$y = x^x\\\\log y = x log x\\\\\frac{1}{y} \frac{dy}{dx} = x \cdot \frac{1}{x} + log x\\\\\frac{1}{y} \frac{dy}{dx} = 1 + log x\\\\\frac{dy}{dx} = y (1 + log x)\\\\\frac{dy}{dx} = x^x(1 + log x)$

7 0

3 years ago

What is the quadratic regression equation that fits these data?

ratelena [41]

Answer:

y = 2.09x2 + 0.33x + 3.06

Step-by-step explanation:

4 0

3 years ago

In any triangle, the three angles add up to 180°. In my triangle, the first angle is twice the second angle, and the second angl

nekit [7.7K]

Answer:

<h3>Therefore the angles of the triangle are 52.5°, 105°,49.5°.</h3>

Step-by-step explanation:

Triangle:

The sum of the angle of triangle = 180°

Heron's formula the area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

s= semi-perimeter $=\frac{a+b+c}{2}$

Given that , first angle is twice the second angle, and the second angle is 30° larger than the third angle.

Consider the second angle of the triangle be x.

Then first angle = twice the second angle

=2× second angle

=2x

The third angle+30° = second angle

⇒third angle= second angle -30°

= x- 30°

We know that,

First angle + second angle+ Third angle = 180°

⇒2x+x+x-30°= 180°

⇒4x = 180° +30°

⇒4x=210°

$\Rightarrow x= \frac{210^\circ}{4}$

⇒x=52.5°

Therefore the angles of the triangle are 52.5°, (2×52.5°),(52.5°-30°)

=52.5°, 105°,49.5°

5 0

3 years ago