A ball is thrown into the air with an upward velocity of 44 ft/s. It’s height h in feet after t seconds is given by the function
1 answer:
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Answer:
- 1.375 seconds
- 35.25 feet
Step-by-step explanation:
A quadratic function y=ax^2 +bx +c is symmetric about the vertical line x=-b/(2a). That is the x-coordinate of the vertex (maximum or minimum).
Here, we have ...
h = -16t^2 +44t +5
t = -44/(2(-16)) = 11/8 = 1.375
It takes 1.375 seconds for the ball to reach its maximum height.
The height at that time is ...
h = (-16(11/8) +44)(11/8) +5 = (-22 +44)(11/8) +5 = 121/4 +5 = 141/4 = 35.25
The maximum height is 35.25 feet.
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<h3>Answer: D) 1692 miles</h3>
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Explanation:
A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram
- Plot point A and make that the home base. Plot point D directly south of point A. I'm skipping B and C because those will be used to form the triangle later.
- Imagine you are standing at point A and looking south at point D. Turn 46 degrees toward the east direction (this is what the notation "bearing of S 46° E" means). Then move 550 miles from A to land on point B. This is the location where the plane makes its first turn.
- Plot the points E and F, which are north and south of point B.
- Imagine we are at point B and looking directly south at point F. Turn 55 degrees toward the west, which is due to the "S 55° W" and then move 483 miles to arrive at point C. This is the plane's location where it turns around to go back to home base.
The diagram below shows all of this visually summarized. We have the segments
- AB = 550 miles
- BC = 483 miles
- AC = x miles
And we have these angles
- Angle DAB = 46 degrees and Angle ABE = 46 degrees (blue)
- Angle ABC = 79 degrees (red)
- Angle ACB = 55 degrees and Angle FBC = 55 degrees (green)
Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.
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Once the diagram is set up, we'll use the law of cosines to find x.
Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.
The interior angles of triangle ABC are
- A = 46 degrees
- B = 79 degrees
- C = 55 degrees
The sides opposite the angles are
- a = 483 (opposite angle A)
- b = x (opposite angle B)
- c = 550 (opposite angle C)
Now we can apply the law of cosines
b^2 = a^2 + c^2 - 2*a*c*cos(B)
x^2 = 483^2 + 550^2 - 2*483*550*cos(79)
x^2 = 434412.180756441
x = sqrt(434412.180756441)
x = 659.099522649229
x = 659
Side AC, or CA, is roughly 659 miles long.
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To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)
Distance Traveled = AB + BC + CA
Distance Traveled = 550 + 483 + 659
Distance Traveled = 1692 miles
Answer: a) 30, b) 120
Step-by-step explanation:
Since we have given that
Let the number of points Scored by Dwayne be 'd'.
Number of points in the last basket ball game = 55 points
According to question, we get that
Let the number of points that Chris's score be 'c'.
Number of points Lebron scored = 45
According to question, number of points scored by Chris is given by
a. How many points did Chris score during the game?
c = 30
b. If these are the only three players who scored, what was the team’s total number of points at the end of the game?
Hence, a) 30, b) 120