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Lapatulllka [165]
2 years ago
9

Please help. Which is the largest?

Mathematics
1 answer:
sergey [27]2 years ago
5 0

Answer:

the first one

Step-by-step explanation:

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2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.
PolarNik [594]

The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put  (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² +  (2/√3)cx + c² = 1

⁴/₃x² +  (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

Read more about Equation of tangent at; brainly.com/question/17040970

#SPJ1

6 0
1 year ago
What is the value of 3^2?<br><br> pls answer quick I'm being timed
Tomtit [17]

Answer:

I believe the value would be 9.

6 0
2 years ago
Read 2 more answers
An airplane is ascending at a constant rate of 15 feet per second what is the change in altitude during 10 minutes of flight
fenix001 [56]

Answer:

9000 ft

Step-by-step explanation:

Given: A airplane is ascending at a constant rate of 15 feet per second,

What we need to know: The change in altitude during 10 minutes of flight,

60 seconds = 1 minute

60 × 10

= 600 seconds

600 × 15

= 9000 ft

Therefore there was a 9000 ft change in altitude during the 10 minutes of the flight.

6 0
2 years ago
Find the quotient and remainder for 52 divided by 8
leva [86]
52/8 is 6.5 on a calculator, hope this helps
6 0
3 years ago
Which function has a maximum with the same maximum value as..?
Bad White [126]

9514 1404 393

Answer:

  C.  -√(x+6) -2

Step-by-step explanation:

The functions x², √x, and |x| all have ranges that are non-negative values. This means the range of the given function f(x) = -|x+3|-2 will be values that are at most 2.

The ranges of the offered answer choices are ...

  A. y ≥ -3

  B. y ≥ -2

  C. y ≤ -2 . . . . . matches that of the given function

  D. y ≤ -3

7 0
2 years ago
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