The quantity U is the sum of two terms, one partly constant and the other varies directly as the square of V .if V is 2and U is 35 ,and When is 5 and U is 203. find the value of V when U is 515
Pls the full answer not the half way done
The quantity U is the sum of two terms, one partly constant and the other varies directly as the square of V .if V is 2and U is 35 ,and When v is 5 and U is 203. find the value of V when U is 515
Well, let's break it down. We have the quantity U, which is the sum of two terms. One term is constant, and the other varies directly as the square of V.
In the first scenario, when V is 2 and U is 35, we can set up an equation:
U = constant + kV^2
Substituting the values, we get:
35 = constant + k(2)^2
35 = constant + 4k
Now, in the second scenario, when V is 5 and U is 203, we can set up another equation:
203 = constant + k(5)^2
203 = constant + 25k
We have two equations with two unknowns. Subtracting the first equation from the second equation eliminates the constant term:
203 - 35 = constant + 25k - (constant + 4k)
168 = 21k
Simplifying, we find:
k = 8
Now, we can substitute this value back into the first equation to find the constant:
35 = constant + 4(8)
35 = constant + 32
constant = 3
Finally, to find the value of V when U is 515, we can set up the equation:
515 = 3 + 8V^2
512 = 8V^2
V^2 = 64
V = 8
So, when U is 515, the value of V is 8.
To find the value of V when U is 515, we need to understand the relationship between U and V. The problem states that U is the sum of two terms, one partly constant and the other varies directly as the square of V.
Let's break it down step by step:
Step 1: Express the relationship between U and V.
The problem states that U can be expressed as the sum of a constant term (C) and a term that varies directly as the square of V (kV^2).
So, we can write the equation for U as: U = C + kV^2
Step 2: Use the given information in the problem to determine the values of C and k.
Using the first set of given values (V = 2, U = 35), we can substitute these values into the equation: 35 = C + k(2^2) = C + 4k.
This gives us one equation.
Using the second set of given values (V = 5, U = 203), we can substitute these values into the equation: 203 = C + k(5^2) = C + 25k.
This gives us another equation.
Step 3: Solve the system of equations to find the values of C and k.
We can subtract the first equation from the second equation to eliminate C:
(203 - 35) = (C + 25k) - (C + 4k)
168 = 25k - 4k
21k = 168
k = 168/21
k = 8
Substitute the value of k back into one of the original equations to solve for C:
35 = C + 4(8)
35 = C + 32
C = 35 - 32
C = 3
So, we have determined that C = 3 and k = 8.
Step 4: Use the obtained values to find the value of V when U is 515.
Now that we have the values of C and k, we can substitute them into our equation: U = C + kV^2
515 = 3 + 8V^2
Rearrange the equation to solve for V:
8V^2 = 515 - 3
8V^2 = 512
V^2 = 512/8
V^2 = 64
Take the square root of both sides to find V:
V = √(64)
V = 8
Therefore, when U is 515, the value of V is 8.
u = a + bv^2
You know that
a + 4b = 35
a + 25b = 203
a=3, b=8
3+8*515^2 = 2,121,803
In a political party primary election,4356 deligates were able to vote for at least one candidates. 750 of them voted for candidates a only, 480 voted for candidates b only and 900 voted for candidates c only. If 210 voted for candidates a and b only, 51 voted for candidates a and c only, 133 voted for candidate b and c only and 405 voted for non of the candidates.
(*)How many voted for all the three candidates
(*)How many voted for at least 2 candidates