Answer:
a.
Step-by-step explanation:
Volume of square = length³
64 = length ³
Taking cube root in both sides
We'll get
Length = 4
Now perimeter of square = 4×L
= 4×4
= 16
F(x) = 36.77e^(-0.72x)
log f(x) = log36.77e^(-0.72x)
log f(x) = log 36.77 + log e^(-0.72x)
log f(x) = 3.6 + (-0.72x)log e
log f(x) = 3.6 - 0.72x
0.72x = 3.6 - log f(x)
x = 5 - 1.39 log f(x)
Answer:
0
Step-by-step explanation:
If we use polar coordinates, the region D can be covered by replacing (x,y) by (r*sin(Θ),rcosΘ)), with 0<r<7, 0<Θ<2π. The differential matrix
![\left[\begin{array}{cc}rcos(\theta)&-rsin(\theta)\\sin(\theta)&cos(\theta)\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Drcos%28%5Ctheta%29%26-rsin%28%5Ctheta%29%5C%5Csin%28%5Ctheta%29%26cos%28%5Ctheta%29%5Cend%7Barray%7D%5Cright%5D)
has determinant equal to r, so we can compute the double integral as follows
(Note that we multiplied by the determinant of the Jacobian, r). A primitive for r³ is r⁴/4, thus, for Barrow's rule we have
A primitive of cos(Θ)sin(Θ) can be obtained using substitution, and it is sin²(Θ)/2 (note that the derivate of sin²(Θ) is 2sin(Θ)cos(Θ)). Therefore, taking both the dividing 4 and the 2 obtained, we have
Hence, the integral is 0.
Declaration
Let the original amount of the paycheck be x
Equation
Paycheck - cost of mower - cost of chainsaw - 180 = 270
x - [(3/8)x + (2/5)x + 180] = 270
Solve
Change 3/8 and 2/5 to a common denominator and add.
3*5/8*5 + 2*8/5*8 = 15/40 + 16/30 = 31/40
x - [(31/40)x + 180] = 270 Remove the outer brackets
x - (31/40)x - 180 = 270 Evaluate the "x"s
40/40x - 31/40x - 180 = 270
9x/40 - 180 = 270 Add 180 to both sides
9x/40 = 180 + 270
9x/40 = 450 Multiply by 40
9x = 18000 Divide by 9
x = 18000/9
x = 2000
His paycheck was 2000 dollars.
Answer:
The slope of the line is 4
Step-by-step explanation:
Those are correct because in y = mx + b
x is always the slope and y is always the y-intercept;
So for y = 4x - 6;
4 is the slope and -6 is the y-intercept.
