I don't know the answer

Mathematics

1 answer:

____ [38]3 years ago

5 0

Answer:

m∠2 = 85°

Step-by-step explanation:

Since ∠1 and ∠2 are complementary you can look at it as..

m∠1 + m∠2 = 90° (Since their sum would have to be 90)

Substitute m∠1 for 5° and solve..

5° + m∠2 = 90°

Take 5°, put in on the right hand side of the equation, and change its sign..

m∠2 = 90° - 5°

Solve:

m∠2 = 85°

Hope this helped!

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Which description of the vector shown is correct ?

BartSMP [9]

Answer:

(B) The magnitude is 7sqrt2, and the direction angle is approximately 135 degrees.

Step-by-step explanation:

From the figure, the coordinate of the tail of the vector,

$(x_1,y_1)=(3,-6).$

The coordinate of the head of the vector,

$(x_2,y_2)=(-4,1).$

The magnitude of a vector is the length between the head and tail of the vector.

By using the distance formula,

the magnitude of the vector $= \sqrt{(1-(-6))^2+(-4-3)^2}$

$=\sqrt{(7^2+(-7)^2}\\\\=\sqrt{98}\\\\=7\sqrt{2}$

Now, let $\theta$ be the angle made by the vector with the positive direction of the x-axis, so

$\tan\theta = \frac{y_2-y_1}{x_2-x_1}\\\\\Rightarrow \tan\theta = \frac{1-(-6)}{-4-3}=\frac{7}{-7}=-1 \\\\\Rightarrow \theta = \tan^{-1}(-1) \\\\\Rightarrow \theta =\pi- \tan^{-1}1 \\\\\Rightarrow \theta = \pi-\frac{\pi}{4} \\\\\Rightarrow \theta =\frac{3\pi}{4} \\\\\Rightarrow \theta = 135 ^{\circ}.$