3 years ago

Use the unit circle to find the following values.

Mathematics

1 answer:

ahrayia [7]3 years ago

7 0

Where is the circle

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If D is an n × n diagonal matrix with entries dii, then det D = d11d22 ∙ ∙ ∙ dnn. Verify this theorem for 2 × 2 matrices.

nadya68 [22]

Answer:

Verified

Step-by-step explanation:

Let the diagonal matrix D with size 2x2 be in the form of

$\left[\begin{array}{cc}a&0\\0&d\end{array}\right]$

Then the determinant of matrix D would be

det(D) = a*d - 0*0 = ad

This is the product of the matrix's diagonal numbers

So the theorem is true for 2x2 matrices

8 0

3 years ago

What grade do you learn imaginary numbers?

nikdorinn [45]

Imaginary numbers are taught in high school algebra, which I think imaginary numbers are taught in 10th or 11th grade.

6 0

3 years ago

Read 2 more answers

Patty is 50 mi. due north of Todd. Emma is due east of Todd. Ifa line were drawn from Emma

zubka84 [21]

Answer:

Correct choice is D

Step-by-step explanation:

Consider right triangle PTE (Patty, Todd, Emma). In thistriangle PT=50 mi - the distanse between Patty and Todd, the distance between Patty and Emma PE and the distance between Emma and Todd ET are unknown. The angle PET has the measure of 40°. Then

$\sin 40^{\circ}=\dfrac{PT}{PE}\Rightarrow PE=\dfrac{PT}{\sin 40^{\circ}}=\dfrac{50}{\sin 40^{\circ}}\approx 78\ mi.$
$\tan 40^{\circ}=\dfrac{PT}{ET}\Rightarrow ET=\dfrac{PT}{\tan 40^{\circ}}=\dfrac{50}{\tan 40^{\circ}}\approx 60\ mi.$