Answer:
The hiker's elevation after 145 minutes will be 1958 meters.
Step-by-step explanation:
The equation of the trend line of the scatter plot showing a hiker's elevation is y = 8.77x + 686 .......... (1), where x is in minutes (say) and y is in meters (say).
Now, we have to predict the hiker's elevation after 145 minutes.
So, from equation (1) we get, y = 8.77 × 145 + 686 = 1957.65 ≈ 1958 meters. (Answer)
10,060 would be the answer.
Answer: e = 33
Keep referring to the picture to understand which part of the figure I am talking about.
Step-by-step explanation:
So starting from the top triangle, one of the angles are 34 and the triangle looks like an Isosceles (a triangle that has 2 equal angles and sides). So to find the other 2 angles you have to take away the already given angle from 180 (as all angles in a triangle add up to 180 degrees) and divide it by 2. So- 180 - 34 = 146.
146 ÷ 2 = 73- angle of each of the remaining 2 sides.
The left side of that triangle is extended to be part of the quadrilateral (the four sided figure with angle e). So to now solve the top left angle of the quadrilateral which is connected to the triangle you have to takeaway the angle which is part of the triangle from 180 (Angles on a line add to 180) So-
180 - 73 = 107 - angle for the top left part of the quadrilateral.
To find the 3rd angle on the bottom right, you need to solve the angles of the bottom triangle connected to it. Use the same method I have shown for the top triangle as the triangle look like an Isosceles like the other one -
180 - 30 = 150
150 ÷ 2 = 75- angle of each of the remaining 2 sides
Coming back to finding the 3rd angle, you have to use the line at the bottom where you found one of angles now. Use the same angles on the same line rule used before-
180 - 75 = 105- angle for the bottom right of the quadrilateral
You now have all the angles in the quadrilateral except for e which you will find by adding up all the known angles in the quadrilateral and take it away from 360 (all angles in a quadrilateral add to 360) So-
115 + 107 + 105 = 327
360 - 327 = 33
Therefore e = 33
Answer:
4 feet
Step-by-step explanation:
Since the whispering gallery is 15 feet high and 60 feet wide, it forms an ellipse with major axis along the width of the gallery and minor axis along the height of the gallery.
Using the equation of an ellipse with major axis along the x-axis, we have
x²/a² + y²/b² = 1 where a = midpoint of the width = 60/2 = 30 feet and b = 15 feet.
c² = a² - b² where c = focus of the ellipse.
So, c² = a² - b²
= 30² - 15²
= 900 - 225
= 675
c = ±√675 = ±25.98 feet
So, the coordinate of the focus is thus (0, ±c) = (0, ±25.98) and the coordinate of the vertex is (0, ±a) = (0, ±30)
So, the distance between the foci and the vertex is the distance from the wall at which each of them should be positioned at the foci.
So, d = a - c
= 30 ft - 25.98 ft
= 4.02 feet
≅ 4 feet
