Prime Factors of 60: 2,3, and 5
Prime Factors of 140: 2,5 and 7
All mental math no work needed.
t= 2.25 secs
Step-by-step explanation:
Step 1 :
Equation for motion with uniform acceleration is v = u+ at
where v is the final velocity
u is the initial velocity
a is the acceleration due to gravity
and t is the time
Step 2 :
Here , v = 0 because at the highest point final velocity is 0.
u = 72 feet/sec
a = -32 ft/sec^2
We need to find the time t.
Substituting in the equation we have,
0 = 72 -32 * t
=> 32 t = 72
=> t = 72/32 = 2.25 secs
You need to do 20 divide by 21 to get a decimal. Then if you multiply the decimal by hundred you should get the percentage.
Answers:
- Total equation: x+y = 80
- Legs equation: 2x+4y = 248
- How many ducks? 36
- How many cows? 44
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Further explanation:
- x = number of ducks
- y = number of cows
x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
- 2x = number of legs from all the ducks only
- 4y = number of legs from all the cows only
- 2x+4y = total number of legs from both types of animals combined
We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
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Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
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Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
Refer to the diagram shown below.
The directrix is y = -4 and the focus is (-2, -2).
Therefore the vertex is at (-2, -3).
Consider an arbitrary point (x,y) on the parabola.
The square of distance from the focus to the point is
(x+2)² + (y+2)²
The square of the distance from the point to the directrix is
(y+4)²
Therefore
(y+4)² = (y+2)² + (x+2)²
y² + 8y + 16 = y² + 4y + 4 + (x+2)²
4y = (x+2)² - 12
y = (1/4)(x+2)² - 3
Answer: