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WITCHER [35]
3 years ago
15

What is the equation of the line that passes through (6, 1) and is perpendicular to the line y 3x+2? CI) At what angle do the li

nes y= 6x +4 and y-2x+3 cross?
Mathematics
1 answer:
Andrews [41]3 years ago
8 0

Answer with explanation:

The equation of any line with slope 'm' and passing through any point (x_1,y_1) is given by

y=mx+(y_1-mx_1)

As we know that the general equation of a line with slope 'm' is y=mx+c

Comparing with the given equation y=3x+2 we can conclude slope of the given line is m_1=3

Now we know that the product of slopes of perpendicular lines is -1

Mathematically we can write for perpendicular lines

m_1\times m_2=-1

Thus the slope of the required line is obtained from the above relation since it is given that they are perpendicular

3\times m_{2}=-1\\\\\therefore m_{2}=\frac{-1}{3}

Hence using the given and the obtained values the equation of the required line is

y=-\frac{1}{3}x+(1-\frac{-1}{3}\times 6)}\\\\y=\frac{-x}{3}+3

Part b)

The angle of intersection between 2 lines with slopes m_{1},m_2 is given by

\theta =tan^{-1}(\frac{m_2-m_1}{1+m_1m_2})

Comparing the equations of given lines

y=6x+3\\\\y=2x+3

with the standard equation we get

m_{1}=6\\\\m_{2}=2

Thus the angle of intersection becomes

\theta =tan^{-1}(\frac{2-6}{1+2\times6})=17.10

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A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all th
Zinaida [17]

Answer:

4/25 = 0.16

Step-by-step explanation:

The shortest stick must be between 0 and 5/3.  The probability that it is longer than 1 is therefore:

(5/3 − 1) / (5/3 − 0)

(2/3) / (5/3)

2/5

So the probability that both of the shortest sticks are longer than 1 is (2/5)² = 4/25.

4 0
3 years ago
 Find sin2x, cos2x, and tan2x if sinx=-15/17 and x terminates in quadrant III
vodka [1.7K]

Given:

\sin x=-\dfrac{15}{17}

x lies in the III quadrant.

To find:

The values of \sin 2x, \cos 2x, \tan 2x.

Solution:

It is given that x lies in the III quadrant. It means only tan and cot are positive and others  are negative.

We know that,

\sin^2 x+\cos^2 x=1

(-\dfrac{15}{17})^2+\cos^2 x=1

\cos^2 x=1-\dfrac{225}{289}

\cos x=\pm\sqrt{\dfrac{289-225}{289}}

x lies in the III quadrant. So,

\cos x=-\sqrt{\dfrac{64}{289}}

\cos x=-\dfrac{8}{17}

Now,

\sin 2x=2\sin x\cos x

\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})

\sin 2x=-\dfrac{240}{289}

And,

\cos 2x=1-2\sin^2x

\cos 2x=1-2(-\dfrac{15}{17})^2

\cos 2x=1-2(\dfrac{225}{289})

\cos 2x=\dfrac{289-450}{289}

\cos 2x=-\dfrac{161}{289}

We know that,

\tan 2x=\dfrac{\sin 2x}{\cos 2x}

\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}

\tan 2x=\dfrac{240}{161}

Therefore, the required values are \sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}.

7 0
2 years ago
50 points! Please help me
Inga [223]

Answer:

x = 8

y = 14

Step-by-step explanation:

2x + 6 = 4x - 10 (Corresponding angles so they're equal)

2x - 4x = -10 - 6

-2x = -16

x = 8

2x + 6 + 13y - 24 = 180 (Supplementary angles so they add up to 180)

2(8) + 6 + 13y - 24 = 180

16 + 6 + 13y - 24 = 180

13y - 2 = 180

13y = 182

y = 14

6 0
2 years ago
HELP HELP WITH THIS PLZ
lawyer [7]
10•10•10=1,000=10^3
1,608 divided by 1,000 equals 1.608
3 0
3 years ago
SOMEONE PLEASE HELP ME PLEASE!!!
tankabanditka [31]

Answer:

193%

Step-by-step explanation:

40.2 - 13.7 = 26.5

26.5 ÷ 13.7 = 1.93

1.93 = 193%

7 0
3 years ago
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