11.
Given:
Differentiate with respect to x, we get
The given point is (3,9)
Substitute x=3 in the derivative, we get
Hence the slope is 3.
12.
Given:
Differentiate with respect to x, we get
The given point is (0,4)
Substitute x=0 in the derivative, we get
Hence the slope is 0.
30° and 60°.
<h3>Further explanation</h3>We will solve the problem of the measures of angles in the triangle.
Recall this condition:
<u>Given that:</u>
The ratio of the measure of the acute angle in a right triangle is ¹/₂.
<u>Question:</u>
Find the measures of the two angles.
<u>The Process:</u>
We call it the triangle ABC. An interior angle inside is a right angle, e.g., ∠A = 90°.
From the ratio of two other acute angles, i.e., 1: 2, we call it ∠B = x and ∠C = 2x.
Let's arrange the three angles in ABC triangle as follows:
Both sides subtracted by 90°.
Both sides divided by 3.
We get
We substitute the value of x back into B and C.
We have succeeded in getting the measures of the two angles.
<h3>Learn more</h3>Keywords: the ratio, the measure, the acute angle, a right triangle, 1/2, 180°, 90°, 30°, 60°, the interior angles
