Answer:
41.7feet
Step-by-step explanation:
From the question we are given the following
angle of depression = 50°
Distance of the pole from the base of the feet = 35feet (Adjacent)
Required
height of the school (opposite)
Using the SOH CAH TOA identity
Tan theta = opp/adj
Tan 50 = H/35
H = 35tan 50
H = 35(1.1918)
H = 41.7feet
Hence the height of the school is 41.7feet
Answer: 56 meters long and 49 meters wide
Step-by-step explanation:
Convert 350% to a decimal. 350% is 3.5. Each lenth is 3.5x larger than the original pond.
16*(3.5) =56 meters length
14*(3.5) = 49 meters width
56 meters long and 49 meters wide
Answer:
answer A shows a rotation
Answer:
![\displaystyle y = \frac{t^2}{16} + 18](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Cfrac%7Bt%5E2%7D%7B16%7D%20%2B%2018)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Functions
- Function Notation
- Coordinates (x, y)
<u>Calculus</u>
Derivatives
Derivative Notation
Antiderivatives - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]: ![\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7Bx%5En%7D%20%5C%2C%20dx%20%3D%20%5Cfrac%7Bx%5E%7Bn%20%2B%201%7D%7D%7Bn%20%2B%201%7D%20%2B%20C)
Integration Property [Multiplied Constant]: ![\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7Bcf%28x%29%7D%20%5C%2C%20dx%20%3D%20c%20%5Cint%20%7Bf%28x%29%7D%20%5C%2C%20dx)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
Point (0, 18)
![\displaystyle \frac{dy}{dt} = \frac{1}{8} t](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B8%7D%20t)
<u>Step 2: Find General Solution</u>
<em>Use integration</em>
- [Derivative] Rewrite:
![\displaystyle dy = \frac{1}{8} t\ dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20dy%20%3D%20%5Cfrac%7B1%7D%7B8%7D%20t%5C%20dt)
- [Equality Property] Integrate both sides:
![\displaystyle \int dy = \int {\frac{1}{8} t} \, dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20dy%20%3D%20%5Cint%20%7B%5Cfrac%7B1%7D%7B8%7D%20t%7D%20%5C%2C%20dt)
- [Left Integral] Integrate [Integration Rule - Reverse Power Rule]:
![\displaystyle y = \int {\frac{1}{8} t} \, dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Cint%20%7B%5Cfrac%7B1%7D%7B8%7D%20t%7D%20%5C%2C%20dt)
- [Right Integral] Rewrite [Integration Property - Multiplied Constant]:
![\displaystyle y = \frac{1}{8}\int {t} \, dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Cfrac%7B1%7D%7B8%7D%5Cint%20%7Bt%7D%20%5C%2C%20dt)
- [Right Integral] Integrate [Integration Rule - Reverse Power Rule]:
![\displaystyle y = \frac{1}{8}(\frac{t^2}{2}) + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Cfrac%7B1%7D%7B8%7D%28%5Cfrac%7Bt%5E2%7D%7B2%7D%29%20%2B%20C)
- Multiply:
![\displaystyle y = \frac{t^2}{16} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Cfrac%7Bt%5E2%7D%7B16%7D%20%2B%20C)
<u>Step 3: Find Particular Solution</u>
- Substitute in point [Function]:
![\displaystyle 18 = \frac{0^2}{16} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%2018%20%3D%20%5Cfrac%7B0%5E2%7D%7B16%7D%20%2B%20C)
- Simplify:
![\displaystyle 18 = 0 + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%2018%20%3D%200%20%2B%20C)
- Add:
![\displaystyle 18 = C](https://tex.z-dn.net/?f=%5Cdisplaystyle%2018%20%3D%20C)
- Rewrite:
![\displaystyle C = 18](https://tex.z-dn.net/?f=%5Cdisplaystyle%20C%20%3D%2018)
- Substitute in <em>C</em> [Function]:
![\displaystyle y = \frac{t^2}{16} + 18](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20%5Cfrac%7Bt%5E2%7D%7B16%7D%20%2B%2018)
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
Answer:
I think you would multiply 20 × 4 and the answer would be 80 that the scientist counted the number of plants in each 4 sections after 20 days.