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3 years ago

Find equation tangent to a circle at given point

1 answer:

7 0

the equation of the tangent line must be passed on a point A (a,b) and perpendicular to the radius of the circle. 
I will take an example for a clear explanation:
let x² + y² = 4 is the equation of the circle, its center is C(0,0). And we assume that the tangent line passes to the point A(2.3).

since the tangent passes to the A(2,3), the line must be perpendicular to the radius of the circle.

Let's find the equation of the line parallel to the radius.

The line passes to the A(2,3) and C (0,0). y= ax+b is the standard form of the equation. AC(-2, -3) is a vector parallel to CM(x, y).

det(AC, CM)= -2y +3x =0, is the equation of the line // to the radius.

let's find the equation of the line perpendicular to this previous line.

let M a point which lies on the line. so MA.AC=0 (scalar product),

it is (2-x, 3-y) . (-2, -3)= -4+4x + -9+3y=4x +3y -13=0 is the equation of tangent

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A stone is thrown vertically upward at a speed of 41.50 m/s at time t=0. A second stone is thrown upward with the same speed 3.0

lubasha [3.4K]

Answer:

t1 = t2 + 3.02 V = 41.5

V t1 - 1/2 g t1^2 = V t2 - 1/2 g t2^2

Both stones reach the same height after the specified times

V (t1 - t2) = g/2 (t1^2 - t2^2) = g/2 (t1 - t2) (t1 + t2)

2 V / g = t1 + t2 = 2t1 + 3.02

t1 = V / g - 1.51 = 41.5 / 9.8 -1.51 = 2.72 s

t2 = t1 + 3.02 = 5.74 sec

Check:

41.5 * 2.72 - 4.9 * 2.72^2 = 76.6 m

41.5 * 5.74 - 4.9 * 5.74^2 = 76.8 m

Speed of second stone = 41.5 - 9.8 * 2.72 = 14.8 m/s

7 0

3 years ago

Light emitting diode (LEDs) light bulbs have become required in recent years, but do they make financial sense? Suppose a typica

kogti [31]

Answer:

The break even cost is $0.0063825

Explanation:

Break-even cost is the amount of money, or change in value, which equates to the amount at which an asset must be sold to equal the cost of acquiring it. For easier understanding it can be thought the amount of money for which a product or service must be sold to cover the costs of manufacturing or providing it.

Wattage = W

Cost per kilo watt hour = C

Number of hours per year = H

Price per bulb/CFL = P

Discount rate = 11%

Life of bulb = 2 years

Price of bulb = $0.39

Wattage consumption of bulb per hours = 60

Life of CFL = 24 years

Price of CFL = $3.10

Wattage consumption of CFL per hour = 15

Calculate the Equated Annual Cost (EAC) of bulb

EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 2years)}/ (PVIFA 11%, 2years)

PVIFA 11%, 2years = Annuity PV Factor = [1 – {(1 + r)^(-n)}]/r, where r is the rate per period and n is the number per periods

PVIFA 11%, 2 years = [1 – {(1 + 0.11)^(-2)}]/0.11 = 1.712523 (for 2 years)

PVIFA 11%, 24 years = [1 – {(1 + 0.11)^(-24)}]/0.11 = 8.348136 (for 2 years)

Calculate the EAC of bulb

EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 2 years)}/ (PVIFA 11%, 2 years)

EAC = {- 0.39 - (60/1000 x H x C) x (1.712523)}/ (1.712523)

EAC = {-0.39 – (51.37570 x C)}/ 1.712523, consider this equation 1

Calculate the EAC of CFL

EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 24 years)}/ (PVIFA 11%, 24 years)

EAC = {- 3.10 - (15/1000 x 500 x C) x (8.348136)}/ (8.348136)

EAC = {-3.10 – (62.61102 x C)}/8.348137, consider this equation 2

Equate 1 and 2 to find the amount of C

{-0.39 – (51.37570 x C)}/ 1.712523 = {-3.10 – (62.61102 x C)}/8.348137

{-0.39 – (51.37570 x C) x 8.348137} = {-3.10 – (62.61102 x C) x 1.712523}

C = $0.0063825

Thus, the break- even cost per kilo – watt is $0.0063825

3 0

3 years ago

Two sources of light of wavelength 700 nm are 9 m away from a pinhole of diameter 1.2 mm. How far apart must the sources be for

Lelechka [254]

Answer:

The distance is $D = 0.000712 \ m$

Explanation:

From the question we are told that

The wavelength of the light source is $\lambda = 700 \ nm = 700 *10^{-9} \ m$

The distance from a pin hole is $x = 9\ m$

The diameter of the pin hole is $d = 1.2 \ mm = 0.0012 \ m$

Generally the distance which the light source need to be in order for their diffraction patterns to be resolved by Rayleigh's criterion is

mathematically represented as

$D = \frac{1.22 \lambda }{d }$

substituting values

$D = \frac{1.22 * 700 *10^{-9} }{ 0.0012 }$

$D = 0.000712 \ m$

5 0

3 years ago

Why is this website not work how i want it this is so annoying

Mice21 [21]

It depends how you want it to work do you want to take a picture oh yea and to do that you must create a account btw

5 0

3 years ago

Read 2 more answers

☆ Correct and rewrite the following statements:

kvv77 [185]

Answer:

<h3>e)</h3><h3>Question:-</h3>

Electroplating is based on magnetic effect of electricity.

<h3>Answer:-</h3>

It's incorrect sentence 
As we know that, while electroplating there are two rods, one becoming cathode and another one becoming anode. During electroplating, when electricity is given through the rods, the anode produces positive ions which gets received at the cathode rod and negative ions produced at cathode collects at anode rod which results to the plating of the desired substance. Here, it is a chemical effect of electricity resulting to plating.

So correct sentence is:

Electroplating is based of chemical effect of electricity.

<h3>f)</h3><h3>Question:-</h3>

An electric bulb glows due to the chemical effect of electricity.

<h3>Answer:-</h3>

It's incorrect sentence 
As we know that, in an electric bulb there is a filament. When electricity is given in that filament of the electric bulb, the filament gets intensely heated up and results to the emission of light. Due to this heating of the filament due to electricity the electric bulb glows.

So correct sentence is:

An electric bulb glows due to the heating effect of electricity.

6 0

2 years ago