Answer:
B
Step-by-step explanation:
B
x - 4 squared provides 2 real zeros that are the same. These two are not distinct.
The other two come from x^2 - 7x + 10 which has a discriminate of
sqrt(7^2 - 4*1*10) = sqrt(9) = +/- 3 leading to something real and different.
Connect the dots to each other
Answer:
The exponential growth function is ![P=145380e^{0.04103t}](https://tex.z-dn.net/?f=P%3D145380e%5E%7B0.04103t%7D)
Step-by-step explanation:
Given: The population of a certain city was 145,380 in 2000 and 219,135 in 2010.
To find: exponential growth function that models the growth of the city
Solution:
The exponential growth function is given by ![P=P_0 e^{kt}](https://tex.z-dn.net/?f=P%3DP_0%20e%5E%7Bkt%7D)
Here, P denotes total population after time t
denotes initial population
k denotes rate of growth
t denotes time
As
,
![145380=P_0e^{0}\\145380=P_0\\P=145380e^{kt}](https://tex.z-dn.net/?f=145380%3DP_0e%5E%7B0%7D%5C%5C145380%3DP_0%5C%5CP%3D145380e%5E%7Bkt%7D)
As ![P(10)=219135](https://tex.z-dn.net/?f=P%2810%29%3D219135)
![219135=145380e^{10k}\\e^{10k}=\frac{219135}{145380}\\=1.507326\\k=\frac{1}{10}\ln (1.507326)\\=0.04103\\\Rightarrow P=145380e^{0.04103t}](https://tex.z-dn.net/?f=219135%3D145380e%5E%7B10k%7D%5C%5Ce%5E%7B10k%7D%3D%5Cfrac%7B219135%7D%7B145380%7D%5C%5C%3D1.507326%5C%5Ck%3D%5Cfrac%7B1%7D%7B10%7D%5Cln%20%281.507326%29%5C%5C%3D0.04103%5C%5C%5CRightarrow%20P%3D145380e%5E%7B0.04103t%7D)
Step-by-step explanation:
5 (m+6)
= 5m+5×6
=5m+30
Answer:
∅ ≈ 56.31°
Step-by-step explanation:
The bird is spotted flying 6000 ft from a tower . The distance of the tower from the bird is 6000 ft. The height of the tower is 9000 ft because the observer spot the distance from the top of the tower at a distance of 9000 ft.
The illustration forms a right angle triangle. The adjacent side of the triangle is 6000 ft and the height or opposite side of the triangle is 9000 ft. Using tangential ratio the angle of depression from the bird to the observer can be found as follows.
Let
∅ = angle of depression
tan ∅ = opposite/adjacent
tan ∅ = 9000/6000
tan ∅ = 1.5
∅ = tan⁻¹ 1.5
∅ = 56.309932474
∅ ≈ 56.31°