Answer:
The height of the cone h = 27(x^4)y
Step-by-step explanation:
Firstly, we calculate the volume of the cylinder.
Mathematically, the volume of the cylinder is pi * r^2 * h
using the radius x and height y
The volume V of the cylinder is ;
V = pi * x^2 * y
Now we know they have the same volume V, the formula for the volume of a cone is ;
1/3 * pi * r^2 * h
Substituting the values of r to be 1/3x and the height which is not given here left as h, we have the volume of the cone to be;
V = 1/3 * pi * (1/3x)^2 * h = pi * x^2 * y
The pi gives way as it cancels out on both sides and we have the following;
h/27x^2 = x^2y
Mathematically h = x^2 * y * 27x^2
h = 27(x^4)y
p.s: I personally feel the radius of the cone was to be given as x/3 and not 1/3x . It is in that way we can have the height of the cone purely in y terms and no x
Answer: Hope this helps you
1/2
Step-by-step explanation:
<em>To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.</em>
8x+2y = 4 ➨ 8x+2*0 = 4
<em>Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:</em>
8x = 4
<em>Now I will divide both sides by 8, which isolates our x.</em>
x = 1/2
The x-int is 1/2.
Answer:
Step-by-step explanation:
h is the height of the pebble after a certain amount of time has gone by. Since we are told to find that time when the pebble is on the ground, we say that h = 0 since the height of something on the ground has no height at all. Then factor the quadratic.
Throw that into the quadratic formula or however you were taught to factor irrational quadratics (maybe completing the square?) to get that
t = 11.27869 sec and t = -10.52869 sec
Since we all know that time will never carry a negative value, we will disregard it and go with 11.27869 seconds. Not sure to where you are told to round.
The answer is A. for this, you have to set up a system of equations. the first one will be the area equation. since you know area=length x width, your equation will be LxW=50. the next equation is L=2W, since the length is two times the width. then, plug in 2W for the L in the other equation and you get 2W^2=50. divide by 2 and get W^2=25. square root both sides and you get W=5. plug back into the other equation to find L=10. Then, add the sides of the rectangle for the perimeter. 10+5+10+5=30.
Answer:
Second option: (-2,-3) and (1,0)
Step-by-step explanation:
Given the system of equations 
, you can rewrite them in this form:
Simplify:
Factor the quadratic equation. Choose two number whose sum be 1 and whose product be -2. These are: 2 and -1, then:
Substitute each value of "x" into any of the original equation to find the values of "y":
Then, the solutions are:
(-2,-3) and (1,0)
