Hat is the gradient of the line parallel to the line 4y+6x=8?
2 answers:
Answer:
gradient = -
Step-by-step explanation:
Parallel lines have equal slopes/ gradients
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
4y + 6x = 8 ( subtract 6x from both sides )
4y = - 6x + 8 ( divide terms by 4 )
y = - x +
y = - x + 2 ← in slope- intercept form
with slope / gradient = -
The gradient of a parallel line is then m = -
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Draw a diagram to illustrate the problem as shown below.
The ball is thrown from A, rises to a maximum height at B, and returns to the original level at C.
Given:
v = 12.0 m/s, vertical component of launch velocity
u = 20 m/s, horizontal component of launch velocity.
Note that g = 9.8 m/s², the acceleration due to gravity.
Wind resistance is ignored.
Part a.
The time, t, required to reach B from A is given by
0 = 12 - 9.8t
t = 12/9.8 = 1.2245 s
Answer: The time is 1.225 s (nearest thousandth)
Part b.
The height attained is
h = 12*1.2245 - 05*9.8*1.2245²
= 7.347 m
Answer: The height attained is 7.35 m (nearest hundredth) above A.
Part c.
When the ball returns the level of point A or C at time t,
0 = 12t - 0.5*9.8t²
t(12 - 4.9t) = 0
t = 0 (point A), or
t = 4.9/2 = 2.45 s (point C)
Notice that 2.45/2 = 1.225 s, which is equal to the time to reach B from A.
Answer:
The time taken to travel from A to C is 2.45 s.
This time is twice the time taken to travel from A to B.
Part d.
The horizontal distance traveled from A to C is
d = 20*2.45 = 49 m
Answer: 49 m
Part e.
x(t) = 20t for horizontal travel
y(t) = 12t - 4.9t² for vertical travel
vy(t) = 12 - 9.8t for vertical velocity
vx(t) = 20 for horizontal velocity.
Graphs of x-t, y-t, vx-t, vy-t are shown below.
The ball is thrown from A, rises to a maximum height at B, and returns to the original level at C.
Given:
v = 12.0 m/s, vertical component of launch velocity
u = 20 m/s, horizontal component of launch velocity.
Note that g = 9.8 m/s², the acceleration due to gravity.
Wind resistance is ignored.
Part a.
The time, t, required to reach B from A is given by
0 = 12 - 9.8t
t = 12/9.8 = 1.2245 s
Answer: The time is 1.225 s (nearest thousandth)
Part b.
The height attained is
h = 12*1.2245 - 05*9.8*1.2245²
= 7.347 m
Answer: The height attained is 7.35 m (nearest hundredth) above A.
Part c.
When the ball returns the level of point A or C at time t,
0 = 12t - 0.5*9.8t²
t(12 - 4.9t) = 0
t = 0 (point A), or
t = 4.9/2 = 2.45 s (point C)
Notice that 2.45/2 = 1.225 s, which is equal to the time to reach B from A.
Answer:
The time taken to travel from A to C is 2.45 s.
This time is twice the time taken to travel from A to B.
Part d.
The horizontal distance traveled from A to C is
d = 20*2.45 = 49 m
Answer: 49 m
Part e.
x(t) = 20t for horizontal travel
y(t) = 12t - 4.9t² for vertical travel
vy(t) = 12 - 9.8t for vertical velocity
vx(t) = 20 for horizontal velocity.
Graphs of x-t, y-t, vx-t, vy-t are shown below.
Answer:
2. "two thirds of the fourth power of <em>r</em>"
4. n + 14
6. 7 +11n
8. (2/5)n^2
__
7. 28
8. 1/5
Step-by-step explanation:
2. "two thirds of the fourth power of <em>r</em>"
__
4. "sum" means the listed items are added. You can use any convenient variable to represent "a number." I often use <em>n</em> for <em>n</em><em>umber</em>.
n + 14
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6. "7 more than" means 7 is added to whatever follows. "11 times a number" means the number is multiplied by 11.
7 + 11n
__
8. "of" means "times". The square of a number is that number to the power of 2.
(2/5)n^2
__
7 & 8 (evaluation). Your calculator can do this. (If not, get one that can.) Note that parentheses are needed around numerators and denominators and anything else that must be treated as a single value.
