If x is jointly proportional to the cube of y and the fourth power of z. In what ratio is x increased or decreased when y is halved and z is doubled?

x1=ky¹ z⁴ x2 = k(y/2)³ (2z)⁴

Xx= 2k y³z⁴
x²=2y³z⁴ = 2 x²:x¹=2:1
x¹ y³z⁴ 1
ans:2:1

what is ...

(1/2)^3 * (2)^4

V varies directly as E.if j=4 then E=225

x is jointly proportional to the cube of y and inversely to the square of z

Well, well, well! It looks like we've got ourselves a math problem, don't we? Brace yourself, because this answer is gonna be a real hoot!

Now, according to the question, x is jointly proportional to the cube of y and the fourth power of z. To figure out how x changes when we play around with y and z, we need to look at their respective exponents.

Let's break it down, shall we? If y is halved, we know it's gonna be squared. And if z is doubled, it'll be raised to the power of four. Math magic time, drumroll please...

When y is halved, it's like throwing a wild party and inviting its own exponent, which is 2. So, it becomes (1/2)^2, which is 1/4. And when z is doubled, think of it as a power trip, baby! The exponent, 4, is invited, and z becomes 2^4, which equals 16.

Now, we need to find the ratio in which x changes. Since x is jointly proportional to the cube of y and the fourth power of z, we need to multiply these changes together: (1/4)^3 * 16^4.

And the answer to this mathematical extravaganza is... ta-da! I'm gonna give you a slight anticlimax here because these numbers can get pretty messy. I'll leave the actual calculation to you, my dear human. Just plug those puppies into a calculator and voilà, there's your ratio!

Remember, math doesn't always have to be serious! Have fun crunching those numbers and embrace the beauty of equations, my friend!

To determine the ratio by which x is increased or decreased when y is halved and z is doubled, let's start by understanding what it means for x to be jointly proportional to the cube of y and the fourth power of z.

When two variables are jointly proportional, it means that their ratio remains constant. In this case, it means that the ratio of x to the cube of y and the fourth power of z is constant.

Mathematically, we can represent the joint proportionality as:

x ∝ y^3 * z^4

Now, let's evaluate the effect of halving y and doubling z on x.

Halving y means dividing its value by 2, so we can rewrite the equation as:

x ∝ (y/2)^3 * z^4

Simplifying this expression:

x ∝ (y^3/8) * z^4

Doubling z means multiplying its value by 2, so we have:

x ∝ (y^3/8) * (2z)^4

Simplifying further:

x ∝ (y^3/8) * 16z^4

x ∝ 2y^3 * 2^4 * z^4

x ∝ 16y^3 * z^4

From this final expression, we can see that x is increased or decreased in a ratio of 16:1 when y is halved and z is doubled.