Answer:
Length of the lake is 97.30 m
Step-by-step explanation:
We have given Caleb starts at one end of the lake and walk 95 m
So ![d_1=95m](https://tex.z-dn.net/?f=d_1%3D95m)
And then he turns at an angle of 60°
So
and then again walk 8 m
So ![d_2=8m](https://tex.z-dn.net/?f=d_2%3D8m)
We have to fond the total length of the lake , that is d
Total length of the lake is given by ![d=\sqrt{d_1^2+d_2^2+2d_1d_2cos\Theta }=\sqrt{95^2+8^2+2\times 95\times 8\times cos60^{\circ}}=97.30m](https://tex.z-dn.net/?f=d%3D%5Csqrt%7Bd_1%5E2%2Bd_2%5E2%2B2d_1d_2cos%5CTheta%20%7D%3D%5Csqrt%7B95%5E2%2B8%5E2%2B2%5Ctimes%2095%5Ctimes%208%5Ctimes%20cos60%5E%7B%5Ccirc%7D%7D%3D97.30m)
So length of the lake is 97.30 m
Initial amount,
.
Final amount,
.
Time taken, t = 6:00 - 2:00 = 4 hour.
We know,
![A=A_o(\dfrac{1}{2})^{\dfrac{t}{h}}\\\\10 = 150 \times \dfrac{1}{2}^{\dfrac{4}{h}}\\\\2^{\dfrac{4}{h}}=15\\\\\dfrac{4}{h}= log_215\\\\h = \dfrac{4}{log_215}\\\\h = 1.024 \ hours](https://tex.z-dn.net/?f=A%3DA_o%28%5Cdfrac%7B1%7D%7B2%7D%29%5E%7B%5Cdfrac%7Bt%7D%7Bh%7D%7D%5C%5C%5C%5C10%20%3D%20150%20%5Ctimes%20%5Cdfrac%7B1%7D%7B2%7D%5E%7B%5Cdfrac%7B4%7D%7Bh%7D%7D%5C%5C%5C%5C2%5E%7B%5Cdfrac%7B4%7D%7Bh%7D%7D%3D15%5C%5C%5C%5C%5Cdfrac%7B4%7D%7Bh%7D%3D%20log_215%5C%5C%5C%5Ch%20%3D%20%5Cdfrac%7B4%7D%7Blog_215%7D%5C%5C%5C%5Ch%20%3D%201.024%20%5C%20hours)
Therefore, the half-life of the isotope is 1.024 hours.
Hence, this is the required solution.
Answer:
96
Step-by-step explanation:
40=4x+8
32=4x
x=8
other side x+4 is 12
area is 12×8
96
Answer:
b. (16 , 4)
Step-by-step explanation:
f(x): 0 -> 1 , 4 -> 16
f⁻¹(x): 1 -> 0 , 16 -> 4