The slope of the tangent line to the curve at a point (x, y) is dy/dx. By the chain rule, this is equivalent to
dy/dθ × dθ/dx = (dy/dθ) / (dx/dθ)
where y = r(θ) sin(θ) and x = r(θ) cos(θ). Then
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
Given r(θ) = cos(3θ), we have
dr/dθ = -3 sin(3θ)
and so
dy/dx = (-3 sin(3θ) sin(θ) + cos(3θ) cos(θ)) / (-3 sin(3θ) cos(θ) - cos(3θ) sin(θ))
When θ = π/3, we end up with a slope of
dy/dx = (-3 sin(π) sin(π/3) + cos(π) cos(π/3)) / (-3 sin(π) cos(π/3) - cos(π) sin(π/3))
dy/dx = -cos(π/3) / sin(π/3)
dy/dx = -cot(π/3) = -1/√3
if the area is 1 then what is the side length of a square?
Answer:
1
Step-by-step explanation:
Since we are taking the area of a square, you can take the square root of its area to find the side lengths.
√1 = 1
Problems 5-9, Find the value of the variable to the nearest tenth of each triangle.
Answer:
35
Step-by-step explanation:
What is the least common multiple of 4 and 12? O 4 O 12 O 24 o ) 48
Answer:
12
Step-by-step explanation:
Least common multiple means what is the smallest number that both numbers go into
List the prime factors
4= 2*2
12 = 2*2*3
The factors that are in needed to make both are 2 and 3
We need 2 of the 2's and 1 3
2*2*3 = 12
Answer:
12
Step-by-step explanation:
I need help plss ( math ) SOMEONE ASAP
26a)729
b)2,457.6
c)3,500
d)8,100
e) 89,600
Step-by-step explanation:
just multiply first and divide with upper number to the lower
Find X
Round to the nearest tenth
Answer:
x=437.3 ft
Step-by-step explanation:
cos(29)=B/H, cos(29)=x/500. x=437.3 ft
EVALUATE: 10x – 2y3 (if x = 5 and y = 2)
Answer:
10*(5) - 2*(2)^3
= 50 - 2*8
= 50 - 16
=34
Answer:
Step-by-step explanation:
với x=5 và y=2
phương trinh trở th a
10* 5 - 2 * 2^ 3
=50 - 2*8
=50 - 16
=34
A man walks at the rate of 88 paces to the minute if the average length of his paces is 0.875m, find the time take to walk 2.31km.
Answer:
30 minutes
Step-by-step explanation:
Walk rate = 88 paces/ minute
Average length of pace = 0.875 m
Time taken to walk 2.31 km ;
The distance in metres :
1000 m = 1 km
2.31 km = (1000 * 2.31) = 2310 m
Recall :
Time taken = distance / speed
Distance walked in a minute = 88 * 0.875 = 77 m
Time taken = 2310 / 77
Time taken = 30 minutes
please help asap, see attached photo!!
what is the equation of the line that passes through (1,5) and (3,1)
Answer:
Below
Step-by-step explanation:
First let's find m
m = Δy / Δx = y2 - y1 / x2 - x1
= 1 - 5 / 3 - 1
= -2
Now to find b, you can sub in the values of (x,y) for (1,5)
5 = (-2)(1) + b
-b = -2 - 5
-b = - 7
b = 7
Final equation
y = -2x + 7
Hope this helped!
Answer:
4x + 2y - 14
Step-by-step explanation:
I hope it is understandable.
Help ! With step by step solution
Answer:
the correct answer is C
Step-by-step explanation:
first step you change the x and y powers to the square root(showing in the pic).
second the number outside of the parenthesis times the numbers inside the parenthesis and then you just figure it out how it works...
Please help I don’t understand math
Answer:
x = 12
Step-by-step explanation:
The sum of the two smaller angles is 140
80+5x = 140
Subtract 80 from each side
80+5x-80 =140-80
5x = 60
Divide each side by 5
5x/5 = 60/5
x = 12
Simplify the complex number √-16+8.
