Answer:
Grace should use her phone for 58 minutes to maintain an average of 55 minutes.
Step-by-step explanation:
Usage of first month = 43 minutes
Second month = 62 minutes
Third Minutes = 57 minutes
Let, the usage of fourth month = k minutes
Mean of the data = 5 minutes
Now, Average of a Data =
⇒
or, 55 x 4 = 162 + k
⇒ 220 - 162 = k
or, k = 58 minutes
So, Grace should use her phone for 58 minutes to maintain an average of 55 minutes.
Answer:
+
*LN(|
|) +C
Step-by-step explanation:
we will have to do a trig sub for this
use x=a*tanθ for sqrt(x^2 +a^2) where a=2
x=2tanθ, dx= 2 sec^2 (θ) dθ
this turns into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ
the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1
then it simplifies into integral(4*sec^3 (θ)) dθ
you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C
then you will need to rework your functions of θ back into functions of x
tanθ will resolve back into (see substitutions) while secθ will resolve into
sec(θ)= is from its ratio identity of hyp/adj where the hyp. is
and adj is 2 (see tan(θ) ratio)
after resolving back into functions of x, substitute ratios for trig functions:
= +
*LN(|
|) +C
The parallel line to y = x + 3 and passes through
the point (0 , 4) is y = x + 4
Step-by-step explanation:
Parallel lines have:
1. The same slopes
2. The different y-intercept
The slope-intercept form of the linear equation is y = m x + c, where
m is the slope of the line and c is the y-intercept
We need to find the equation of the line that is parallel to
y = x + 3 and passes through the point (0 , 4)
∵ The two lines are parallel
∴ Their slopes are equal
∵ The equation of the given line is y = x + 3
∵ The form of the equation is y = m x + c
∴ m =
∴ The slope of the line is
∵ The equation of the line is y = mx + c
∵ m =
∴ The equation of the line is y = x + c
- To find c substitute x and y in the equation by the coordinates of
a point lies on the line
∵ The line passes through the point (0 , 4)
∴ x = 0 , y = 4
∴ 4 = (0) + c
∴ c = 4
∴ The equation of the line is y = x + 4
The parallel line to y = x + 3 and passes through
the point (0 , 4) is y = x + 4
Learn more:
You can learn more about equations of parallel lines in brainly.com/question/8628615
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