Volume of the tablet is height times pi r squared = .4cm x pi x .5^2 = pi cm^3
So, the tablet has a volume of pi cubic centimeters (cc).
We want the capsule to have the same volume. The two hemispherical ends put together make one sphere. The volume of a sphere is 4/3 pi r^3. And the cylindrical part is the same formula as the first one, but we don't know what r is,
height x pi x r^2.
pi cc = height x pie x r^2 + 4/3 pi r^3 Here, we took the value from the original problem and made it equal to the two ends of the capsule (together were the sphere) PLUS the rest (which is a cylinder.)
Now, divide everything by pi to factor it out of the equation.
cc = height x r^2 + 4/3 r^3 The problem told us that the total length is 5/3 cm, this means the cylinder height + the radius times two = 5/3. (Wish I could draw you a picture) So height in the equation at the beginning of this paragraph is 5/3 - 2r.
Now we have volume in cc = (5/3 - 2r)r^2 + 4/3 r^3 =
5/3r^2 - 2r^3 + 4/3r^3
simplified by combining common terms, and written in standard form,
volume in cc = 2 r^3 + 5/3 r^2 = 1 = r^2 ( r - 5/3) , factoring out the r^2.
this means that r^2 is the reciprocal of r - 5/3, or r^2 = 1/(r - 5/3), and this is a quadratic equation.
r^2 - r + .6 = 0 and r^2 -r + .25 = -.6 + .25 by completing the square
or (r - .25)^2 = -.35. Solve for r: square root of r - .25 = square root of .35 or .59
r = .84 cm
Answer:
The solution is (-10,-7)
Step-by-step explanation:
y=2/5x-3 and x=-10
We know x = -10
Substitute the second equation into the first equation to find y
y = 2/5 (-10) -3
y = -4 -3
y = -7
The solution is (-10,-7)
Ok so first You look at the number:8,699. Where's the Tens place? The tens place is easy to find by using expanded notation......8,000 + 600 + 90 + 9.
90 is the tens place you see? So in order to answer this right,You keep Every number on the right side of 90 and add it to 90 So.......90+9 = 99 .
99 is the area you going to round. In order to round you look at the one place
(the 9) and and see if its a number bigger than the number 5 which it is!
so read this.........4 or below let it go,5 or above give it a shove. So because it bigger than 5 you round it up. so.......8,6(99) rounded up would be simple.....
99 goes up so 90 (the tens place) goes to 100. BUT 8,6100 is wrong and you should now that so just do this.
99 turned to 100 so 600 (Hundreds place) + 100 (tens place rounded) = 700
Answer to this Number 8,700
<span>Multiply equation(2) with 4 so that coefficient of become same in both the equations(You can make coefficient of y same and can follow the following procedure.)
</span><span>* Subtract (3) from (1)
* </span>Divide both sides by -19
*Subtract 21 from both sides.
*Divide both sides by 4
so the solution is x= 3 and y= -7
Hope I helped you :)
