1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Brut [27]
2 years ago
9

R = sec(θ) − 2cos(θ), where -π/2 < θ < π/2

Mathematics
1 answer:
Alex2 years ago
4 0

Answer:

  y = (x/(1-x))√(1-x²)

Step-by-step explanation:

The equation can be translated to rectangular coordinates by using the relationships between polar and rectangular coordinates:

  x = r·cos(θ)

  y = r·sin(θ)

  x² +y² = r²

__

  r = sec(θ) -2cos(θ)

  r·cos(θ) = 1 -2cos(θ)² . . . . . . . . multiply by cos(θ)

  r²·r·cos(θ) = r² -2r²·cos(θ)² . . . multiply by r²

  (x² +y²)x = x² +y² -2x² . . . . . . . substitute rectangular relations

  x²(x +1) = y²(1 -x) . . . . . . . . . . . subtract xy²-x², factor

  y² = x²(1 +x)/(1 -x) = x²(1 -x²)/(1 -x)² . . . . multiply by (1-x)/(1-x)

  \boxed{y=\dfrac{x\sqrt{1-x^2}}{1-x}}

__

The attached graph shows the equivalence of the polar and rectangular forms.

You might be interested in
Someone please answer this correctly!!
Luda [366]

Answer:

1.98 × 10^10

Step-by-step explanation:

First solve for how many text messages were sent out per one month:

22,000,000 × 900

19,800,000,000

Convert into scientific notation:

1.98 × 10^10

In scientific notation, there can only be one number before the decimal. The rest of the numbers must be after the decimal; hence, why I put the numbers 9 and 8 after the decimal. If the rest of the numbers are zeros, you do not have to add them after the decimal. Instead, starting from right to left, count the number places until you reach your decimal. The number you have counted will be your exponent. I counted nine 0's, one 8, and one 9 which made this exponent 10 as there were 10 decimal placements.

6 0
2 years ago
HURRY PLEASEEEEE I RLLY NEED THISSS
NemiM [27]
The answer is option 2
3 0
2 years ago
Read 2 more answers
175% of what number is 44?<br> Provide an exact fraction answer.
Soloha48 [4]

Answer:

x =  \frac{176}{7}  \: or \: 25 \frac{1}{7}

Step-by-step explanation:

let the unknown number be = x

\frac{175}{100}  \times x = 44

<h3>bring 175/100 to the right-hand side and change its symbol to ÷ </h3>

x = 44  \div  \frac{175}{100}

<h3>x =  \frac{176}{7}  \: or \: 25 \frac{1}{7}</h3>

5 0
2 years ago
Find the area of the trapezoid
maria [59]

Answer: 1. 54, 2. 48

Step-by-step explanation: To find the area of a trapezoid you add the top base and the bottom base then divide them by two, and multiply them by the height.For #1. 8+10/2= 9 then 9x6=54 For #2. 4+12/2=8 then 8 x 6=48.

8 0
3 years ago
Read 2 more answers
I need to solve for x
irina [24]

Answer:

Fig.2⇒ x = 10.642

Fig.3⇒ x = 32.005°

Fig.4⇒ x = 41.810°

Fig.5⇒ x = 9.419

Fig.6⇒ x = 42.844

Fig.7⇒ x = 45.573°

Step-by-step explanation:

We will use the trigonometry functions

∵ Δ Is a right angle triangle in all figures:

Figure(2) ∵ cos20° = 10/x

∴ x = 10/cos20° = 10.642

Figure(3) ∵ tanx = 5/8

∴ x = tan^{-1} \frac{5}{8} = 32.005°

Figure(4) ∵ sinx = 10/15

∴ x = sin^{-1} \frac{10}{15} = 41.810°

Figure(5) ∵ sin48° = 7/x

∴ x = 7/sin48° = 9.419

Figure(6) ∵ tan35° = 30/x

∴ x = 30/tan35° = 42.844

Figure(7) ∵ cosx = 14/20

∴ x = cos^{-1} \frac{14}{20} = 45.573°

4 0
3 years ago
Other questions:
  • Tell me were the numbers go
    11·1 answer
  • Find the perimeter and area of each figure below.
    14·1 answer
  • PLEASE HELP!! Is the discriminant of f positive,zero, or negative
    8·2 answers
  • The sum of two consecutive integers is no more than 209. what is the larger of the two integers? enter your answer in the box.
    13·2 answers
  • A sphere with a diameter of 30 inches is placed in a cube. The sphere touches the lateral faces
    5·1 answer
  • 1. If f(x) = 4x — 7 and , find each value:<br> a. f(3)<br> b. f(0)
    14·2 answers
  • Anybody know ??????
    12·1 answer
  • 3 + (2 + 8)2 ÷ 4 × 1/ 2 to the power of 4
    7·1 answer
  • Use the given information to write an equation and solve the problem.<br> (28-31 in the picture)
    5·2 answers
  • Graph a triangle (ABC) and reflect it over the x-axis to create triangle A'B'C. Describe the transformation using words. Make su
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!