Answer:
- 240
Step-by-step explanation:
We have to find the value of the following determinant

Now, we know that the value of a general determinant
is given by [a( ei - fh) + b(fg - di) + c(dh - eg)]
Therefore, the value of the given determinant is
= 4[0 × 4 - (-1)(-2)] + 8[3(-1) - 4 × 4] + 10[4(-2) - 3 × 0]
= - 8 - 152 - 80 = - 240 (Answer)
The perimeter of a triangle with length of sides a, b and c:
P = a + b + c
a = 2, b = 5, c = 10x
Substitute:
P = 2 + 5 + 10x = 7 + 10x
<h3>Answer: 7 + 10x</h3>
Given:
The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by

To find:
The current which will produce the maximum power.
Solution:
We have,


Differentiate with respect to x.

...(i)
To find the extreme point equate P'(x)=0.


Divide both sides by -30.

Differentiate (i) with respect to x.

(Maximum)
It means, the given function is maximum at x=4.
Therefore, the current of 4 amperes will produce the maximum power.
Using the discriminant of a quadratic equation, it is found that the quadratic equation would have one repeated solution for m = -3.
<h3>What is the quadratic equation?</h3>
The quadratic equation is given as follows:
mx² + 12x - 12.
<h3>What is the discriminant of a quadratic equation and how does it influence the solutions?</h3>
A quadratic equation is modeled by:

The discriminant is:

The solutions are as follows:
- If
, it has 2 real solutions.
- If
, it has 1 real solutions.
- If
, it has 2 complex solutions.
For this problem, the coefficients are:
a = m, b = 12, c = -12.
Hence the discriminant is:
b² - 4ac = 144 + 48m.
We want it to be of 0, hence:
144 + 48m = 0
m = -144/48
m = -3.
More can be learned about the discriminant of a quadratic equation at brainly.com/question/19776811
#SPJ1