To draw a distance-time graph to show Don's journey, we need to follow the following steps:Step 1: Convert time to hours45 minutes = 0.75 hours90 minutes = 1.5 hours2 pm to 3:45 pm = 1.75 hours3:45 pm to 5:15 pm = 1.5 hoursStep 2: Calculate the distance Don's journey can be divided into three parts.
The distance covered in each part is as follows: Part 1: Don drives for 45 minutes. Since he does not mention the speed, we assume that he drives at a constant speed of 60 miles/hour. Therefore, the distance covered in the first part = 60 x 0.75 = 45 miles. Part 2: Don stops for 90 minutes. He does not move during this time, so the distance covered in the second part is 0 miles. Part 3: Don drives back home. We are given that he drives at an average speed of 15 miles/hour. Therefore, the distance covered in the third part = 15 x 1.5 = 22.5 miles. Step 3: Plot the graph The x-axis represents time, and the y-axis represents distance. We plot the three parts as follows: Part 1: Plot a line from the origin to (0.75, 45).
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PLEASE HELP FAST!! WILL GIVE BRAINLIEST! The rectangle ABCD has diagonals that intersect at point O and ABD = 30. Find BC if AC = 16 in
The length of BC in the rectangle ABCD is 16 units.
To find the length of BC in the rectangle ABCD, we can use the properties of rectangles and the intersecting diagonals.
Let's consider the given information:
AC = 16 (given)
ABD = 30° (given)
In a rectangle, the diagonals are equal in length. Therefore, AO = CO and BO = DO.
Since ABD is a right triangle, we can use trigonometric ratios to find the length of AO. In triangle ABD, the angle ABD is 90°, and we know ABD = 30°. Therefore, the remaining angle BDA is 180° - 90° - 30° = 60°.
Using the trigonometric ratio for a right triangle:
sin(BDA) = AO / AB
sin(60°) = AO / AB
√3 / 2 = AO / AB
Since AB is the length of the diagonal of the rectangle, we can represent it as d:
√3 / 2 = AO / d
Now, we can find AO:
AO = (√3 / 2) * d
Since AO = CO and BO = DO, we can conclude that BO and CO also have lengths of (√3 / 2) * d.
Now, let's consider triangle AOC. We know that AC = 16, and AO = CO = (√3 / 2) * d. We can use the Pythagorean theorem to find OC:
OC^2 = AC^2 - AO^2
OC^2 = 16^2 - [(√3 / 2) * d]^2
OC^2 = 256 - (3/4) * d^2
OC = √(256 - (3/4) * d^2)
Similarly, in triangle BOC, we have BO = (√3 / 2) * d and OC = √(256 - (3/4) * d^2). We can again use the Pythagorean theorem to find BC:
BC^2 = BO^2 + OC^2
BC^2 = [ (√3 / 2) * d ]^2 + [ √(256 - (3/4) * d^2) ]^2
BC^2 = (3/4) * d^2 + 256 - (3/4) * d^2
BC^2 = 256
Taking the square root of both sides:
BC = √256 = 16
Therefore, BC = 16.
So, the length of BC in the rectangle ABCD is 16 units.
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