V varies partly as the square of Q.when V 34,Q 2,and when V 190,Q 5.find V when Q 10.
I'm guessing you meant
v = a + bq^2
and then you provide two points:
a+4b = 34
a+25b = 190
Solve to find a and b, and then find v(10) = a+100b
V = kQ^2 + C , where k and C are constants
case1, V = 34, Q = 2 (you have a typo in that data, no equal sign)
34 = 4k + C
case2, V = 190, Q = 5
190 = 25k + C
subtract them:
156 = 21k
k = 52/7
from 34 = 4k + C, C = 30/7
V = (52Q^2 + 30)/7
so when Q = 10
V = (52*100+30)/7 = appr 747.14
Let's solve this step-by-step.
Step 1: Write the relationship between V and Q in equation form. We know that V varies partly as the square of Q, so the equation can be written as:
V = kQ^2
where k is the constant of variation.
Step 2: Use the given values to find the value of k. We are given two sets of values (V, Q) -- (34, 2) and (190, 5).
Using the first set of values (34, 2):
34 = k * 2^2
34 = 4k
k = 34/4
k = 8.5
Using the second set of values (190, 5):
190 = k * 5^2
190 = 25k
k = 190/25
k = 7.6
Step 3: Find V when Q = 10. Now that we have the value of k, we can substitute it into the equation to find the corresponding value of V.
V = kQ^2
V = 7.6 * 10^2
V = 7.6 * 100
V = 760
Therefore, when Q = 10, V is equal to 760.
To find the value of V when Q is 10, we need to first understand the relation between V and Q. The problem states that V varies partly as the square of Q. This means that V can be expressed as a function of Q, with the square of Q as a component of that function.
Given two points on the graph of V and Q: (Q1,V1) = (2, 34) and (Q2,V2) = (5, 190), we can use these values to determine the equation of the relationship between V and Q.
Here's how to do it step by step:
1. Start by writing the equation in general form: V = kQ^2, where k is a constant.
2. Use the first set of values (Q1,V1) = (2, 34) to solve for k. Substitute these values into the equation: 34 = k * 2^2. Simplify the equation: 34 = 4k.
Solve for k: k = 34/4 = 8.5.
3. Now that we know the value of k, we can write the equation with this specific value: V = 8.5Q^2.
4. Finally, plug in Q = 10 into the equation to find the value of V. Substitute Q = 10 into V = 8.5Q^2: V = 8.5 * 10^2.
Calculate: V = 8.5 * 100 = 850.
Therefore, when Q = 10, V is equal to 850.