First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have
Which means that the roots are
Next, we can expand the function definition:
In this form, it is much easier to compute the derivative:
If we evaluate the derivative in the points of interest, we have
This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation
is what we need. The three lines are:
This is the tangent at x = -2
This is the tangent at x = 0
This is the tangent at x = 1
Answer: B. 31
Step-by-step explanation:
This linear regression was constructed by relating the hours practiced per week and the number of competitions won.
Going by this graph, the number of competitions they can expect to win at 5 practices a week is 31.
This is derived by looking for the point where 5 competitions on the x-axis intersects with the line. This point is at 31 competitions on the y axis which would make it the answer.
1. 2.85 I'm dumb at math so I will just give the first answer.. xD
Answer:
A ≈ 9.0 ft²
Step-by-step explanation:
70° = 7π/18 radians
Area of the arc section
A = ½(7π/18)8² = 12⁴/₉π ft² = 39.09537 ft²
As the triangle is isosceles, the other two angles are (180 - 70) / 2 = 55°
law of sines 8 / sin55 = L / sin 70 L = 9.17722
so the triangle height = √(8² - (9.17722/2)²) = 6.55321
Area of triangle ½(6.55321)(9.17722) = 30.07016
Area = 39.09537 - 30.07016 = 9.025211 ≈ 9.0 ft²
One way it's useful is in the application of phasors in physics. Phasors require you to add up vectors of two different angles, so the cosine angle addition formula can be used if you already know the cosine and sine of the original vector angles.
