Find the values of the variables.
[-12 -w^2] = [2k -81
2f 3 -14 3
Please help me. I don't know how to do this at all, and can you show your work so I can understand better. Thanks
Well, don't worry, I'm here to help! Let's solve this step by step:
First of all, let's equate the corresponding components on both sides of the equation:
-12 = 2k - 81
-w^2 = -14
Now, let's solve the first equation for k:
2k - 81 = -12
Adding 81 to both sides:
2k = 69
Dividing by 2:
k = 34.5
Now, let's solve the second equation for w:
-w^2 = -14
Multiplying both sides by -1 to get rid of the negative sign:
w^2 = 14
Taking the square root of both sides:
w = ±√14
So, the values we found are:
k = 34.5
w = ±√14
Now, I hope that gave you a better understanding of how to solve this problem! And remember, if math ever gets too overwhelming, just juggle the numbers and laugh it off!
To find the values of the variables in the equations, we need to equate the corresponding elements on both sides of the equation.
From the first row of the equation, we have:
-12 = 2k - 81
To solve for "k," we will first isolate "k" on one side of the equation. Let's start by adding 81 to both sides:
-12 + 81 = 2k - 81 + 81
69 = 2k
Next, we divide both sides of the equation by 2 to solve for "k":
69/2 = (2k)/2
34.5 = k
So the value of "k" is 34.5.
Moving to the second row of the equation, we have:
- w^2 = -14
To solve for "w," we need to isolate "w^2" first. Taking the square root of both sides gives us:
√(- w^2) = √(-14)
Remember that the square root of (-14) is not a real number. Therefore, this equation has no real solutions for "w."
Finally, for the third row of the equation, we have:
2f = 3
We can solve for "f" by dividing both sides by 2:
2f/2 = 3/2
f = 3/2
So the value of "f" is 3/2.
In summary, we found that "k" is 34.5, "w" has no real solutions, and "f" is 3/2.
To find the values of the variables in the given system of equations, we can set up an equation for each element (number) in the matrices.
Let's start by comparing the corresponding elements position-wise:
For the first row, we have:
-12 = 2k - 81 --(1)
-w^2 = -14
For the second row, we have:
2f = 3
3 = -14
Now let's solve each equation step by step:
From equation (1), we have:
-12 = 2k - 81
To isolate k, let's add 81 to both sides:
-12 + 81 = 2k - 81 + 81
69 = 2k
Next, divide both sides by 2:
69/2 = 2k/2
34.5 = k
So the value of k is 34.5.
For the second row, we have:
-w^2 = -14
To solve for w^2, multiply both sides by -1 (to remove the negative sign):
w^2 = 14
To find w, take the square root of both sides:
w = √14
So the value of w is √14.
In the second row, we have:
2f = 3
To solve for f, divide both sides by 2:
2f/2 = 3/2
f = 3/2
So the value of f is 3/2.
Finally, the last element is already given:
3 = -14
This equation is not true, and there is no value that can make it true. Therefore, the system of equations is inconsistent, and there is no value for the last variable.
To summarize:
k = 34.5
w = √14
f = 3/2
However, it's important to note that the last variable does not have a valid value in this system of equations.
you have mismatched brackets
what are the spaces supposed to mean?
"2f 3 -14 3" makes no sense
and there's no "=" sign to make an equation.
Geez - check what you write, willya?