A net can be folded to form a cube with a side length of 20 units.
2 answers:
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Question is Incomplete; Complete question is given below;
Roger is having a picnic for 78 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine how many packages of hot dogs Roger will need to buy?
1)
2)
3)
4)
Answer:
2)
Step-by-step explanation:
Given:
Number of guest in the picnic = 78 guest
Number of hot dog each guest will have = 1
Number of hot dogs in each package = 8 hot dogs.
We need to write the In equality used to determine the number of packages of hot dogs roger must buy
Solution:
Let the number of packages be 'p'.
First we will find the total number of hot dogs required.
so we can say that;
total number of hot dogs required is equal Number of guest in the picnic multiplied by Number of hot dog each guest will have.
framing in equation form we get;
total number of hot dogs required =
Now we can say that;
Number of hot dogs in each package multiplied by number of packages should be greater than or equal to total number of hot dogs required.
framing in equation form we get;
Hence The In equality used to determine the number of packages of hot dogs roger must buy is .
Answer:
Step-by-step explanation:
I'm not sure if this problem is physics based or calculus based. So I used calculus because it just makes more sense to do so.
If the projectile is fired from 190 feet in the air, then h0 in our quadratic will be 190. Since we are being asked to find both the displacement in the x-dimension and in the y-dimension, we need a bit of physics here as well. The velocity in the y-dimension is found in
and the velocity in the x-dimension is found in
Since the sin and the cos of 45 is the same, it's made a bit simpler for us. The velocity in both the x and the y dimension is 35.35533906 feet per second.
We can use that now to write the quadratic we need to start solving these rather tedious problems.
The position function for the projectile is
I'm going to kind of mix things up a bit, because in order to find the distance in the horizontal dimension that the object is when it's at its max height, we need to first find out how long it takes to get to its max height. We will first take the derivative of the position function to get the velocity function of the projectile. The first derivative of the position function is
Remember that the first derivative is the velocity function of the projectile. You should know from either physics or calculus that at its max height, the velocity of an object is 0 (because it has to stop in the air in order to turn around and come back down). Setting the velocity function equal to 0 and solving for time will give us the time that the object is at the max height.
I'm going to factor out the -32 to make things easier:
which gives us that at approximately 1.10485 seconds the object is at its max height.
Moving over to the horizontal distance question now. The displacement the object experiences in the horizontal dimension is found in d = rt. We know the horizontal velocity and now we know how long it takes to get to its max height, so the horizontal distance is found in
d = (35.35533906(1.10485) so
d = 39.06 feet When the object is at its max height the object is a horizontal distance of 39.06 feet from the face of the cliff. That's a.
Now to find the max height, we will use again how long it took to get to the max height and sub it in for t in the position function.
s(1.10485) = -16(1.10485)^2 + 35.35533906(1.10485) + 190 to get that the max height is
209 feet. That's b.
Now for c. We are asked when the object will hit the water. We know that when the object hits the water it is no longer in the air and has a height of 0 above the water. Sub in a 0 for s(t) in the original position function and factor to solve for t:
35.35533906t + 190 and solve for t by factoring however you find to be the easiest. Quadratic formula works great!
We find that the times are -2.51394 seconds and 4.72365 seconds. Since time will NEVER be negative, we know that the time it takes to hit the water is 4.72365 seconds.
Whew!!!