Age of tom=t
age of john=j
age of andy=a
t<a
if j is not older than t, then he is less than or equal to t so
j ≤ t
but there is an oldest so therefor we assume that j < t
t < a
j < t
subsitute
j<t<a
andy is oldest
tom is second
john is youngest
Step 1. Take out the constants
3/9 y^2y^4
Step 2. Simplify 3/9 to 1/3
1/3 y^2y^4
Step 3. Simplify
y^2y^4/3
Step 4. Use the Product Rule
y^2 + 4/3
Step 5. Simplify 2 + 4 to 6
y^6/3
Answer:
An hour
Step-by-step explanation:
assuming the speed adds the half hour, three times the speed would take out an hour and a half (going by half hour marks)
Answer:
Part 5) The length of the ski lift is ![1.15\ miles](https://tex.z-dn.net/?f=1.15%5C%20miles)
Part 6) The height of the tree is 18.12 m
Step-by-step explanation:
Part 5)
Let
A -----> Beginning of the ski lift
B -----> Top of the mountain
C -----> Base of mountain
we have
![b=0.75\ miles](https://tex.z-dn.net/?f=b%3D0.75%5C%20miles)
![A=20\°](https://tex.z-dn.net/?f=A%3D20%5C%C2%B0)
----> by supplementary angles
Find the measure of angle B
Remember that the sum of the interior angles must be equal to 180 degrees
![B=180\°-A-C](https://tex.z-dn.net/?f=B%3D180%5C%C2%B0-A-C)
substitute
![B=180\°-20\°-130\°=30\°](https://tex.z-dn.net/?f=B%3D180%5C%C2%B0-20%5C%C2%B0-130%5C%C2%B0%3D30%5C%C2%B0)
Applying the law of sines
![\frac{b}{sin(B)}=\frac{c}{sin(C)}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%3D%5Cfrac%7Bc%7D%7Bsin%28C%29%7D)
substitute
![\frac{0.75}{sin(30\°)}=\frac{c}{sin(130\°)}](https://tex.z-dn.net/?f=%5Cfrac%7B0.75%7D%7Bsin%2830%5C%C2%B0%29%7D%3D%5Cfrac%7Bc%7D%7Bsin%28130%5C%C2%B0%29%7D)
![c=\frac{0.75}{sin(30\°)}(sin(130\°))](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B0.75%7D%7Bsin%2830%5C%C2%B0%29%7D%28sin%28130%5C%C2%B0%29%29)
![c=1.15\ miles](https://tex.z-dn.net/?f=c%3D1.15%5C%20miles)
Par 6)
see the attached figure with letters to better understand the problem
<u><em>Applying the law of sines in the right triangle BDC</em></u>
In the right triangle BDC 20 degrees is the complement of 70 degrees
![\frac{BC}{sin(70\°)}=\frac{x}{sin(20\°)}](https://tex.z-dn.net/?f=%5Cfrac%7BBC%7D%7Bsin%2870%5C%C2%B0%29%7D%3D%5Cfrac%7Bx%7D%7Bsin%2820%5C%C2%B0%29%7D)
-----> equation A
<u><em>Applying the law of sines in the right triangle ABC</em></u>
In the right triangle ABC 50 degrees is the complement of 40 degrees
![\frac{BC}{sin(40\°)}=\frac{x+15}{sin(50\°)}](https://tex.z-dn.net/?f=%5Cfrac%7BBC%7D%7Bsin%2840%5C%C2%B0%29%7D%3D%5Cfrac%7Bx%2B15%7D%7Bsin%2850%5C%C2%B0%29%7D)
-----> equation B
Equate equation A and equation B and solve for x
![(sin(70\°))\frac{x}{sin(20\°)}=(sin(40\°))\frac{x+15}{sin(50\°)}\\\\2.7475x=0.8391(x+15)\\\\2.7475x=0.8391x+12.5865\\\\2.7475x-0.8391x=12.5865\\\\x=6.60\ m](https://tex.z-dn.net/?f=%28sin%2870%5C%C2%B0%29%29%5Cfrac%7Bx%7D%7Bsin%2820%5C%C2%B0%29%7D%3D%28sin%2840%5C%C2%B0%29%29%5Cfrac%7Bx%2B15%7D%7Bsin%2850%5C%C2%B0%29%7D%5C%5C%5C%5C2.7475x%3D0.8391%28x%2B15%29%5C%5C%5C%5C2.7475x%3D0.8391x%2B12.5865%5C%5C%5C%5C2.7475x-0.8391x%3D12.5865%5C%5C%5C%5Cx%3D6.60%5C%20m)
<u><em>Find the value of BC</em></u>
![BC=(sin(70\°))\frac{6.6}{sin(20\°)}](https://tex.z-dn.net/?f=BC%3D%28sin%2870%5C%C2%B0%29%29%5Cfrac%7B6.6%7D%7Bsin%2820%5C%C2%B0%29%7D)
![BC=18.12\ m](https://tex.z-dn.net/?f=BC%3D18.12%5C%20m)
therefore
The height of the tree is 18.12 m
Answer:
Step-by-step explanation:
1/9 < 1/√n < 1/7
9 > √n > 7
81 > n > 49
n = 50, 51, 52, ..., 80
n has 31 possible values