Consider the polar curve defined by the function r = 3 − 5 sin θ as
shown in the accompanying graph.
c) Find the equation of the rightmost vertical tangent of the outer loop.
d) Find the equation of the horizontal tangent of the inner loop.
Please Help! I can't find a question like this anywhere and was never taught this. I have no idea how to do this.
Answers
c. The equation of the vertical tangent of the outer loop is r = 5
d. The equation of the horizontal tangent of the inner loop is r = 2
What is the equation of a tangent to a curve?The equation of the tangent to a polar curve is the equation of the line that touches the curve at one point and tangent to it.
c. Since we have the polar curve defined by the function r = 3 − 5 sin θ
To find the equation of the equation of the rightmost vertical tangent, we draw a vertical line that touches the rightmost curve and intersects the horizontal r - axis. The point at which the line touches the horizontal r - axis is the equation of the tangent line.
So, from the graph, the vertical line touches the horizontal r-axis at r = 5
So, the equation of the vertical tangent of the outer loop is r = 5
d. Since we have the polar curve defined by the function r = 3 − 5 sin θ
To find the equation of the equation of the horizontal tangent of the inner loop, we draw a horizontal line that touches the innermost curve and intersects the vertical r - axis. The point at which the line touches the vertical r - axis is the equation of the tangent line.
So, from the graph, the horizontal line touches the vertical r-axis at r = 2
So, the equation of the horizontal tangent of the inner loop is r = 2
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Related Questions
Someone, please explain how to solve this problem... I've tried multiple times and used all my resources, I keep getting the incorrect answer and it's frustrating. So if someone could help I'd be very grateful.
6/7 of the party delegates were proclaiming their positions if 1100 or not involved in this Behavior, how many delegates were there in all
Answers
Answer:
34
Step-by-step explanation:
Answer:
157 party delegates is 1/7 of 1100. Multiply that by 6/1 to get 6/7. 157 multiplied by 6 is 942. 942/110
Add 157 + 942 to get 1100
I've tried this before and for me it was pretty confusing but I eventually figured it out
I hope this helps!
Using the information below. Find the velocity with which a ball reaches the ground when it is dropped from a height of 64 m. If a ball is dropped on the ground from a height of h m, then the ball reaches the ground with the velocity 4.43 √h m/sec.
Answers
The ball reaches a speed of
\(4.43\sqrt[]{h}\text{ }\frac{m}{s}\)when dropped from a height of h meters.
When dropped from a height of 64 meters, the terminal speed would be
\(4.43\sqrt[]{64}\rightarrow35.44\text{ }\frac{m}{s}\)The weight of Jane and Jessica was in the ratio of 8 : 9. Jane gained 2 kg while Jessica lost 4 kg. They then had the same weight. What was Jane's weight at first?
Answers
Answer:
48 kg
Step-by-step explanation:
The given relations can be used to write a system of equations for the two weights. Those can be solved to find Jane's weight.
__
setupLet x and y represent Jane's and Jessica's original weight, respectively. The ratio of weights was ...
x/y = 8/9
After the changes in weight, they were equal:
x+2 = y-4
__
solutionAdding 4 to the second equation, we have an expression for y that can be substituted into the first equation.
y = x +6 . . . . . . . . . . solve the second equation for y
x/(x+6) = 8/9 . . . . . . substitute for y in the first equation
9x = 8(x +6) . . . . . . . multiply by 9(x+6)
x = 48 . . . . . . . . . . . simplify and subtract 8x
Jane weighed 48 kg at first.
_____
Alternate solution
The original difference in "ratio units" was 9-8 = 1 ratio unit. We find that this corresponds to 6 kg after the weight changes make the weights equal. Then 8 ratio units will be 8(6 kg) = 48 kg—Jane's original weight.
(This mental solution is virtually the same as the solution using equations shown above.)
Is it possible for PQ to have two
distinct midpoints, M₁(a, b) and M₂(c,d)?
Answers
A line segment cannot have two distinct mid points.
What is midpoint of a line?
The midpoint of a line is the middle point of a line segment.
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Coordinate of midpoint of a line divided by ratiofor external division: (x,y) = ([(mx2 + nx1) / (m + n )], [(my2 + ny1)/(m+n)])
for internal division: (x, y) = ([(mx2 - nx1) / (m -n)], [(my2 - ny1)/(m - n)])
where;
m, and n are ratio of line divisionx, and y are the coordinates of the midpointsThus, a line segment cannot have two distinct mid points.
