At point of intersection the two equations are equal,
hence, 6x³ =6x²
6x³-6x²=0
6x²(x-1)=0 , the values of x are 0 and 1
The points of intersection are therefore, (0,0) and (1,6)
To find the slopes of the tangents at the points of intersection we find dy/dx
for curve 1, dy/dx=12x, and the other curve dy/dx=18x²
At x=0, dy/dx=12x =0, dy/dx=18x² = 0, hence the angle between the tangents is 0, because the tangents to the two curves have the same slope which is 0 and pass the same point (0,0) origin.
At x=1, dy/dx =12x = 12, dy/dx= 18x² =18, Hence the angle between the two tangents will be given by arctan 18 -arctan 12
= 86.8202 - 85.2364 ≈ 1.5838, because the slope of the lines is equal to tan α where α is the angle of inclination of the line.
3/6 of the beads are purple
3/6 simplified = 1/2
1/2 of 18, or 18/2 = 9
9 beads are purple
hope this helps
Answer:
Step-by-step explanation:
It is given that the two figures are similar. This means that the ratio between the corresponding sides is equal. In essence, a side in the larger figure over its corresponding side in the smaller figure is equal to another side in the larger figure over its corresponding side in the smaller figure. Therefore, one can set up a proportion and solve to find the unknown side.
Substitute,
Simplify,
Inverse operations,
Answer:
<h2>The slope is 2</h2>
Step-by-step explanation:
Step one:
we are required to find the slope of the given data points
A(4,6) B(5,8)
hence the x and y values correspond to
x1=4
y1=6
x2=5
y2=8
Step two:
Required is the slope which is
slope= y2-y1/x2-x1
Slope=8-6/5-4
Slope= 2/1
<em><u>Hence the slope of the ordered pair is 2</u></em>
Log[8/(36*3)]
Log[2/27]
Hope I really help you !
