The given curve has equation
r(θ) = 9 + 8 cos(θ)
and its derivative is
dr/dθ = -8 sin(θ)
When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.
Differentiate these with respect to θ :
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
In polar coordinates, we have
y(θ) = r(θ) sin(θ)
x(θ) = r(θ) cos(θ)
and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.
The slope of the tangent line to the curve is dy/dx. By the chain rule,
dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)
dy/dx = (dr/dθ sin(θ) + r(θ) cos(θ)) / (dr/dθ cos(θ) - r(θ) sin(θ))
When θ = π/3, the slope is
dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))
dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))
dy/dx = - 1/(17√3)
So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is
y - 13√3/2 = -1/(17√3) (x - 13/2)
y = -(x - 338)/(17√3)
If y varies directly as x and as the square of z, and y =25/9 when x=5 and z=1, find y when x =1 and z=4
Answer:
y= 80/9
Step-by-step explanation:
Given
" y varies directly as x" and "as the square of z" so y = x* z²* some number
if y =25/9 when x= 5, z= 1 and y = x*z²* some number
then 25/9 = 5 * 1² * some number
5*(5/9) = 5 * some number
therefore y = x* z²* (5/9)
y= ? when x=1 , z= 4
y = x * z² * (5/9)
y = 1 * 4² * (5/9)
y = 16*5 / 9
y = 80/9
percent change of 3.25 to 2.95
Answer:
-9.23%
Step-by-step explanation:
.
Round 0.0625 to the nearest hundredth
Please someone draw where these are supposed to go on paper (WILL MARK BRAINLEST)
Answer:
youre not pretty jjdbfjjfkdksjsjd
I bought 3,000,000 shares at .000007. what would my gain be if it reached .01 .
If 1 share had an initial cost of $0.000007, then 3,000,000 shares would be worth
(3,000,000 shares) × ($0.000007/share) = $21
If the price increases to $0.01 per share, then the same number of shares would have a value of
(3,000,000 shares) × ($0.01/share) = $30,000
So you've gained a net profit of $30,000 - $21 = $29,979, which corresponds to a
$29,979 / $21 = 1,427.57 = 142,757%
increase in value.
A tugboat goes 72 miles upstream in 9 hours. The return trip downstream takes 4 hours. Find the speed of the tugboat without a current and find the speed of the current.
Step-by-step explanation:
72÷9= 8, so the boat was only doing 8mph going upstream (against the current) the return trip downstream only took 4 hours. 72÷18=4 meaning the boat was traveling at 18mph downstream (no current) there is a 10mph difference between upstream and downstream therefore the current had to be running at 10 mph. so the speed of the tug boat is 8mph without a current and the current is running at 10mph.
I really need this last question please anyone's help is very appreciated
Answer:
y = (5/2)x + 13/2
y = 3
y = -2x + 6
Step-by-step explanation:
The left part of the function which is a line sloping up to the right contains points (-3, -1) and (-1, 4) which can be read off the graph.
Since we have two points, we can find the equation.
You can use the slope formula given two points, but I will read it off the graph with rise and run.
Go from point (-3, -1) to point (-1, 4) by going up 5 (the rise) and going right 2 (the run).
slope = rise/run = 5/2
y = mx + b
y = (5/2)x + b
Use point (-1, 4) for x and y and solve for b.
4 = (5/2)(-1) + b
8/2 + 5/2 = b
b = 13/2
y = (5/2)x + 13/2
This is the first answer.
The middle part is a horizontal line in which every point has y-coordinate 3.
The equation is:
y = 3
This is the second answer.
The right part is the line that slopes down to the right. We can read two points easily. Use points (3, 0) and (2, 2).
Start at (3, 0). Go left 1 (run of -1) and up 2 (rise of 2). Now you are at point (2, 2).
slope = rise/run = 2/(-1) = -2
Now we find the y-intercept on the graph. After you get to (2, 2), keep moving with the same run and rise of the slope. Go left 1 and up 2 to point (1, 4). Go again left 1 and up 2 to (0, 6). Point (0, 6) is on the y-axis, so it is the y-intercept.
b = 6
y = mx + b
y = -2x + 6
This is the third answer.
