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.
Step-by-step explanation:
if you mean the area of the triangle then it is S = 1/2*x(x-7)
Answer:
the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis
Answer:
C
Step-by-step explanation:
To get rid of the absolute value bars you have to get two different equations which would be 2x+4>-8 AND 2x+4>8. Pay attention to the signs, if there is greater than or equal to then it would have a line underneath the sign, which neither of the equations should have since you haven't moved a negative. solve normally and you'll get -6 blank circle and 2 blank circle.
Answer:
431,707
Step-by-step explanation:
To figure out the total number, you need to divide the part of the whole by the percentage it is of the whole. This means that you need to divide 35,400 by 8.2%.
Before dividing the percentage, you need to convert it to a decimal.
8.2% = 0.082
Divide the number to find the answer.
35,400/0.082 = 431,707.3
Converted to the nearest whole number, the answer is 431,707.