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For triangle ABC (shown here), the value of angle BCD is equal to 30 degrees. If CD is the height of the triangle and is 12 centimeters, then what is the perimeter of triangle ABC?
Answers
The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.
What is the perimeter?
The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.
Let's call the length of AB x and the length of BC y.
First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:
Area of triangle ABC = 1/2 * CD * AB
Substituting the given values, we have:
1/2 * 12 * x = 6x
So the area of triangle ABC is 6x square centimeters.
We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:
tan(30) = x/y
Simplifying, we get:
y = x/tan(30) = x/(1/√(3)) = √(3) * x
Now we can use the formula for the area of a triangle in terms of its sides:
Area of triangle ABC = 1/2 * AB * BC * sin(B)
where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:
Area of triangle ABC = 1/2 * x * √3 * x * sin(60)
Simplifying, we get:
Area of triangle ABC = 1/4 * √3 * x²
Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:
6x = 1/4 * √(3) * x²
Multiplying both sides by 4/√3, we get:
24/√(3) * x = x²
Simplifying, we get:
x² - 24/√(3) * x = 0
Using the quadratic formula, we get:
x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1
Simplifying, we get:
x = 16√(3) / 3 or x = 8 √(3) / 3
Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:
y = √(3) * x
Therefore, we have two possible triangles:
Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3
Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3
The perimeter of each triangle is the sum of its side lengths. Therefore:
Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm
Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm
hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.
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Help pls I don’t know anything
Answers
Answer:
Step-by-step explanation:
first do this
A rectangle is 3 yards long and į yards wide . What is the area of the rectangle? Enter your answer as a fraction in simplest form by filling in the boxes
Answers
Answer:
the area is 3i as a fraction would be 3i/1
Step-by-step explanation:
Thanks
What expression is equivalent to 3+2(x+4)(x-4)
Answers
Answer:
\(\large\boxed{\tt 2x^{2} - 29}\)
Step-by-step explanation:
\(\textsf{We are asked what expression is equivalent to the given expression.}\)
\(\textsf{Note that we can find an equivalent expression by simplifying the expression we}\)
\(\textsf{already have. We can combine like terms, and simplify by using the \boxed{\textsf{FOIL}} method.}\)
\(\large\underline{\textsf{What is the FOIL Method?}}\)
\(\textsf{The FOIL Method is a method that can broken down which tells us how to}\)
\(\textsf{multiply 2 binomials. Remember that binomials are expressions with 2 terms.}\)
\(\underline{\textsf{FOIL Means;}}\)
\(\textsf{F - Front terms.}\)
\(\tt (\ \boxed{\tt4x}+3)(\ \boxed{\tt 3x}+1)\)
\(\textsf{O - Outer terms.}\)
\(\tt (\ \boxed{\tt 4x}+3 )(3x+ \boxed{\tt 1} \ )\)
\(\textsf{I - Inside terms.}\)
\(\tt (4x+\boxed{\tt3} \ )(\ \boxed{\tt 3x}+1)\)
\(\textsf{L - Last Terms.}\)
\(\tt (4x+\boxed{\tt3} \ )(3x+ \boxed{\tt 1} \ )\)
\(\textsf{We should also use the Distributive Property.}\)
\(\boxed{ \begin{minipage}{20 em} \\ \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the \underline{left} of the parentheses into the terms \underline{inside} the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c) = ab+\tt ac \\ \textsf{A will multiply with b and c as a is the term to the left of the parentheses, and b and c are inside the parentheses.}\end{minipage}}\)
\(\large\underline{\textsf{Solving;}}\)
\(\tt 3+2(x+4)(x-4)\)
\(\underline{\textsf{Use the Distributive Property;}}\)
\(\tt 2(x+4) = 2x + 8\)
\(\tt 3+(2x+8)(x-4)\)
\(\underline{\textsf{Use the FOIL Method;}}\)
\(\textsf{F - Front terms.}\)
\(\tt (\ \boxed{\tt2x}+8)(\ \boxed{\tt x}-4)\)
\(\textsf{O - Outer terms.}\)
\(\tt (\ \boxed{\tt 2x}+8 )(x- \boxed{\tt 4} \ )\)
\(\textsf{I - Inside terms.}\)
\(\tt (2x+\boxed{\tt 8} \ )(\ \boxed{\tt x}-4)\)
\(\textsf{L - Last Terms.}\)
\(\tt (2x+\boxed{\tt 8} \ )(x- \boxed{\tt 4} \ )\)
\(\underline{\textsf{We should have;}}\)
\(\large\boxed{\tt 2x^{2} - 29}\)
\(\textsf{(After Combining Like Terms)}\)
Please awnser asap I will brainlist
Answers
They can buy 120 vans, 60 small trucks, and 80 large trucks.
