Can anyone help me solve these math problems?
1 answer:
Answer:
- x = 2
- r = 48
- 3536 ft
- √10
- 10°
Step-by-step explanation:
1. The Pythagorean theorem applies, so the sum of the squares of the legs is equal to the square of the hypotenuse.
x² + (x+3)² = (√29)²
2x² +6x +9 = 29 . . . . . . eliminate parentheses, collect terms
2x² +6x -20 = 0 . . . . . . subtract 29
x² +3x -10 = 0 . . . . . . . . divide by 2
(x +5)(x -2) = 0 . . . . . . . . factor
x = -5 or +2 . . . . . . . . . . . . values that make the factors zero (-5 is extraneous)
The value of x is 2.
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2. Even though the figure is drawn incorrectly the Pythagorean theorem still applies. (The second attachment shows the circle in the right place. The figure is not to scale.)
14² + r² = (r+2)²
196 + r² = r² +4r +4 . . . . eliminate parentheses
192 = 4r . . . . . . . . . . . . . .subtract r²+4 from both sides
48 = r . . . . . . . . . . . . . . . . divide by 4
The value of r is 48.
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3. You will recognize that the triangle involving the distance above the ground, the distance along the ground, and the straight-line bullet path is an isosceles right triangle. So, the hypotenuse is √2 times the length of either leg. The path length of the bullet is ...
(2500 ft)√2 ≈ 3536 ft
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4. see below for the diagram
The length to the terminal point is found using the Pythagorean theorem:
d = √(3² +(-1)²) = √10
The distance from the origin to the terminal point is √10 ≈ 3.16.
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5. Angles "a" and "8a" total 90°, so we have ...
a + 8a = 90°
9a = 90° . . . . . . . . collect terms
a = 10° . . . . . . . . . . divide by 9
The value of a is 10°.
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This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).
Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:
sin θ = opposite side / hypotenuse
sin 45 = 68 miles per hr / flight
flight = 68 miles per hr / sin 45
<span>flight = 96.17 miles per hr</span>
