If the equation of the circle is x^2+ y^2 = 41, we must first understand the parts of the equation.
A general circle's equation is (x-h)^2+(y-k)^2= r^2
(h.k) is the radius of the circle
r is the radius of the circle
Another useful fact to know is that tangent lines touch the circle at one point (4,5)
Since in our original equation there are no h or k values, we can assume that the center of the circle is (0,0).
The formula for slope is <u>Y1-Y2</u>
X1-X2
We can break this down with our two points (center and tangent)
(0,0) and (-4,-5)
(X1,Y1) and (X2,Y2)
therefore, we will put the equation as such
<u>0-(-5)= 5</u> = <em> </em><u><em>5</em></u>
0-(-4)= 4 <em> 4</em>
<em>this is our slope from the center to the point of tangency.</em>
We know that tangent lines are perpendicular to the radius, which we've already found the slope of. Perpendicular lines are opposite reciprocals of the line they are perpendicular to.
Therefore, we take our slope from center to the tangent, and make it opposite and then take the reciprocal of that slope, which will give us the slope of the tangent line itself. (note: reciprocal means flip the numerator and denominator)
<u>5</u> = <u>-5</u> = <u>-4</u><u>
</u>4 4 5
Now, we have a point on the line, and the line's slope. We can use slope-intercept equation to find the equation of the line.
Slope-int y=mx+b
(x,y) is a point,
m is the slope
b is the y intercept ( the point where x=0, or where its on the y axis)
now we plug things in
(-4,-5) is our point,
<u>-4</u> is our slope
5
-5=<u>-4</u>(-4)+b After we plug things in, solve for b
5
-5= 3.2+b
-1.8= b or b= <u />1 <u>4</u>
5
Now we just need to rewrite our equation with all our components.
(-4.-5) = point
<u>-4</u> = slope<u>
</u>5
1 <u>4</u> = y-intercept<u>
</u> 5
<em>y=</em><u><em>-4</em></u><em> x+ 1 </em><u><em>4</em></u><em> This is the equation of the tangent line</em><u>
</u><em> 5 5</em>
Hope that helped
Hello,
Let's place the last digit: it must be 2 or 4 or 8 (3 possibilities)
It remainds 4 digits and the number of permutations fo 4 numbers is 4!=4*3*2*1=24
Thus there are 3*24=72 possibilities.
Answer A
If you do'nt believe run this programm
DIM n(5) AS INTEGER, i1 AS INTEGER, i2 AS INTEGER, i3 AS INTEGER, i4 AS INTEGER, i5 AS INTEGER, nb AS LONG, tot AS LONG
tot = 0
n(1) = 1
n(2) = 2
n(3) = 4
n(4) = 7
n(5) = 8
FOR i1 = 1 TO 5
FOR i2 = 1 TO 5
IF i2 <> i1 THEN
FOR i3 = 1 TO 5
IF i3 <> i2 AND i3 <> i1 THEN
FOR i4 = 1 TO 5
IF i4 <> i3 AND i4 <> i2 AND i4 <> i1 THEN
FOR i5 = 1 TO 5
IF i5 <> i4 AND i5 <> i3 AND i5 <> i2 AND i5 <> i1 THEN
nb = ((((n(i1) * 10) + n(i2)) * 10 + n(i3)) * 10 + n(i4)) * 10 + n(i5)
IF nb MOD 2 = 0 THEN
tot = tot + 1
END IF
END IF
NEXT i5
END IF
NEXT i4
END IF
NEXT i3
END IF
NEXT i2
NEXT i1
PRINT "tot="; tot
END
Answer:
190 inches²
Step-by-step explanation:
Answer: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). ... the line y = x is the point (y, x). The reflection of the point (x,y) across. the line y = -x is the point (-y, -x).
Step-by-step explanation: I hope this helped! Actually, I just hope that my answer is correct but whatevs lol :)
Answer:
The answer is 2
Step-by-step explanation:
sin60°+ 2 tan45° - cos30°
sin60° = √3/2
2 tan45° = 1
cos30° = √3/2
sin60°+ 2 tan45° - cos30°
√3/2 + 2(1) - √3/2
√3/2 - √3/2 + 2(1)
0 + 2 = 2
Thus, The answer is 2
<u>-TheUnknownScientist</u>