Fill the table so it represents a linear function
Answer:
Hey mate.....can't see the attached picture....please check again
Answer:
what table??
Step-by-step explanation:
What is reciprocal of 2 1/2
Answer:
0.4
Step-by-step explanation:
type in a calculator 1 divide by 2.5 to get the answer
Math 1 Graded Assignment Unit Test, Part 21 Polynor
(Score for Question 3:___ of 5 points)
3. Multiply the polynomials (+3a-7) and (24 - a + 4). Simplify the answer. Show your work.
Answer:
Answer:
9a-3
Step-by-step explanation:
a^2=2a+3a=5a-7+4=5a-3+(4a-a)=3a+5a=9a-3
1. Which of the following should you do first when solving the equation 3x + 2 = 4x – 5(x + 6)?
A. divide both sides by 3
B. subtract 2 from both sides
C. distribute the - 5 through the parenthesis (x+6)
D. subtract 4x from both sides
Answer:
(x+6)
Step-by-step explanation: remember gemdas
Groups
Exponents
Multipy
Divide
Add
Ssubtract
I need super help with this one.
Which expression is equivalent to 8k+10+9k+1?
-k+11 18k+10
-k+9 or 11+17k
Answer:
[tex]8k + 10 + 9k + 1 = k(8 + 9) + (10 + 1) \\ = 17k + 11[/tex]
Find the perimeter P of
v
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with vertices J(-3,-2), K(-5, -5), L(1, -5), and M(3,-2). Round your answer to the nearest tenth, if
necessary
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lab
Answer:
P = 3.6 + 6 + 3.6 + 6 = 19.2 units
Step-by-step explanation:
distance between (-3,-2) and (-5,-5) =
Sqrt[(-5-3)^2+(-5 - -2)^2]
Sqrt (4+9) = 3.6
d = (-5,-5) and (1,-5) =
Sqrt[(1 - - 5)^2 + (-5 - - 5)^2]
= sqrt (36 + 0) = 6
d = (1,5) and (3,-2)
Sqrt[(1 - - 3)^2 + (-5 - - 2)^2]
Sqrt(4+9) = 3.6
d = (3,-2) and (-3,-2)
Sqrt[(-3-3)^2 + (-2 - - 2)^2]
Sqrt (36+0) = 6
what is 200 x 300 kakakkakakakakkaakkkak
Answer:
60000 ty ..............
Answer:
60000
..............
what a difficult question !!! Do not ask such difficult questions ..lol
Simplify
8/9
____
5/6
Answer: 16/15
decimal: 1.0666
mixed number: 1 1/15
Step-by-step explanation:
An airport has an electronic system that randomly selects bags for extra security screening. Each bag has a 14% percent probability of being selected for extra screening, and one bag being selected or not doesn't affect whether or not another bag will be selected. Suppose that 222 bags go through the system, one after the other. What is the probability that both bags are selected for extra screening? Round your answer to two decimal places.
Probabilities are used to determine the chances of an event.
The probability that the two bags are selected for extra screening is 0.02
The given parameters are:
[tex]n = 2[/tex] --- number of bags
[tex]p = 14\%[/tex] --- the probability that a bag is selected for extra screening
The probability that the two bags are selected for extra screening is:
[tex]P(2) = p^n[/tex]
So, we have:
[tex]P(2) = (14\%)^2[/tex]
Express percentage as decimal
[tex]P(2) = (0.14)^2[/tex]
[tex]P(2) = 0.0196[/tex]
Approximate
[tex]P(2) = 0.02[/tex]
Hence, the required probability is 0.02
Read more about probabilities at:
https://brainly.com/question/11234923
Answer:
0.02 i did khan academy pls mark brainliest
Step-by-step explanation:
a(b+c)=a(d-e) solve for b
Answer:
b = - c + d - e
abcdefghijklmnopqrstuvwxyz
Select the correct answer.
Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina?
A.
The equation that represents this situation is t − 3 = 18. Tina is 21.
B.
The equation that represents this situation is t + 3 = 18. Tina is 15.
C.
The equation that represents this situation is 3 − t = 18. Tina is 21.
D.
