$\text{We know that the tangent at any point on a circle is perpendicular}\\
\text{to the radius at that point.}\\
\\
\text{so first we find the equation of the line joining (0,0) and (3,4)}\\
\text{and then using the slope, we find the line perperndicular to it at (3,4)}\\
\\
\text{the equation of the line passing through (0,0) and (3,4) is}\\
\\
y-0=\frac{4-0}{3-0}(x-0)$

$\Rightarrow y=\frac{4}{3}x\\
\\
\text{so the slope of radius is }m=\frac{4}{3}.\\
\\
\text{we know that the product of the perpendicular lines is }-1. \\
\\
\text{so the slope of the perpendicular line would be}=-\frac{1}{4/3}=-\frac{3}{4}\\
\\
\text{So the equation of the tangent line has slope }-\frac{3}{4} \text{ and}\\
\text{passing through (3,4). so equation of tangent line is}$

$y-4=-\frac{3}{4}(x-3)\\
\\
\Rightarrow y-4=-\frac{3}{4}x+\frac{9}{4}\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9}{4}+4\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9+16}{4}\\
\\
\text{so the equation of tangent line is:} y=-\frac{3}{4}x+\frac{25}{4}$

5 0

4 years ago

The spinner shown is spun 5 times. What is the probability that you will spin white exactly 3 times?

telo118 [61]

Answer:

3 / 5

Step-by-step explanation:

Total = 5

Probability of spinning white exactly 3 = 3 / 5

3 0

2 years ago

Show the work of 42% of 16

Sveta_85 [38]

16 x 0.42 = 6.72

Post any other questions.

7 0

3 years ago

If QRST is a rectangle with QT = 30 and RS = 4x + 10, find x.

ArbitrLikvidat [17]

The opposite side pairs in a rectangle are congruent, so basically QT would be congruent to RS when you draw the rectangle and label the points.
4x+10=30
4x=20
x=5

4 0

3 years ago