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allsm [11]
3 years ago
5

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = cos(θ) + sin(10

θ) y = sin(θ) + cos(10θ) θ = 0 y(x) =
Mathematics
1 answer:
vivado [14]3 years ago
6 0

Answer:

Step-by-step explanation:

x = cos θ + sin(10θ)

y = sin θ + cos(10θ)

Take derivative with respect to θ:

dx/dθ = -sin θ + 10 cos(10θ)

dy/dθ = cos θ - 10 sin(10θ)

Divide:

dy/dx = (dy/dθ) / (dx/dθ)

dy/dx = (cos θ - 10 sin(10θ)) / (-sin θ + 10 cos(10θ))

Evaluate the derivative at θ=0:

dy/dx = (cos 0 - 10 sin 0) / (-sin 0 + 10 cos 0)

dy/dx = 1/10

Evaluate the parametric functions at θ=0:

x = cos 0 + sin 0 = 1

y = sin 0 + cos 0 = 1

Writing the equation of the tangent line in point-slope form:

y - 1 = 1/10 (x - 1)

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8 0
3 years ago
A new car is purchased for 22400 dollars. The value of the car depreciates at 11% per year. To the nearest tenth of a year , how
m_a_m_a [10]

Answer:

t= 12.9 years

Step-by-step explanation:

Value after t years = initial value ( 1 - r )^t

Where,

Value after t years= $5000

Initial value = $22,400

r= depreciation rate = 11%

t= length of time (years)

Value after t years = initial value ( 1 - r )^t

5000 = 22,400 ( 1 - 0.11)^t

5000 = 22,400(0.89)^t

Divide both sides by 22,400

(0.89)^t = 5000 / 22,400

(0.89)^t = 0.2232

Take the log of both sides

t log 0.89 = log 0.2232

t= log 0.2232 / log 0.89

= -0.6513 / -0.0506

= 12.87

t= 12.9 years

5 0
3 years ago
TO WHOEVER ANSWERS THIS QUESTION WILL RECIEVE A BRAINLIEST! I NEED THIS IN 1 HR SO PLEASE RESPOND AS SOON AS POSSIBLE!! THANKS!!
xz_007 [3.2K]

51.25 per month which is $615 per year

They save 5 per month if they pay full year


(51.25-5)= 46.25 per month is $555


so it costs $555 if they pay all at once.

5 0
2 years ago
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2/7 of the pupils in Year 9 say their favourite colour is red. There are 119 pupils in Year 9. How many students said red is the
aev [14]

Answer:

34 say red is their favorite color

Step-by-step explanation:

Take the number of students and multiply by the fraction that like red

2/7 * 119

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3 years ago
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In a cookie jar 1/4 of the cookies are chocolate chip and 1/2 of the rest are peanut butter. What fraction of all the cookies is
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multiply the first fraction by the second one

which is

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3 years ago
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