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!!!
First, write out all the values:
40,41,41,45,48,48,49,49,49,50
Then to find the mean, you add all the values and divide by the number of values (there are 10 values)
(40+41+41+45+48+48+49+49+49+50)/10
460/10
=46
Hope this helps
The first x=1
the second x=-7
*the scatter plot of the question is attached below
Answer:
Strong negative correlation
Step-by-step explanation:
In the scatter plot attached below, as the variable in the x-axis increases, the variable on the y-axis decreases. Thus, if a line of best fit is drawn, it would show a line that slopes downwards to our right. This shows a negative correlation between both variables in the scatter plot.
Also, we also see that the data points represented on the scatter plot are clustered more closely along the slope, showing strong negative correlation.
Therefore, the phrase that best describes the scatter plot is: strong negative correlation.
Answer:
g(x) = 5x + 2.
r(x) = x
b(x) = 1/2 x³
k(x) = - 3 x + 1
Step-by-step explanation:
The function notation ⇒ it is the form to write the function, It is meant to be a precise way of giving information about the function, like f(x) , v(x) and so on.
Given the following:
g(x) = 5x + 2.
y = 1 x
h = x²
r(x) = x
f/x = x⁵ - 3
b(x) = 1/2 x³
p/x = -7x
k(x) = - 3 x + 1
y = mx + b
fx = -x³ + 4
So, in the given options the following are in function notations:
g(x) = 5x + 2.
r(x) = x
b(x) = 1/2 x³
k(x) = - 3 x + 1
