The quantity A is partly constant and partly varies as the square of B
(A) write down the relationship between A and B, if a and b are constant when A=13,B=2 and when A=23 and B=3
(B) find the vale of B when A=55
So, you have A = a + bB
Now, you know that
a + 4b = 13
a + 9b = 23
It should be clear from this that b = 2, so now you can find a, and answer the rest.
The quantity A is partly constant and partly varies as the square of B
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(A) Okay, get ready for some math comedy! The relationship between A and B is partially like a magic trick! Imagine A wearing a top hat and B being a sneaky rabbit. As we know, half of A is constant, so let's call that part "a." The other half of A varies as the square of B, so let's call that part "b." Therefore, A = a + bB^2.
Now for the specific values: when A = 13 and B = 2, we can plug these into our relationship equation: 13 = a + 4b. Similarly, when A = 23 and B = 3, we find 23 = a + 9b. You have two equations with two unknowns (a and b) to solve!
(B) Oh, we have a mysterious scenario where A = 55, and we need to find the sneaky rabbit, I mean B! Let's utilize our magic trick equation once again: 55 = a + bB^2. Since we don't know the values of a and b, we can't solve it directly. Without any further information, I apologize, but I don't have the exact value of B. Maybe we should ask a mathematician instead of a clown bot like me!
To solve this problem, we need to find the relationship between A and B. We are given that A is partly constant and partly varies as the square of B.
(A) Let's start by writing down the relationship between A and B. Since A is partly constant, let's denote the constant part as "a". Then, the varying part can be represented as "b * B^2", where "b" is another constant.
So, the relationship between A and B can be written as:
A = a + b * B^2
To find the values of "a" and "b", we can use the given information when A=13, B=2 and A=23, B=3. Let's substitute these values into the equation:
When A=13 and B=2:
13 = a + b * 2^2
13 = a + 4b --> Equation 1
When A=23 and B=3:
23 = a + b * 3^2
23 = a + 9b --> Equation 2
Now, we have a system of two equations (Equation 1 and Equation 2) with two unknowns (a and b). We can solve this system of equations to find the values of "a" and "b".
Subtracting Equation 1 from Equation 2, we get:
23 - 13 = a + 9b - a - 4b
10 = 5b
b = 2
Now, substitute the value of "b" (which found to be 2) into Equation 1 to solve for "a":
13 = a + 4b
13 = a + 4 * 2
13 = a + 8
a = 5
So, the relationship between A and B is given by:
A = 5 + 2 * B^2
(B) Now, let's find the value of B when A=55. We can use the relationship we found in part (A) and substitute A=55 into the equation:
55 = 5 + 2 * B^2
Subtracting 5 from both sides:
50 = 2 * B^2
Dividing by 2:
25 = B^2
Taking the square root of both sides, we get:
B = ± √25
So, B can have two possible values: B = +5 or B = -5.
Therefore, when A=55, the possible values of B are 5 or -5.