Answer:
FD = 25.9
Step-by-step explanation:
13x - 16 = 4x + 11
9x = 27
x = 3
using Pythagorean theorem:
FD² = 12² + [4(3) + 11]²
FD² = 144 + 23² = 144 + 529 = 673
FD = 25.94
The perpendicular equation would include a slope that is the opposite reciprocal of the original slope.
Steps:
1. Get x to the other side in the original equation. This making the slope -4 or -4/1.
2. Turn the slope into it’s opposite reciprocal m = 1/4.
3. If you use point-slope form, y - y1 = m( x - x1 ), you can substitute y1 and x1 with the numbers in the point given. But since we previously found the opposite reciprocal, we will replace “m” as well. *By the way, the subtraction of a negative makes a positive. [y + 3 = 1/4( x + 4 )]
4. Solve:
A: Distribute (y + 3 = 1/4x + 1)
B: Subtract 3 from both sides (y = 1/4x -2)
Perpendicular Equation: y = 1/4x - 2
The true speed and direction of the football thrown by the quarterback is 30.185 mph and 9⁰ respectively.
<h3>
Relative velocity of the football</h3>
The true speed and direction of the football is determined by applying the concept of relative velocity.
Vr/w = Vb - Vw
where;
- Vr/w is the velocity of the football with respect to the wind
- Vb is the velocity of the football
- Vw is the velocity of the wind
Vr/w = 41 mph - 11 mph = 30 mph
The direction speed can be determined by sketching a triangle
Direction of the speed, θ = (360 - 339) - (180 - 168)
θ = 21 - 12 = 9⁰
<h3>Resultant speed;</h3>
R² = 41² + 11² - 2(41 x 11 x cos9)
R² = 911.105
R = √911.105
R = 30.185 mph
Thus, the true speed and direction of the football thrown by the quarterback is 30.185 mph and 9⁰ respectively.
Learn more about relative velocity here: brainly.com/question/17228388
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Answer:
70, 140, 280, 350
Step-by-step explanation:
Obviously, it must have the factors 2, 5, 7 as a minimum, so the smallest value is 2×5×7 = 70.
Any of these primes can be added to the product. In increasing order, the smallest additional factors will be 2, 4, 5, 7, 8, 10, ...
So, the four smallest numbers with prime factors of 2, 5, and 7 are ...
70 = 2·5·7
140 = 2²·5·7
280 = 2³·5·7
350 = 2·5²·7
