V varies partly as q and partly as square of q .When V = 34 q = 2 ,and when V = 190, q = 5 .Find V when q = 10
v varies partly as q and partly as square of q
v = aq + bq^2
When v = 34 q = 2 ,and when v = 190, q = 5 .Find v when q = 10
2a + 4b = 34
5a + 25b = 190
Solve for a and b, then plug in q=10
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To find the value of V when q = 10, we need to first understand how V varies with respect to q.
It is given that V varies partly as q and partly as the square of q. This can be expressed as:
V = a * q + b * q^2
where a and b are constants to be determined.
Now, we have two sets of values for V and q: V = 34 and q = 2, and V = 190 and q = 5. We can use these values to form equations and solve for the constants a and b.
For the first set of values (V = 34 and q = 2), we substitute them into the equation:
34 = a * 2 + b * 2^2
34 = 2a + 4b
For the second set of values (V = 190 and q = 5), we substitute them into the equation:
190 = a * 5 + b * 5^2
190 = 5a + 25b
Now, we have a system of two equations:
2a + 4b = 34
5a + 25b = 190
We can solve this system of equations to find the values of a and b.
Multiplying the first equation by 5, we get:
10a + 20b = 170
Now, we can subtract this equation from the second equation:
(5a + 25b) - (10a + 20b) = 190 - 170
-5a + 5b = 20
Dividing this equation by 5, we get:
-a + b = 4
We can now solve this simplified equation for b in terms of a:
b = a + 4
Substituting this value of b into the first equation:
2a + 4(a + 4) = 34
2a + 4a + 16 = 34
6a = 34 - 16
6a = 18
a = 3
Now that we have found the value of a, we can substitute it back into the equation to find the value of b:
b = 3 + 4
b = 7
Therefore, the equation that describes the relationship between V and q is:
V = 3q + 7q^2
To find the value of V when q = 10, substitute q = 10 into the equation:
V = 3(10) + 7(10)^2
V = 30 + 7(100)
V = 30 + 700
V = 730
Therefore, when q = 10, V = 730.
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