Answer:
k=20.
Explanation: First we find where f(x) has its local extrema: f'(x)=3x2−10x+3. The critical points are roots of the equation: 3x2−10x+3=0.
A polygon has the following coordinates: A(3,1), B(5,3), C(2,5), D(-1,5), E(-4,3), F(-2,1). Find the length of DC.
nlexa [21]
To find the length of a line given two points, we are going to use the distance formula, which is defined below:
(
and 
are the two points)
The points in this problem are (2, 5) and (-1, 5). We can find the distance of DC by substituting these values into the distance formula and simplifying, as shown below:
- Substitute values into formula
- Combine like terms and then simplify
to 0
- Compute
- Compute
The length of DC is 3.
Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
Answer:
x = 8.8
Step-by-step explanation:
take 20 degree as reference angle .the,
hypotenuse = OQ = x (hypotenuse is always opposite of 90 degree)
perpendicular(opposite) = PQ 3 (opposite of reference angle is perpendicular or also called as opposite)
base(adjacent) = OP (side which lies on the same line where 90 degree and reference angle)
using sin rule
sin 20 = opposite / hypotenuse
0.34 = 3 / x
x = 3/0.34
x = 8.82
x = 8.8
