Step-by-step explanation:
Derivation using Product rule : -
To find the derivative of f(x) = sin 2x by the product rule, we have to express sin 2x as the product of two functions. Using the double angle formula of sin, sin 2x = 2 sin x cos x. Let us assume that u = 2 sin x and v = cos x. Then u' = 2 cos x and v' = -sin x. By product rule,
f '(x) = uv' + vu'
= (2 sin x) (- sin x) + (cos x) (2 cos x)
= 2 (cos2x - sin2x)
= 2 cos 2x
This is because, by the double angle formula of cos, cos 2x = cos2x - sin2x.
Thus, derivation of sin 2x has been found by using the product rule.
Answer:
When to lines intersect they create four angles. Each angle is opposite to another and form a pair of what are called opposite angles. Angles a and c are opposite angles. Angles b and d are opposite angles. Opposite angles are equal.
Answer:
28 and 30
Step-by-step explanation:
'x' = 1st consecutive #
'x+2' = 2nd consecutive #
x + x+2 = 58
2x + 2 = 58
2x = 56
x = 28
x+2 = 30
Answer: 2/3 feet per minute
Step-by-step explanation:
From the question, we are informed that a caterpillar moves across the grass at a rate of 4 2/3 feet every 7 minutes.
The rate at which the caterpillar move in feet per minute will be:
= 4 2/3 ÷ 7
= 14/3 ÷ 7
= 14/3 × 1/7
= 14/21
= 2/3 feet per minute
The normal vector to the plane <em>x</em> + 3<em>y</em> + <em>z</em> = 5 is <em>n</em> = (1, 3, 1). The line we want is parallel to this normal vector.
Scale this normal vector by any real number <em>t</em> to get the equation of the line through the point (1, 3, 1) and the origin, then translate it by the vector (1, 0, 6) to get the equation of the line we want:
(1, 0, 6) + (1, 3, 1)<em>t</em> = (1 + <em>t</em>, 3<em>t</em>, 6 + <em>t</em>)
This is the vector equation; getting the parametric form is just a matter of delineating
<em>x</em>(<em>t</em>) = 1 + <em>t</em>
<em>y</em>(<em>t</em>) = 3<em>t</em>
<em>z</em>(<em>t</em>) = 6 + <em>t</em>
