Answer:
Explanation:
We have been given with the equation -3x+1+10x=x+4
We will collect the terms that are written in variable of x in one side and the constant values on the other side we will get
-3x+10x-x=4-1
After simplification we will get 6x=3
which implies x=1/2
When x from right hand side shift will shift to left hand side it will change its sign and similarly when 1 from left hand side shift to right hand side change its sign.
Therefore, x=1/2
Answer:
Step-by-step explanation:
From what I understand about parabolic motion in the English system, the equation for flight is
where is the initial upwards velocity and
is the initial height from which the object was launched. Filling in that equation with those values gives you
. That's a.
In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function. The absolute max is the heighest that the ball will go. Completing the square is the way to solve this. Begin by setting the equation equal to 0, the moving the 3 over by subtraction:
Now factor out the -16 since the leading coefficient HAS to be a positive 1:
Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:
BUT since you added in a 4*-16 on the left you have to add it in on the right:
which simplifies to
Now bring the 67 over by addition and you have your vertex:
.
The vertex is (2, 67). The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.
How long it will be in the air is found by factoring to find the zeros. These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046
So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at
x = 4.05 seconds. Which makes sense if you know anything about parabolic motion and physics. The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark. Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds. And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters). Sorry it's so long, but it's not a question that can be answered with just a few sentences.
Answer:
sand = 3450 pounds
3/4 inch stones =6750 pounds
1 inch stones =4800 pounds.
Step-by-step explanation:
The mixture composition is :
45% three-quarter inch stones
32% inch stones and
sand for balance
The percent here is by mass of material used.
Weight of mixture is 15,000 pounds before oil addition.
Use the percent by weight for the two types of stones and calculate real values in pounds
Formula to apply is:
Mass percent = (mass of a material/ total mass of mixture) * 100
For 3/4 inch stones it will be:
The 3/4 inch stones weigh 6750 pounds
The 1 inch stones will be
The 1 inch stones weigh = 4800 pounds
Total for the two items : 4800+6750 =11550 pounds
The sand used weighs : 15000 - 11550 = 3450 pounds