How to find the number of van, small trucks and large truck needed?The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck
Therefore,
let
s = number of small truck
number of van = v
let
l = number of large truck
v + s + l = 260
25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000
v + 2s + 2l = 400
Hence,
v = 2s
So,
2s + 2s + 2l = 400
4s + 2l = 400
2s + s + l = 260
3s + l = 260
2s + l = 200
s = 60
l = 200 - 2(60)
l = 200 - 120
l = 80
v = 2(600 = 120
Therefore, they can buy the following:
number of small truck = 60
number of van = 120
number of large truck = 80
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103/8-9/14*14/17 please help thx
Answers
Answer:
12.3455882353
Step-by-step explanation:
(103/8) = 12.875
(9/14) = 0.64285714285
0.64285714285 x 14 = 9
(9/17) = 0.5294117647
12.875 - 0.5294117647 = 12.3455882353
The function D(t) = 20e–0.4t represents the milligrams of a drug that remain in a person’s system t hours after the drug was administered. What does 20 represent?
A. the decay rate
xxxxB. initial dosage in milligrams
C. hours until no amount remaining
D. amount of drug that remains in the system
Its B
Answers
The "number 20" in the function D(t)=20e–0.4t which tells about the milligrams of a drug that remain in a person’s system t hours after the drug was administered, represent the initial dosage in milligrams.
What is known as a function?A function refers to a rule or law that defines the relationship between one variable (independent variable) and another variable (dependent variable). They are often ubiquitous and are essential for formulating physical relationships in the sciences.
As the main function represents the milligrams of a drug that remain in a person's system t hours after the drug was administered, however, the "20" means the initial dosage in milligrams of the administered drug.
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Answer:
Step-by-step explanation:
It is B (initial dosage in miligrams)
EDGE answer
find the slope and y intercept, then write out the linear equation (y=mx+b) below
Answers
Answer:
y = 2x + 3
Step-by-step explanation:
You can find the slope on the graph by looking at the points. From one point to the next you go Up2Over1.
Up2Over1 is the slope and in actual algebra it is 2/1, which is just 2.
The slope is 2. Fill in 2 in place of m in
y = mx + b
y = 2x + b
Next the y-intercept which is the b, can also be seen on the graph. The y-intercept is where the graph crosses the y-axis. The line crosses the y-axis at 3. Fill in 3 in place of the b.
y = 2x + 3
Which equations can be used to determine the area of the irregular figure?
Answers
Answer:
the first option put I'm not 100% sure so if I get it wrong I apologize
Will pi(π) ever end?
Answers
Answer:
Being an irrational number, π cannot be expressed as a common fraction, although fractions such as 227 are commonly used to approximate it. Equivalently, its decimal representation never ends and never settles into a permanently repeating pattern.
Answer:
Technically no
Step-by-step explanation:
hope it helps
If you spin the spinner, on which numbers is there an equal chance of landing?
Answers
Answer:
the answer to this question is simple it's 4 because it has the larger amount while the others have very little to compete with.
\(\huge\color{aqua}{ \colorbox{orange}{\colorbox{white} {Answer:}}}\)
It could land in 4 because there is an 50% chance that it could land there.
\(\huge\color{purple}{ \colorbox{orange}{\colorbox{white} {ChaEunWoo2009}}}\)
#CarryOnLearning
Felix used 1.64 meters of fabric to make a pair of pants. Alicia used 1.71 meters of fabric to make a skirt. Who used more fabric and how did you get the answer?
Answers
Given:
∠1 and ∠2 are supplementary angles
Prove:
l || m
Answers
Hello
just a second
people reading this please complete because you will help me a lot.
