Answer:
3
Step-by-step explanation:
The scale factor multiplies each coordinate value. If the scale factor is k, then we have ...
D' = kD
(36, -12) = k(12, -4) = (12k, -4k)
k = 36/12 = -12/-4 = 3
The scale factor of the dilation is 3.
M = 1.2*
![e^{0.25*t}](https://tex.z-dn.net/?f=e%5E%7B0.25%2At%7D%20)
+ 0.13
If M = 19,
ln((19-0.13)/1.2)/.25 = t
Answer:
d = -9
Step-by-step explanation:
First lets input our x value for g(x)
This gives us the integral
![g(6) = \int\limits^6_{-4} {f(x)} \, dx](https://tex.z-dn.net/?f=g%286%29%20%3D%20%5Cint%5Climits%5E6_%7B-4%7D%20%7Bf%28x%29%7D%20%5C%2C%20dx)
First, we need to split this integral into the different aspects of the piecewise function. This will give us
![g(6)=\int\limits^0_{-4} {4} \, dx +\int\limits^5_0 {-5} \, dx +\int\limits^6_5 {0} \, dx](https://tex.z-dn.net/?f=g%286%29%3D%5Cint%5Climits%5E0_%7B-4%7D%20%7B4%7D%20%5C%2C%20dx%20%2B%5Cint%5Climits%5E5_0%20%7B-5%7D%20%5C%2C%20dx%20%2B%5Cint%5Climits%5E6_5%20%7B0%7D%20%5C%2C%20dx)
Now, we need to evaluate each of these integrals
![\int\limits^0_{-4} {4} \, dx=4x|\limits^0_{-4}\\\\4(0)-4(-4)=16](https://tex.z-dn.net/?f=%5Cint%5Climits%5E0_%7B-4%7D%20%7B4%7D%20%5C%2C%20dx%3D4x%7C%5Climits%5E0_%7B-4%7D%5C%5C%5C%5C4%280%29-4%28-4%29%3D16)
![\int\limits^5_0 {-5} \, dx=-5x|\limits^5_0\\\\-5(5)--5(0)\\\\-25](https://tex.z-dn.net/?f=%5Cint%5Climits%5E5_0%20%7B-5%7D%20%5C%2C%20dx%3D-5x%7C%5Climits%5E5_0%5C%5C%5C%5C-5%285%29--5%280%29%5C%5C%5C%5C-25)
![\int\limits^6_5 {0} \, dx=0](https://tex.z-dn.net/?f=%5Cint%5Climits%5E6_5%20%7B0%7D%20%5C%2C%20dx%3D0)
Now all we need to do is add the values of each of these integrals
![16-25=-9](https://tex.z-dn.net/?f=16-25%3D-9)
The calculation for circumference is 2πr or 2 × π (pi=3.14) × radius of a circle
Since the diameter of this circle is 7cm, and the radius is half of the diameter, 7 ÷ 2 = 3.5
So, 2×3.14(π)×3.5=21.98
Step-by-step explanation:
a(n) = a +(n-1)d
a=2
d=6-2=10-6=14-10=4
°.° a(n) = 2 +(n–1)4
hope this helps