Given that a√b^2-c = 5k, find the value of:
1. k when a = 3, b = 6 and c = 20
2. c when a = 4, b = 7, and k = 11
Explain your working please
Very bad to finish
To find the value of k and c, we will substitute the given values of a, b, and c into the equation a√b^2-c = 5k.
1. Let's substitute a = 3, b = 6, and c = 20 into the equation:
3√(6^2 - 20) = 5k
First, we calculate inside the square root, so 6^2 - 20 = 36 - 20 = 16.
Next, we substitute the calculated value into the equation:
3√16 = 5k
The cube root of 16 is 2, so we have:
3 * 2 = 5k
Now we can solve for k by dividing both sides of the equation by 5:
6/5 = k
Hence, when a = 3, b = 6, and c = 20, the value of k is 6/5 or 1.2.
2. Now, let's find the value of c when a = 4, b = 7, and k = 11. Substituting these values into the equation:
4√(7^2 - c) = 5 * 11
Again, we need to calculate inside the square root, so 7^2 - c = 49 - c.
Substituting the value and solving the equation:
4√(49 - c) = 55
We divide both sides of the equation by 4 to isolate the square root:
√(49 - c) = 55/4
To remove the square root, we square both sides of the equation:
49 - c = (55/4)^2
Calculating, we get:
49 - c = 3025/16
Next, we isolate the variable c by subtracting 49 from both sides:
-c = 3025/16 - 49
To simplify the equation, let's first find a common denominator for 16 and 1:
-c = (3025 - 784)/16
Simplifying further:
-c = 2241/16
Finally, we solve for c by multiplying both sides of the equation by -1 to isolate c:
c = - (2241/16)
Hence, when a = 4, b = 7, and k = 11, the value of c is - (2241/16).
Are sure that the equation is NOT
a√(b^2-c) = 5k ?
or else the way you have it, it would simply become
ab -c = 5k
So I will assume it is a√(b^2-c) = 5k
I will do the 2nd, you do the first
2.
a√(b^2-c) = 5k
4√49-c) = 55
√(49-c) = 55/4
square both sides
49-c = 3025/16
-c = 3025/16 - 49
-c = 2241/16
c = - 2241/16
√b^2 = b
Therefore, the equation is really:
ab - c = 5k
Insert values and calculate.
Is the formula correct? √b^2? That's just b
However, if you mean √(b^2-c) then just plug in the numbers!
5k = 3*√(36-20) = 3*4 = 12
not so hard, eh?