I am an Indian girl my name is Lamer and am 13 years old.
I Just got this new device after working at a farm for 2 years.
I used to use brainly at my friend device she had money to buy brainly plus.
I cant please help me get points so I can get good marks and my dad let me complete my education instead of getting married.
Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri will need [Blank] glass tiles. The dimentions are...26 , 15, 8.
Answers
The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.
What is the Surface Area of a Box?The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.
What is the Surface Area of a Box?SA = 2(lw + lh + hw), where:
l = lengthw = widthh = height of the boxThe image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:
The surface area to be covered = surface area of the box - area of the bottom rectangular face
The surface area to be covered = 2(lw + lh + hw) - (l)(w)
l = 26
w = 15
h = 8
Substitute
The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =
The surface area to be covered = 1436 - 390 = 1,046 cm
Area of one tile = 1 cm square
Number of tiles needed = 1,046/1
Number of tiles needed = 1,046 tiles.
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2. How many radians are in 27"?
Answers
The answer is 0.471 radians.
FORMULA:
Just do 27° × π/180 = 0.4712rad but then cut off the two.
HELP PLEASE FAST!!!!!
Answers
Answer:
part a: y = -5/2 + 100
part b: because the line is descending from left to right, moving down by 5 units, and moving across by 2 units, the slope is -5/2. the y-intercept can be found by looking at the y-value where the line crosses the y-axis- which is 100.
part c: the slope represents the relation of a cellphone's battery percentage with the number of hours that pass.
Step-by-step explanation:
hope this helped, good luck!
1 European euro = 1.3687 US dollars. While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent.
Answers
Answer:
Its actually 44.70
Step-by-step explanation:
i took the test
An electrician cuts a 50 ft piece of wire into 3 pieces. The first piece is 4 ft longer than the second piece and the third piece is 2 feet shorter than the second piece. How long are the pieces?
Answers
Answer: 1st is 20 2nd is 16 and 3rd is 14
Step-by-step explanation:
Question 1
A company makes a book bag and charges a one-time design fee of $100 and then $5 for each bag made. What equation shows how the cost of a book bag order depends on the number of bags, n?
Answers
Answer:
C = 5n + 100
Step-by-step explanation:
The cost (C) to make a book bag is an initial fee of $100 with an additional $5 for each bag (n) made. The equation will look like
C = 5n + 100
Plz help
What is |5 x -3|?
-15
⊝
-8
⊝
15
⊝
8
Answers
Answer:
What type of math is this
Step-by-step explanation:
Cassie bought a new sweater
Answers
Answer:
Ok, sup
Step-by-step explanation:
Hello random community i have a question to ask what is 7/8 - 3/4
Answers
Answer: 1/8
Step-by-step explanation:
First make the bottom half the same:
3/4*2/2=6/8
We don’t need to change the first portion since they have a common factor
7/8-6/8=1/8
25.3 + x= 32 what is the answer to this problem
Answers
Answer:
6.7
Step-by-step explanation:
Answer:
6.700
Step-by-step explanation:
hope this helped
10. Olivia charges $6.50 per hour to babysit.
She babysat for 3 hours on Friday and
some hours on Saturday. Write two
equivalent expressions for her total wages.
Answers
The two equivalent expressions for her total wages.
T=6.5*3+6.5h
T=6.5(h+3)
This is further explained below.
Write two equivalent expressions for her total wages.?Generally, the equation for expressions is mathematically given as
F=6.5*3
S=6.5h
T=6.5*3+6.5h
T=6.5(h+3)
In conclusion,
T=6.5*3+6.5h
T=6.5(h+3)
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in the formula C= prn, p stands for
A. percent
B. period
C. price per item
D. promotion
Answers
Answer:
C.
Step-by-step explanation:
derivate (cos(3x^2). (5x^3 -1)^1/3 +sin 4x^3)^4
\( \: \: \: \: find \: first \: derivative \\ ( cos(3x {}^{2} ) \times ( \sqrt[3]{5x {}^{3} - 1} ) + \sin(4x {}^{3} ) {}^{4} \)
Answers
Answer:
Step-by-step explanation:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)
Lets look at the derivative part:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)
\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)
Substituting in eq(1), we have:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)