Function tangent of an angle in a right triangle equals
- opposite side / adjacent side
- sine of the angle / cosine of the angle
For this reason, all answers choices are correct except the fourth one, which is the cotangent of angle PAB.
Answer:
141 km
Step-by-step explanation:
This is because as the boat travels at a constant speed, it will travel the same distance each hour. The boat travels at 35.25 km/h, so you must multiply this number by 4.
This gets the answer 141 km.
Answer:
- hits the ground at x = -0.732, and x = 2.732
- only the positive solution is reasonable
Step-by-step explanation:
The acorn will hit the ground where the value of x is such that y=0. We can find these values of x by solving the quadratic using any of several means.
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<h3>graphing</h3>
The attachment shows a graphing calculator solution to the equation
-3x^2 + 6x + 6 = 0
The values of x are -0.732 and 2.732. The negative value is the point where the acorn would have originated from if its parabolic path were extrapolated backward in time. Only the positive horizontal distance is a reasonable solution.
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<h3>completing the square</h3>
We can also solve the equation algebraically. One of the simplest methods is "completing the square."
-3x^2 +6x +6 = 0
x^2 -2x = 2 . . . . . . . . divide by -3 and add 2
x^2 -2x +1 = 2 +1 . . . . add 1 to complete the square
(x -1)^2 = 3 . . . . . . . . written as a square
x -1 = ±√3 . . . . . . . take the square root
x = 1 ±√3 . . . . . . . add 1; where the acorn hits the ground
The numerical values of these solutions are approximately ...
x ≈ {-0.732, 2.732}
The solutions to the equation say the acorn hits the ground at a distance of -0.732 behind Jacob, and at a distance of 2.732 in front of Jacob. The "behind" distance represents and extrapolation of the acorn's path backward in time before Jacob threw it. Only the positive solution is reasonable.
Answer and Step-by-step explanation:
When making a perpendicular line, you take 2 points on a straight line.
- You put the compass on the two points, making marks above and below to be able to draw the line.
When making an angle bisector line, you use the angle and 2 points to make a straight line that will bisect the angle.
- You put the compass on the angle, making an arc from the two lines that join to make the angle. Then, you put your compass on where the arc meets the lines, and make a mark, which you then draw a line through.
<u><em>#teamtrees #PAW (Plant and Water)</em></u>