Please help with this! Thanks

Please help with this

12345 [234]

The answers would be: B, D, and E

4 0

3 years ago

Rewrite the Cartesian equation y=-3 as a polar equation.

andreev551 [17]

r

sin

θ

=

−

3

Explanation:

Imagine we have a point

P

with Rectangular (also called Cartesian) coordinates

(

x

,

y

)

and Polar coordinates

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides

x

,

y

and

r

, as well as an angle

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from

cartesian to polar

∙

x

=

r

cos

θ

and

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

4 0

2 years ago

X2+8x=-1 complete the square

Sophie [7]

(X+4)^2-15

This is the answer

6 0

2 years ago

The equation of a circle is (x + 6)^2 + (y - 4)^2 = 16. The point (-6, 8) is on the circle.

pantera1 [17]

Answer:

y = 8 is the equation of tangent.

Step-by-step explanation:

The equation of the tangent to the circle at (-6,8) is of the form:

y = mx + c

where m is the slope of the tangent and c is the y-intercept.

The point (-6,8) lies on the circle and the tangent line as well.

Hence (-6,8) satisfies the line equation:

8 = m(-6) + c ⇒ c-6m = 8 -------------1

We know that slope of two perpendicular lines are related as:

$m_{1}\times m_{2}=-1$

At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.

Hence :

$m_{normal} \times m_{tangent}=-1$

We can find the slope of the normal at point (-6,8) as it passes through the centre of the circle (-6,4) by using the two-points formula for slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{8-4}{-6+6}$

= ∞

Slope of the normal is infinity and hence slope of tangent is -1/∞ = 0

Hence m=0

Putting m=0 in equation 1 we get:

c = 8

The equation of tangent line at (-6,8) is:

y = 8

6 0

2 years ago

Help please! I don't really understand :/

hram777 [196]

So you take 2 hours and multiply it by 5 cause you get $5 per hour. Then multiply 6.25 by 5. Add those together to get your answer!! So 5x2= 10. 6.25x5= 31.25. THE ANSWER SHOULD BE 41.25!

4 0

2 years ago