Answer:
Step-by-step explanation:
<u>Given</u>
<u>Substitute and solve for n:</u>
- 42 = n² + n
- n² + 2*1/2n + 1/4 = 42.25
- (n + 0.5)² = 42.25
- n + 0.5 = √42.25
- n + 0.5 = 6.5
- n = 6
Correct option is C
Yes, we can obtain a diagonal matrix by multiplying two non diagonal matrix.
Consider the matrix multiplication below
![\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{cc}e&f\\g&h\end{array}\right] = \left[\begin{array}{cc}a e+b g&a f+b h\\c e+d g&c f+d h\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7De%26f%5C%5Cg%26h%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%20e%2Bb%20g%26a%20f%2Bb%20h%5C%5Cc%20e%2Bd%20g%26c%20f%2Bd%20h%5Cend%7Barray%7D%5Cright%5D%20)
For the product to be a diagonal matrix,
a f + b h = 0 ⇒ a f = -b h
and c e + d g = 0 ⇒ c e = -d g
Consider the following sets of values

The the matrix product becomes:
![\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}\frac{1}{3}&-1\\-\frac{1}{4}&\frac{1}{2}\end{array}\right] = \left[\begin{array}{cc}\frac{1}{3}-\frac{1}{2}&-1+1\\1-1&-3+2\end{array}\right]= \left[\begin{array}{cc}-\frac{1}{6}&0\\0&-1\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%262%5C%5C3%264%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B1%7D%7B3%7D%26-1%5C%5C-%5Cfrac%7B1%7D%7B4%7D%26%5Cfrac%7B1%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B1%7D%7B3%7D-%5Cfrac%7B1%7D%7B2%7D%26-1%2B1%5C%5C1-1%26-3%2B2%5Cend%7Barray%7D%5Cright%5D%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5Cfrac%7B1%7D%7B6%7D%260%5C%5C0%26-1%5Cend%7Barray%7D%5Cright%5D)
Thus, as can be seen we can obtain a diagonal matrix that is a product of non diagonal matrices.
Answer:
a = 
b= 4
Step-by-step explanation:
It's a 30-60-90 triangle based on the given picture. A right triangle too
Use sine, cosine, and tangent to solve for the side.
To find b, you can use sin(30) = b/8 because sin(angle) = opposite/hypotenuse.
OR you can use the rule for 30-60-90 triangle, which is x for short leg, 2x for hypotenuse, and
for long leg
So either way, b = 4
To find a, you can use cos(30) = a/8 because cos(angle) = adjacent/hypotenuse.
OR you can use the same rule, 30-60-90 triangle to save time
a will end up = 
Answer:
T4 = -2°F
Step-by-step explanation:
Given the following data;
Current temperature = 10°F
Constant, K = 3°F
Time, t = 4 hours
In four (4) hours, we have;
T = kt
Substituting into the equation, we have;
T = 3 * 4
T = 12°F
T4 = current temp - new temp
T4 = 10°F - 12°F
T4 = -2°F
Therefore, the temperature it will be in 4 hours is - 2°F.

When c = 4 and it is applied to this equation, the answer is 32.
⭐ Answered by Hyperrspace (Ace) ⭐
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