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3 years ago

Which of the following parametric equations are equivalent to the polar equation r=3 cos theta

Mathematics

2 answers:

Allushta [10]3 years ago

5 0

To solve the problem you must know that to change from Cartesian to polar coordinates you must write:
x = rcos (θ)
Where "r" is the radius
Likewise y = rsin (θ)
Therefore, in the expression r = 3cos (θ) one can write r as:
r = x / cos (θ)
So:
x / cos (θ) = 3cos (θ)
x = 3cos ^ 2 (θ)
The same for y ...
y = rsin (θ)
y = 3cos (θ) sin (θ).

Finally the correct answer is option 2.
x = 3cos ^ 2 (θ) y = 3cos (θ) sin (θ).

cupoosta [38]3 years ago

3 0

Answer:

Step-by-step explanation:

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Solve by completing the square x^2-10x-24=0

BabaBlast [244]

Step-by-step explanation:

=x²-10x-24

=x²-4x+6x-24

=x(x-4)+6(x-4)

=(x-4)(x+6)

hope it helps.

4 0

3 years ago

Find all two digit positive integers in which the difference between the integer and the product of its two digits is 12

mojhsa [17]

Let ab be a 2 digit number, then ab=10a+b, where a and b are digits, a≠0.

"the difference between the integer and the product of its two digits is 12"

10a+b - (a*b)=12

10a+b-ab=12

factorize b:

10a+b(1-a)=12

subtract 10 from both sides, to produce a factor (1-a) or (a-1) and then factorize:

10a-10+b(1-a)=2

10(a-1)+b(1-a)=2

(a-1)(10-b)=2

(a-1)(10-b) can be (1,2), (2, 1), (-1, -2), (-2, -1)

if a-1=1 and 10-b=2, then a=2, b=8
if a-1=2, and 10-b=1, then a=3, b=9
if a-1=-1, then a=0, which is not possible
if a-1=-2, then a=-1, which is not possible

so the solutions (a, b) are (2, 8) and (3, 9)

Then the integers are 28, 39

Answer: 28, 39

4 0

3 years ago

The supplement of a 60∘ angle is an angle that measures how many degrees?

MatroZZZ [7]

Answer:

120 Degrees

Step-by-step explanation:

Supplementary means angles that add up to 180 Degrees, so 180 - 60

4 0

3 years ago

Read 2 more answers

Plz solve the 7th question immediately ....Help me......

Lynna [10]

Answer:

The value of x is 8cm. The length of 3 sides are 8cm, 15cm and 17cm.

Step-by-step explanation:

Using Pythagoras' Theorem, a²+b² = c² :

Let a be x cm,

Let b be x+7 cm,

Let c be 2x+1 cm

x² + (x+7)² = (2x+1)²

x² + x² + 14x + 49 = 4x² + 4x + 1

2x² + 14x + 49 = 4x² + 4x + 1

Then, move all the variables to one side and solve it to find the value of x :

4x² + 4x + 1 - 2x² - 14x - 49 = 0

2x² - 10x - 48 = 0

2(x² - 5x - 24) = 0

x² - 5x - 24 = 0

(x-8)(x+3) = 0

x - 8 = 0

x = 8 cm

x + 3 = 0

x = -3 cm (rejected)

Substitute the x value into the length of a,b and c :

a = x

= 8 cm

b = x + 7

= 8 + 7

= 15 cm

c = 2x + 1

= 2(8) + 1

= 16 + 1

= 17 cm

3 0

4 years ago

If you rent a car for one day and drive 225 miles, the cost is $80. If you drive 350 miles in one day, the cost is $105. Let cm)

kolezko [41]

Answer:

a) $(x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105)$

And we want to find a function:

$C (m) = b_1 m + b_0$

We can find the slope with this formula:

$b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2$

And then we can use the point $(x_1 = 225, y_1 = 80)$ to find the intercept $b_o$ and we got:

$80 = 0.2*225 +b_0$

$b_0 = 80-45 = 35$

So then the linear function is given by:

$C(m) = 0.2 m + 35$

b) For this case we have that m = 475 so we can replace into the function to find the cost like this:

$C(m =475) = 0.2*475 + 35 = 130$

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

$m= \frac{120}{0.2}= 600 mi$

Step-by-step explanation:

For this case we can define the following notation:

m= represent the miles travelled

C= represent the cost

Part a

For this case we have the following two points given:

$(x_1 = 225, y_1 = 80) , (x_2 = 350, y_2 = 105)$

And we want to find a function:

$C (m) = b_1 m + b_0$

We can find the slope with this formula:

$b_1= \frac{105-80}{350-225}= \frac{25}{125}=0.2$

And then we can use the point $(x_1 = 225, y_1 = 80)$ to find the intercept $b_o$ and we got:

$80 = 0.2*225 +b_0$

$b_0 = 80-45 = 35$

So then the linear function is given by:

$C(m) = 0.2 m + 35$

Part b

For this case we have that m = 475 so we can replace into the function to find the cost like this:

$C(m =475) = 0.2*475 + 35 = 130$

And for the other case we have a cost of 155 and we want to find the number of miles associated so we can do this:

$155 = 0.2m + 35$

$155-35= 120 = 0.2 m$

$m= \frac{120}{0.2}= 600 mi$

6 0

3 years ago