100 Points! Which of the following expressions shows how to rewrite 8 − 9 using the additive inverse and displays the expression
correctly on a number line?
2 answers:
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Answer:
First type of fruit drinks: 48 pints
Second type of fruit drinks: 32 pints
Step-by-step explanation:
Let's call A the amount of first type of fruit drinks. 55% pure fruit juice
Let's call B the amount of second type of fruit drinks. 80% pure fruit juice
The resulting mixture should have 65% pure fruit juice and 80 pints.
Then we know that the total amount of mixture will be:
Then the total amount of pure fruit juice in the mixture will be:
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:
+
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We substitute the value of A into one of the two equations and solve for B.
Answer:
George is 43.20 ft East of his starting point.
Step-by-step explanation:
Let Paula's speed be x ft/s
George's speed = 9 ft/s
Note that speed = (distance)/(time)
Distance = (speed) × (time)
George takes 50 s to run a lap of the track at a speed of y ft/s
Meaning that the length of the circular track = y × 50 = 50y ft
George and Paula meet 14 seconds after the start of the run.
Distance covered by George in 14 seconds = 9 × 14 = 126 ft
Distance covered by Paula in 14 seconds = y × 14 = 14y ft
But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track
That is,
126 + 14y = 50y
50y - 14y = 126
36y = 126
y = (126/36) = 3.5 ft/s.
Hence, Paula's speed = 3.5 ft/s
Length of the circular track = 50y = 50 × 3.5 = 175 ft
So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of
9 × 240 = 2160 ft.
2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.
Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft
So, 60 ft along a circular track subtends an angle θ at the centre of the circle.
Length of an arc = (θ/360°) × 2πr
2πr = total length of the circular track = 175
r = (175/2π) = 27.85 ft
Length of an arc = (θ/360) × 2πr
60 = (θ/360°) × 175
(θ/360°) = (60/175) = 0.343
θ = 0.343 × 360° = 123.45°
The image of this incomplete lap is shown in the attached image,
The distance of George from his starting point along the centre of the circular track = (r + a)
But, a can be obtained using trigonometric relations.
Cos 56.55° = (a/r) = (a/27.85)
a = 27.85 cos 56.55° = 15.35 ft
r + a = 27.85 + 15.35 = 43.20 ft.
Hence, George is 43.20 ft East of his starting point.
Hope this Helps!!!
To solve this we are going to use the kinematic equation for final velocity: 
where
is the final velocity
is the initial velocity
is the acceleration
is the time
We know for our problem that the the velocity at the beginning of the slope is
, so 
. We also know that the speed ad the bottom of the slope is 
, so 
. We also know that the acceleration is 
, so 
. Lets replace those values in our formula and solve for :
seconds
We can conclude that it takes the roller coaster 3 seconds to reach the bottom of the slope.
where
We know for our problem that the the velocity at the beginning of the slope is
We can conclude that it takes the roller coaster 3 seconds to reach the bottom of the slope.