The space covered by the square in the two-dimensional plane will be the area of the square. Square actually covers the area with four equal sides.
The formula for the area of the square will be given as:-
A=Side x Side
A= 2 1/2 x2 1/2
A=5/2x5/2
A=2.5x2.5
A= 6.25 square cm
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Toni bought these items for
an art project. The sales tax
is 8.5%. What is the total cost including tax, rounded to the nearest cent?
Answer: D, 43.38
Step-by-step explanation:
add all of the items up and then divide by sales tax percent. then add up the original number by the sales tax amount
HEEEEEEEEEEEEEEEEEEEEEEEEEEELP!
Answer: It's a 180 degree angle.
Step-by-step explanation:
The two dot plots show the number of goals per game. The data for each is taken from a random sample within a soccer league over a 1-month period. Complete the statements below. Goals Scored in English League A dot plot.
Answer:
first blank is 3
second blank is 2.5
last blank is 0.5
Step-by-step explanation:
Answer: Look at the attachment
3
2.5
0.5
Step-by-step explanation:
What can be said about the velocities of two cars that are both going 60 mph heading in opposite directions?
Answer:
0
Step-by-step explanation:
because they are heading in the same direction
Share what you already know about third grade math.
Answer:
6×6=36
Step-by-step explanation:
2×3=5
6×10=60
50×10=50
What is the slope below?? Please answer quickly! Due tonight.
If [tex]f(x)=[[x+2]][/tex] find [tex]f(1.5)[/tex]
Please Explain Answer Please. Thank you!
Answer:
f ( 1.5 ) = 1.5 + 2 = 3.5
If in the case you need any other help , let me know. [ You need to pay me] :) Thanks!
Answer: ⇒ 3.5
Step-by-step explanation:
⇒ f(1.5) = 1.5 + 2
⇒ f(1.5) = 3.5
simplify this expression
6x -8y -5x + 3y
Answer:
x-5y
Step-by-step explanation:
combine the X's and Y's
8 sandwiches cost £18.40
Find the cost of 5 sandwiches.
Answer:
11.5
because
8 18.40
5 ?
5×18.40=92
92÷8=11.5
Answer:
£11.50
Step-by-step explanation:
Well to solve this equation you must divide the total cost of the 8 sandwhiches by 18.40
18.40 divided by 8 is 2.30
So that means the cost per sandwhich is £2.30
Then all you have to do is multiply 2.30 by 5
2.30 divided by 5 is 11.50
So the cost of 5 sandwiches would be £11.50
Which type of function is shown in the table below?
Answer:
Exponential
Mark brainliest :)
Please help me with this it's algebra WILL GIVE BRAINLIEST and 5 points
10 in
12 in
6 in
8 in
Surface Area =
I need the surface area
Answer: the answer is 312in
when the number in pattern H is 48 what is the corresponding term in pattern G
Answer:
explain it better please
help me with this algebra equation
Answer:
it's D
Step-by-step explanation:
it's d because i guessed it was
What is the value of c? Round to the nearest tenth.
Answer:
30%
Step-by-step explanation:
Bobby has a party while his parents are away for the weekend. Bobby estimated that if his 9 friends hep him to clean the house, they will finish in time if they start 8 hours before his parents return. But after only two hours of cleaning, Bobby's parents call and say they are just two hours from home. How many more friends does Bobby need to call to help finish cleaning in time.
Using an inverse rule of three, it is found that Bobby needs to call 18 more people.
What will be the number of friends?This question is solved by proportions, applying a rule of three.The number of people working and the time needed to complete the work are inversely proportional, as more people means less time, thus, instead of cross multiplication, we multiply the lines, which is an inverse rule of three.When Bobby's parents call, with 9 people, they will need 6 hours to finish the job. How many people are needed to finish the job in 2 hours?
The rule of three is:
9 people - 6 hours
x people - 2 hours.
Multiplying by line:
2x = 6 x 9
x = 3 x 9
x = 27
Already has 9 people, in total needs 97, so he needs to call 27 - 9 = 18 more people.
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2yx^0/x^4
Simplify. I give Brainliest,.
Answer:
2y/x^4
Step-by-step explanation:
Apply the exponent rule: a^0 = 1, assuming a [tex]\neq[/tex] 0
Hence,
x^0 = 1
2y * 1/x^4
Multiply 2 and 1
2*1 = 2
= 2y/x^4
PLease Help me its a math question Is the function represented by the following table linear, quadratic or exponential?
Answer:
Exponential
Step-by-step explanation:
From the table :
3⁰ = 13¹ = 33² = 93³ = 273⁴ = 81Hence, the function is :
y = 3ˣAs the x-value is an exponential value, the function is exponential
Is the function represented by the following table linear, quadratic or exponential?
Linear
Quadratic
ExponentialExplanation:
a 3. A card is pulled from a standard deck of cards.
Can you find P(queen or hearts)? (make sure you aren't double counting!!!)
Answer:
row 4 answer 6 i just took the quiz
four plastic bottles, each with a radius of 2 inches, are packed into a cardboard box. The glasses touch each other and the sides of the box. What is the area of the bottom of the box? (The area of a circle is equal to pi times radius squared)
The area of a 2D form is the amount of space within its perimeter. The area of the bottom of the box is 64 square inches.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or other quadrilateral, multiply its length by its width.
Given the radius of the base of the plastic bottle is 2 inches, and there are four bottles arranged as shown below, therefore, the area of the bottom of the box is,
[tex]\rm \text{Area of the bottom of the box} = 8 \times 8 = 64\ in^2[/tex]
Hence, the area of the bottom of the box is 64 square inches.
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