9514 1404 393
Answer:
Step-by-step explanation:
The tangent of the angle can be found using the identity for the tangent of the difference of angles.
tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))
The tangent of the angle of each vector is the ratio of the j coefficient to the i coefficient.
tan(α) = -2/3
tan(β) = 4/7
tan(α-β) = (-2/3 -4/7)/(1 +(-2/3)(4/7))
= (-14-12)/(21 -8) = -26/13 = -2
Then the magnitude of the angle between the vectors is ...
arctan(2) ≈ 63.43°
Answer:
= 18 red marbles
Step-by-step explanation:
Let x be the number of red marbles that must be added
Therefore;
New number or red marbles = x+12
Total marbles will be x+32
Thus;
The probability of selecting a red marble = (x+12)/(x+32)
Therefore;
(x+12)/(x+32)=3/5
5(x+12)=3(x+32)
5x+60+3x+96
2x=36
x=18
Subtract 6g from both sides.
-3g = -7
Divide both sites with 3.
-g = -7/3
Multiply both sides with -1
g = 7/3
4th degree, so the ends both point in same direction
positive leading coefient so both ends point up
factor it to see wheere the roots are
the roots are r1,r2,r3,r4 in P(x)=(x-r1)(x-r2)(x-r3)(x-r4)
factor
P(x)=(x-3)(x-2)(x+1)(x+3)
the roots are
3,2,-1,-3
disregard negative roots becasue you can't have negative time or something
3 or 2
see my rough graph
here is rough scetch
<u>Answer:</u>

<u>Step-by-step explanation:</u>
- Given a slope and a point on the line, you can use point slope form and then rearrage your terms into slope-intercept form
- <u>SLOPE-INTERCEPT FORM</u>:
, where "m" is your slope and "b" is your y-intercept - <u>POINT-SLOPE FORM: </u>
, where
represents the y-coordinate of your point,
represents the x-coordinate of your point, and
represents the slope


