Final Answer: 
Steps/Reasons/Explanation:
Question: Solve 
.
<u>Step 1</u>: Simplify 
to 
.
<u>Step 2</u>: Regroup terms.
<u>Step 3</u>: Add 
to both sides.
<u>Step 4</u>: Simplify 
to 
.
<u>Step 5</u>: Multiply both sides by 
.
× 
<u>Step 6</u>: Simplify × to 
.
<u>Step 7</u>: Divide both sides by 
.
<u>Step 8</u>: Simplify 
to 
.
<u>Step 9</u>: Switch sides.
~I hope I helped you :)~
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:
Option C.
Step-by-step explanation:
We need to find the correct definition of like terms.
Like terms :Two or more terms are called like terms if they have the same variables and same powers.
For example : 4xy and 9xy are like terms.
Option A is incorrect because 3x and 3 are not like terms.
Option B is incorrect because 6x and 9 are not like terms.
Option C is correct because like terms are terms that have the same variable factors as well as the same number of factors of each type. For example, 3x and 5x are like terms.
Option D is incorrect because 3x and 5 are not like terms.
Therefore, the correct option is C.
The answer is A) x = 9
We know this because every four sided figure has angles that measure up to 360. So we can subtract all of the angles and then use the remaining angle to solve the problem.
360 - 90 - 90 - 99 = 81.
So with the remaining angle being 81, we can solve for x.
x^2 = 81
x = +/-9
Since +9 is the only answer that makes sense in this case, x = 9.
