Answer:
The height of tree house is 70.71 feet
Step-by-step explanation:
We are given that A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground
Refer the attached figure
Length of rope AC = Hypotenuse =100 feet
The top of a tree house to the ground forms a 45∘ angle of elevation from the ground =
We are supposed to find the height of tree house i.e.AB = Perpendicular
So, Using trigonometric ratio
![Sin \theta = \frac{perpendicular}{Hypotenuse}\\Sin 45= \frac{AB}{AC}\\\frac{1}{\sqrt{2}}=\frac{AB}{100}\\100 \times \frac{1}{\sqrt{2}}=AB\\70.71=AB](https://tex.z-dn.net/?f=Sin%20%5Ctheta%20%3D%20%5Cfrac%7Bperpendicular%7D%7BHypotenuse%7D%5C%5CSin%2045%3D%20%5Cfrac%7BAB%7D%7BAC%7D%5C%5C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%3D%5Cfrac%7BAB%7D%7B100%7D%5C%5C100%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%3DAB%5C%5C70.71%3DAB)
Hence The height of tree house is 70.71 feet
Answer:
(-2, -4)
Step-by-step explanation:
Given:
The system of equations to solve is given as:
![y=2x\\\\x+y=-6](https://tex.z-dn.net/?f=y%3D2x%5C%5C%5C%5Cx%2By%3D-6)
In order to solve this system of linear equations, we use substitution method.
In substitution method, we substitute the value of any one variable in the other equation.
So, we substitute the value of 'y' from first equation in the second equation.
This gives,
![x+2x=-6\\\\3x=-6](https://tex.z-dn.net/?f=x%2B2x%3D-6%5C%5C%5C%5C3x%3D-6)
Dividing both sides by 3, we get:
![\frac{3x}{3}=\frac{-6}{3}\\\\x=-2](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%5Cfrac%7B-6%7D%7B3%7D%5C%5C%5C%5Cx%3D-2)
Now, ![y=2x=2\times -2=-4](https://tex.z-dn.net/?f=y%3D2x%3D2%5Ctimes%20-2%3D-4)
Therefore, the solution is (-2, -4)
The exponential function to model the quail population is 910*(1.2)^t
Concept: An exponential function is a mathematical function denoted f(x)=\exp or e^{x}. Unless otherwise stated, the term generally refers to a positive function of a real variable, although it may be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.
Given data
Initial population= 910 quail
Rate= 20%
Now using the model below:
A= P(1+r)^t
r= 0.2
A= 910(1+0.2)^t
A= 910*(1.2)^t
Hence the expression to model the population is 910*(1.2)^t
For more information about exponential function, visit brainly.com/question/2456547
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The 100th term that’s what I think