Answer:
[tex]\sqrt{-16} +8[/tex]
[tex]=4i+8[/tex]
OAmalOHopeO
WILL GIVE BRAINLIEST
How many integers n between 1 and 100 inclusive are there, such that n^2 + n is divisible by 99
Answer:
It is 121
Step-by-step explanation:
Which statement best describes the function h(t) = 210 - 15t?
Oh is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable.
O h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.
O t is the function name; h(t) is the input, or independent variable; and h is the output, or dependent variable.
Ot is the function name; h is the input, or independent variable; and h(t) is the output, or dependent variable.
Answer:
h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.
Step-by-step explanation:
The explanation is in the answer.
h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable is correct statement.
The given function is h(t) = 210 - 15t
The function is named h, and it takes an input value t (the independent variable) and produces an output value 15t (the dependent variable).
The function is often written as h(t) = 15t to make it clear that h is a function of t.
Hence, h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable is correct statement.
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Which linear inequality is represented by the graph?
Answer:
D
Step-by-step explanation:
The correct answer is D
Answer:
D
Step-by-step explanation:
y<2/3 x-1 is the answer
Use the function below to find F(-4).
F(x) = 2^x
Answer:
Step-by-step explanation:
F(x)=2^x
[tex]F(-2)=2^{-2} =\frac{1}{2^2} =\frac{1}{4}[/tex]
BRAINLIST!! 20 POINTS! PLEASE HELP ILL FAIL IF I DONT PASS THIS TEST!!!
What type of counting problem is this?
How many different sums of money exist if we can choose 4 coins from any number of pennies, nickels, dimes, and quarters?
Combination without repetition
Permutation with repetition
Combination with repetition
Permutation without repetition
Answer:
the third one: Combination with repetition
Step-by-step explanation:
it says there are any number of pennies, nickels, dimes, and quarters, so there is repetition. the order doesn't matter because it asks for the different sums, so it's a combination with repetition
"How many different sums of money exist if we can choose 4 coins from any number of pennies, nickels, dimes, and quarters?" is a Combination with repetition problem.
What is combination with repetition?A combination with repetition involves a multiset. A multiset allows elements to be repeated unlike an ordinary set.
Number of ways to select r things from n possibilities: C (n + r − 1, r)
Since he can choose any coin any number of time, repetition is there. Also, order in which coins are chosen is not important, thus it is a combination.
Therefore, the third option is correct. This is a combination with repetition problem.
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Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
Answer:
Hello,
Step-by-step explanation:
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
[tex]P(t)=125*e^{0.035*t}\\a)\\P(2000)=125*e^{0.035*(2000-1990)}=177.38...\\\\b)\\P'(t)=125*0.035*e^{0.035*t}\\\\c)\\\\P'(2000)=125*0.035*e^{0.035*(2000-1990)}=6.2084...[/tex]
Kathryn plants two different types of tomato plant. She records the number of tomatoes that she picks from each plant every day. Her records are shown below:
Plant A: 4, 6, 7, 3, 5, 2, 1, 3, 6, 5
Plant B: 5, 6, 7, 6, 8, 9, 6, 7, 7, 9
Which plant has the more consistent yield of tomatoes?
not enough information to tell
they produce about the same amount of plants
Plant A
Plant B
Answer:
Plant B
Step-by-step explanation:
When you compare the number of tomatoes she picks from plant B with plant A, you will notice that plant B has not produced less tomatoes than plant A in any day but it has either produced the same or more number of tomatoes.
brianna practices the panio 30 minutes each day write an expression for the number of hours she practises in d days
Which function can be used to find r, the total amount the teacher pays in dollars when
z scissors are ordered?
A teacher is ordering scissors for her classroom.
• the teacher pays a one-time fee of $8.
• the teacher also pays $2 for each pair of scissors ordered.
