slope-intercept form is y = mx + b
3x - 7y = 35
<u> -3x -3x
</u> -7y = -3x + 35 (divide each side by -7)
y = -3/-7x + 35/-7
y = 3/7x - 5
Answer:
Diameter = 19.33
Step-by-step explanation:
Imaging a radius line from O to the endpoints of the 7. call this line R.
Label the part of the vertical line from O to the 90 degree intersection y.
Now you have a right triangle.
Using the Pythagorean theorem:
R² = 7² + y²
also
y = R - 3
substitute for y:
R² = 49 + (R-3)²
R² = 49 + R² - 6R + 9
simplify:
0 = 58 - 6R
6R = 58
R = 9.6667
Diameter = 2(9.6667) = 19.33
Answer:
The maximum value of the function = 11, at x = 3 and y = 5
The minimum value of the function = -21, at x = 3 and y = -3
Step-by-step explanation:
Given;
F = 4y - 3x
The function is subject to y ≤ 2x - 1,
y ≥ -2x + 3,
x ≤ 3
y ≤ 2x - 1
- ( y ≥ -2x + 3)
-------------------
0 ≤ 4x - 4
4 ≤ 4x
1 ≤ x
thus, 1 ≤ x ≤ 3
When x = 3
y ≤ 2x - 1 ⇒ y ≤ 2(3) - 1, ⇒ y ≤ 5
y ≥ -2x + 3, ⇒ y ≥ -2(3) + 3, ⇒ y ≥ - 3
thus, -3 ≤ y ≤ 5
When x = 1
y ≤ 2x - 1 ⇒ y ≤ 2(1) - 1, ⇒ y ≤ 1
y ≥ -2x + 3, ⇒ y ≥ -2(1) + 3, ⇒ y ≥ 1
when x = 1 and y = 1
F = 4(1) - 3(1)
F = 1
when y = -3, and x = 3
F = 4(-3) - 3(3)
F = -12 - 9
F = - 21
When y = 5 and x = 3
F = 4(5) - 3(3)
F = 20 - 9
F = 11
Therefore, the maximum value of the function = 11, at x = 3 and y = 5
The minimum value of the function = -21, at x = 3 and y = -3
Step-by-step explanation:
<em>Solving part D only</em>
<em>See the attached for better understanding</em>
The balloon is at ground level, zero on y-coordinate, at 10 seconds and beyond.
There is no chance for the ball to change its y-coordinate at 16 seconds, it will not go up since no more energy to lift it up and it won't go below since zero is the ground level.