125x^3 = (5x)^3
125x^3 is the cube of 5x.
169 = 13^2
169 is the square of 13, but not the cube of a rational number.
The statement is false.
The mass of lead cylinder is: 859.10 grams
Step-by-step explanation:
In order to find the mass of a cylinder we have to find the volume first
Given
Radius = r = 2 cm
Height = h = 6 cm
The volume of cylinder is given by:
Putting the values
Now,
Density of lead per cm^3 = 11.4g
The mass of lead cylinder is: 859.10 grams
Keywords: Volume, Density
Learn more about volume at:
#LearnwithBrainly
8/ (1 1/2) = 36/x....8 muffins to 1 1/2 tsp = 36 ( 3 doz) muffins to x tsp
this is a proportion, so we cross multiply
(8)(x) = (1 1/2)(36)
8x = 3/2 * 36
8x = 108/2
8x = 54
x = 54/8
x = 6 3/4 <=== 6 3/4 tsps are needed to make 3 doz muffins
If there aren't any specific requirements for the equation, here are a few choices:
2³ = 8
64 / 8 = 8
2x + 4 = y (where x = 2)
x² - 1 = y (where x = 3)
The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.
The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.
This leaves us with the second choice. Recall that
1 + tan²(x) = sec²(x)
and the derivative of tangent,
(tan(x))' = sec²(x)
Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then
y' = sec²(x³/3 + 2) • x²
and substituting y and y' into the ODE gives
sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))
x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)
which is an identity.
So the solution is y = tan(x³/3 + 2).