Verify that –(-x) is the same as x , for x = −4/5
Answer:
Step-by-step explanation:
-(--4,5)= -(4,5)= -4,5
Find the missing length indicated
Answer:
x = 240
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of large triangle)² = ( part of hypotenuse below it) × (whole hypotenuse)
x² = 144 × 400 = 57600 ( take the square root of both sides )
x = [tex]\sqrt{57600}[/tex] = 240
x = 240
Using Pythagoras' theorem on the 3 triangles of sides (as shown in the graphic - the 2 smaller inner triangles and the large main triangle) it can be shown that the height is the square root of the product of both segments of the baseline.
let's call the 2 segments p and q.
p+q = 400
p = 144
q = 400 - 144 = 256
so, as said before, height = sqrt(p×q) = sqrt(144×256) = 192
now the main Pythagoras with the smallest triangle to get x
x² = 192² + 144² = 36864 + 20736 = 57600
x = 240
now, FYI, why is that formula true ?
as we said, we called the segments of the long baseline p and q.
then we can the sides of the main triangle x and y.
and the height is simply h.
so, then we have for the main rectangular triangle
(p+q)² = x² + y²
and for the 2 smaller triangles
x² = p² + h²
y² = q² + h²
=>
p² +2pq + q² = p² + h² + q² + h²
2pq = 2h²
h² = pq
h = sqrt(pq)
and there you have it. just as simple as that.
find the value of trigonometric ratio
Answer:
3/5
Step-by-step explanation:
Cos C = adjacent/hypotenuse
or, Cos C = 21/35 = 3/4
Answered by GAUTHMATH
To earn $60 for the skateboard, Waheeda decides to run a lemonade stand. If she sells each glass of lemonade for $1.50, how many glasses of lemonade will she need to sell? Write and solve an equation to find the answer.
Cost of skateboard : $60
Cost of each lemonade = $1.50
Total glasses of lemonade to be sold = 60/1.5
= 60/15×10
= 4×10
= 40
Therefore she has to sell 40 glasses of lemonade
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What is the quadratic regression equation that fits these data?
Number of seconds Helght (In feet)
0
12
1
14
2
15
3
14
4
10
5
6
O A. y=-1.94x2 + 0.62x+ 9.62
B. y = -3.69x2 + 2.08x+8.07
O C. y = 15.68(0.88)
O D. y=-0.89x2 + 3.24x+11.93
SUBMIT
Answer:
Step-by-step explanation:
The answer is D. Use the Stat and then Edit button on your TI calculator to edit the values in L1 and L2 tables. In L1 enter 0, 1, 2, 3, 4, 5 and then arrow over and enter the y values into L2 the same way. Enter the number 12, then hit enter; enter the number 14, hit enter; enter the number 15 and then hit enter, etc. Do the same for the values that are going into L1.
When that is done, hit the Stat button again and arrow down to QuadReg and hit enter. Depending upon your calculator, you may have to arrow down to "calculate" or the calculator may display the equation immediately after hitting QuadReg. Again, it all depends upon your calculator.
The required correct quadratic regression equation that fits the given data is y = -0.89x² + 3.24x+11.93. Option D is correct.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
To find the quadratic regression equation, we need to use a calculator or software that can perform a quadratic regression analysis. Using such a tool, we obtain the following equation:
y = -0.89x² + 3.24x+11.93
This equation fits the data points (0, 12), (1, 14), (2, 15), (3, 14), (4, 10), and (5, 6) with a high degree of accuracy.
The equation is in the form of a quadratic function, which has a parabolic shape when graphed. The coefficient of the x² term (-0.89) indicates that the parabola is downward-facing, while the other coefficients determine the exact shape and position of the parabola.
Option A is incorrect because its equation does not fit the data points accurately. Option B is also incorrect because it is not a quadratic equation, and option C is incorrect because its equation also does not fit the data points accurately.
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using Euclids division algorithm, find the largest number that divides 475 and 871 leaving 7 as the remainder in each case
Answer:36
Step-by-step explanation:
gcd(475-7,871-7)=gcd(468,864)=36
[tex]\begin{array}{c|c|c|c|c|c}&0&1&1&5&2\\468&864&468&396&72&\boxed{36}\\468&396&72&36&0\\\end{array}[/tex]
answer please it's urgent
Answer:
HOPE IT HELP YOU . Plz tell me if it is write or wrong .
Geometry homework I need help pls pls pls
Answer:
vertex of 4 is 2
Step-by-step explanation:
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Let f(x)=1/2|x−2|. Write a function g whose graph is a translation 7 units to the left of the graph of f.
Answer:
g(x) = -2(x - 6) - 7
Step-by-step explanation:
Sorry if I'm wrong
