Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange x - 2y = - 3 into this form
Subtract x from both sides
- 2y = - x - 3 ( divide all terms by - 2 )
y = 
x + 
← in slope- intercept form
with m =
• Parallel lines have equal slopes, thus
y = x + c ← is the partial equation
To find c substitute (- 1, 2) into the partial equation
2 = - + c ⇒ c = 2 + = 
y = x + ← in slope- intercept form
Multiply through by 2
2y = x + 5 ( subtract 2y from both sides )
0 = x - 2y + 5 ( subtract 5 from both sides )
- 5 = x - 2y, thus
x - 2y = - 5 ← in standard form
First see how many times can 8 go into 52. So 8 goes 6 times, and it equals to; 48
Now subtract 48 from 52; 52-48= 4
Finally bring down the 0 next to the 4; 40
Now to get you final answer find out how many times can 8 go into 40; 5
Since it goes exactly 5 times then your final answer would be; 65
Hope this helps! :)
Answer:
30 km
Step-by-step explanation:
1 kilometer = 100 meters.
1 meter = 100 cm
therefore, 1 km = 10,000
and then, 300000 cm is 30 km
OK, so the graph is a parabola, with points x=0,y=0; x=6,y=-9; and x=12,y=0
Because the roots of the equation are 0 and 12, we know the formula is therefore of the form
y = ax(x - 12), for some a
So put in x = 6
-9 = 6a(-6)
9 = 36a
a = 1/4
So the parabola has a curve y = x(x-12) / 4, which can also be written y = 0.25x² - 3x
The gradient of this is dy/dx = 0.5x - 3
The key property of a parabolic dish is that it focuses radio waves travelling parallel to the y axis to a single point. So we should arrive at the same focal point no matter what point we chose to look at. So we can pick any point we like - e.g. the point x = 4, y = -8
Gradient of the parabolic mirror at x = 4 is -1
So the gradient of the normal to the mirror at x = 4 is therefore 1.
Radio waves initially travelling vertically downwards are reflected about the normal - which has a gradient of 1, so they're reflected so that they are travelling horizontally. So they arrive parallel to the y axis, and leave parallel to the x axis.
So the focal point is at y = -8, i.e. 1 metre above the back of the dish.