The equation that represents this situation is -3 − t = 18. Tina is 15.
solve inequality: |7x+15|>-0.5
9514 1404 393
Answer:
true for all values of x
Step-by-step explanation:
The absolute value of a linear function is always at least 0, so is always greater than -0.5. The inequality is true for all real numbers.
susan and teo play soccer susans team plays every five days and teos team plays every six days when will they play on the same day
Answer: On day 30
Step-by-step explanation:
1. skip count by both 5 and 6 and look for the first number they have in
common 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
6, 12,18, 24, 30, 36, 42, 48, 54, 60
30 is the first number in common
(-6,7) (0,3)
I'm having treble finding the slop I need the sem
Did you use the formula
gradient =
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
??
I'm not shear but i think that run to -6 then 3 is the correct sorry am learning it
Anna drives her car at a speed of 70 km per hour. How much distance will she cover in 3 hours 30 minutes?
Distance» [tex]speed \times time[/tex]
Distance» [tex]70 \times \frac{7}{2} [/tex]
Distance» [tex] \frac{490}{2} [/tex]
Distance» 245
Answer:
245 units
Step-by-step explanation:
Anna drives her car at a speed of = 70 kmph
To Find:
How much distance will she cover in 3 hours 30 minutes.
Solution:
We'll use here the formula of Speed,then plug the values which are given.
Speed = Distance/Time
Speed = 70 kmphDistance = 3 hr 3 mins = 7/2 hrs70 = D/7/2
7/2*70 = Distance
7*35 = Distance
Distance = 245
We can conclude that Anna can cover 245 units in 3 hrs 30 mins.
In ΔPQR, r = 640 inches, q = 310 inches and ∠Q=30°. Find all possible values of ∠R, to the nearest degree.
Answer:
No Possible Triangles
Step-by-step explanation:
sinA/a = sinB/b
From the reference sheet (reciprocal version).
sinR/640 = sin30/310
Plug in values.
sinR= (640 (sin30))/ 310≈1.0322581
Evaluate.
R=sin −1 (1.0322581)=ERROR
Sine cannot be greater than 1.
Solve for x: 1 < x + 3 < 4
4 > x > 7
4 < x < 7
−2 > x > 1
−2 < x < 1
100 points!!!
Answer:
Solve for x: x < 1
Step-by-step explanation:
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cuanto es 21:45 dividido a 7:15?
Answer:
Entraría 3 veces.
Step-by-step explanation:
Podemos probar esto encontrando el máximo común divisor entre 21 y 45
21: 1,3,7,21
45: 1,3,5,9.15,45
Encontramos que 3 es el máximo factor común. Entonces dividimos ambos números por 3. Para obtener 7:15.
Find the missing dimension of the prism.
Answer:
10
Step-by-step explanation:
To find volume you have to multiply all 3 sides 7*8*x=560 = 56*x=560 we divide it by 56 and get x=10
(-10) + 3 please help
Answer:
The answer is -7 the answer is-7
Answer:
-7
Step-by-step explanation:
(-10)+3
-10+3=-7
-4-6=-10
-10+7=-3
IGNORE THE BOTTOM ONE PLEASE HELP
Answer:
see explanation
Step-by-step explanation:
∠ A and ∠ FCE are corresponding angles and are congruent , then
∠ A = 150°
∠ FCE and ∠ C are vertically opposite angles and are congruent , then
∠ C = 150°
∠ FCE and ∠ ECB are adjacent angles on a straight line and sum to 180°
∠ ECB = 180° - ∠FCE = 180° - 150° = 30°
∠ E = 180° - (30 + 45)° ← sum of angles in a triangle
∠ E = 180° - 75° = 105°
∠ CBE and ∠ D are same- side interior angles and sum to 180° , then
∠ D = 180° - 45° = 135°
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answer:
722 kg
Step-by-step explanation:
551:29=x:38
551*38=29x
20938/29=x
x=722 kg
Find the least common denominator (LCD) of 5/8
and 1/4
Answer:
8
Step-by-step explanation:
1. 1/4 × 2/2 = 2/8 (denominator is 8)
2. 5/8 × 1 = 5/8 (denominator is 8)
Therefore, the common denominator is 8.