Having problems with this question please help solve. Suppose y varies jointly with x and z. When x=4 and z=8, then y=16. Find the constant of variation and the joint variation equation.
"y varies jointly with x and z" means
y = k(xz)
when x = 4, z = 8, y = 16
16 = k(4)(8)
k = 16/32 = 1/2
y = (1/2)xz
y u lie @Hisoka?
Oh, I see you're having some trouble with joint variation. Well, fear not - Clown Bot is here to help juggle those numbers!
To find the constant of variation, we can start by setting up the equation for joint variation: y = kxz, where k is the constant of variation.
Now, let's plug in the values we have: x = 4, z = 8, and y = 16.
Using these values, we can rewrite the equation as 16 = k * 4 * 8.
Let's do some math to solve this. 4 times 8 is 32, so we have 16 equals 32k.
Divide both sides by 32, and you get k = 16/32, which simplifies to k = 1/2.
So, the constant of variation is 1/2.
Now, let's put it all together to form the joint variation equation: y = (1/2)xz.
And there you have it! The constant of variation is 1/2, and the joint variation equation is y = (1/2)xz. If you need any more clown-inspired mathematical assistance, just give me a honk!
To solve this question, we need to use the concept of joint variation. Joint variation implies that two or more variables are directly proportional to each other. In other words, if one variable increases, the other variables also increase in proportion.
In this case, we are told that y varies jointly with x and z. We are given specific values for x, z, and y. Let's use this information to find the constant of variation and the joint variation equation.
Step 1: Write the general form of the joint variation equation.
The joint variation equation can be written as:
y = k * x * z
where k is the constant of variation.
Step 2: Substitute the given values into the joint variation equation.
We are given that when x = 4 and z = 8, y = 16. Let's substitute these values into the equation:
16 = k * 4 * 8
Step 3: Solve for the constant of variation (k).
To find k, we need to isolate it in the equation. Dividing both sides of the equation by (4 * 8):
16 / (4 * 8) = k
Simplifying the arithmetic:
16 / 32 = k
1/2 = k
So, the constant of variation (k) is 1/2.
Step 4: Write the joint variation equation.
Now that we know the value of k, we can write the joint variation equation:
y = (1/2) * x * z
This is the joint variation equation for this problem.
To recap:
The constant of variation (k) is 1/2, and the joint variation equation is y = (1/2) * x * z.
Thanks
1.A
2.A
3.C
4.A
5.D
6.B
7.C
8.A
9.B
10.D
11.D
12.B
13.A
14.B
15.A
16-18 are open ended, someone else can give you those answers.