It the second equation. I used subsitution to find that out.
Answer:
C. 6.3cm
Step-by-step explanation:
The length of the arc is calculated using the formula;
![l=\frac{Central\:angle}{360\degree} \times 2\pi r](https://tex.z-dn.net/?f=l%3D%5Cfrac%7BCentral%5C%3Aangle%7D%7B360%5Cdegree%7D%20%5Ctimes%202%5Cpi%20r)
The radius of the circle is r=10cm
The central angle is 36 degrees.
![l=\frac{36\degree}{360\degree} \times 2\times3.14\times10](https://tex.z-dn.net/?f=l%3D%5Cfrac%7B36%5Cdegree%7D%7B360%5Cdegree%7D%20%5Ctimes%202%5Ctimes3.14%5Ctimes10)
We simplify to get;
![l=\frac{1}{10} \times 3.14\times 20](https://tex.z-dn.net/?f=l%3D%5Cfrac%7B1%7D%7B10%7D%20%5Ctimes%203.14%5Ctimes%2020)
![l=3.14\times 2=6.3cm](https://tex.z-dn.net/?f=l%3D3.14%5Ctimes%202%3D6.3cm)
Answer:
![A(4)=-4\pi](https://tex.z-dn.net/?f=A%284%29%3D-4%5Cpi%20)
![A(8)=-4\pi +8](https://tex.z-dn.net/?f=A%288%29%3D-4%5Cpi%20%2B8)
![A(12)=-4\pi +16](https://tex.z-dn.net/?f=A%2812%29%3D-4%5Cpi%20%2B16)
![A(14)=-4\pi +15](https://tex.z-dn.net/?f=A%2814%29%3D-4%5Cpi%20%2B15)
Step-by-step explanation:
we are given
![A(x)=\int\limits^x_0 f{x} \, dx](https://tex.z-dn.net/?f=A%28x%29%3D%5Cint%5Climits%5Ex_0%20f%7Bx%7D%20%5C%2C%20dx)
Calculation of A(4):
we can plug x=4
![A(4)=\int\limits^4_0 f{x} \, dx](https://tex.z-dn.net/?f=A%284%29%3D%5Cint%5Climits%5E4_0%20f%7Bx%7D%20%5C%2C%20dx)
Since, this curve is below x-axis
so, the value of integral must be negative
and it is quarter of circle
so, we can find area of quarter circle
radius =4
![A(4)=-\frac{1}{4}\times \pi \times (4)^2](https://tex.z-dn.net/?f=A%284%29%3D-%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cpi%20%5Ctimes%20%284%29%5E2)
![A(4)=-4\pi](https://tex.z-dn.net/?f=A%284%29%3D-4%5Cpi%20)
Calculation of A(8):
we can plug x=8
![A(8)=\int\limits^8_0 f{x} \, dx](https://tex.z-dn.net/?f=A%288%29%3D%5Cint%5Climits%5E8_0%20f%7Bx%7D%20%5C%2C%20dx)
we can break into two parts
![A(8)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx](https://tex.z-dn.net/?f=A%288%29%3D%5Cint%5Climits%5E4_0%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E8_4%20f%7Bx%7D%20%5C%2C%20dx)
now, we can find area and then combine them
![A(8)=-4\pi +\frac{1}{2}\times 4\times 4](https://tex.z-dn.net/?f=A%288%29%3D-4%5Cpi%20%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%204%5Ctimes%204)
![A(8)=-4\pi +8](https://tex.z-dn.net/?f=A%288%29%3D-4%5Cpi%20%2B8)
Calculation of A(12):
we can plug x=12
![A(12)=\int\limits^12_0 f{x} \, dx](https://tex.z-dn.net/?f=A%2812%29%3D%5Cint%5Climits%5E12_0%20f%7Bx%7D%20%5C%2C%20dx)
we can break into two parts
![A(12)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx+\int\limits^12_8 f{x} \, dx](https://tex.z-dn.net/?f=A%2812%29%3D%5Cint%5Climits%5E4_0%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E8_4%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E12_8%20f%7Bx%7D%20%5C%2C%20dx)
now, we can find area and then combine them
![A(12)=-4\pi +\frac{1}{2}\times 8\times 4](https://tex.z-dn.net/?f=A%2812%29%3D-4%5Cpi%20%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%208%5Ctimes%204)
![A(12)=-4\pi +16](https://tex.z-dn.net/?f=A%2812%29%3D-4%5Cpi%20%2B16)
Calculation of A(14):
we can plug x=14
![A(14)=\int\limits^14_0 f{x} \, dx](https://tex.z-dn.net/?f=A%2814%29%3D%5Cint%5Climits%5E14_0%20f%7Bx%7D%20%5C%2C%20dx)
we can break into two parts
![A(14)=\int\limits^4_0 f{x} \, dx+\int\limits^8_4 f{x} \, dx+\int\limits^12_8 f{x} \, dx+\int\limits^14_12 f{x} \, dx](https://tex.z-dn.net/?f=A%2814%29%3D%5Cint%5Climits%5E4_0%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E8_4%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E12_8%20f%7Bx%7D%20%5C%2C%20dx%2B%5Cint%5Climits%5E14_12%20f%7Bx%7D%20%5C%2C%20dx)
now, we can find area and then combine them
![A(14)=-4\pi +\frac{1}{2}\times 8\times 4-\frac{1}{2}\times 1\times 2](https://tex.z-dn.net/?f=A%2814%29%3D-4%5Cpi%20%2B%5Cfrac%7B1%7D%7B2%7D%5Ctimes%208%5Ctimes%204-%5Cfrac%7B1%7D%7B2%7D%5Ctimes%201%5Ctimes%202)
![A(14)=-4\pi +16-1](https://tex.z-dn.net/?f=A%2814%29%3D-4%5Cpi%20%2B16-1)
![A(14)=-4\pi +15](https://tex.z-dn.net/?f=A%2814%29%3D-4%5Cpi%20%2B15)
Answer:
Explanation:
• The initial dose of the Insulin = 10 Units
The insulin breaks down by about 5% each minute, therefore:
• The decay rate, r= 5%
We want to determine the time it will take for the remaining dosage to be half (5 units) of the original dose.
We use the exponential decay function:
![N(t)=N_o(1-r)^t](https://tex.z-dn.net/?f=N%28t%29%3DN_o%281-r%29%5Et)
Substituting the given values, we have:
![\begin{gathered} 5=10(1-0.05)^t \\ \frac{5}{10}=0.95^t \\ 0.5=0.95^t \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%205%3D10%281-0.05%29%5Et%20%5C%5C%20%5Cfrac%7B5%7D%7B10%7D%3D0.95%5Et%20%5C%5C%200.5%3D0.95%5Et%20%5Cend%7Bgathered%7D)
To solve for t, we change to logarithm form.
Answer:
bad boy
Step-by-step explanation:
jajaj