Answer:
Angle CED must also measure 60°.
Because angle m is shown to be congruent to angles ABC and CDE, this means that angle m has a measure of 60 degrees.
There can only be 180 degrees in a triangle, so the measure of angle ACB must be 180-60-60, which equals 60 degrees.
Using the Vertical Angles Theorem, the measure of angle ACB is the same as the measure of angle CED.
Therefore, angle CED measures 60°.
Step-by-step explanation:
m, because Triangle ABC is similar to triangle EDC
m over 2, because Triangle ABC is congruent to triangle DCE
m + 60 degrees, because Triangle ABC is similar to triangle DCE
120 degrees − m, because Triangle ABC is congruent to triangle DCE
Answer:
A= 254.34 m²
Step-by-step explanation:
to find area of a circle use this formula, A=
r²
now just plug it in
A=
9²
A=
81
A= 254.34 m²
Answer:
While factoring may not always be successful, the Quadratic Formula can always find the solution. The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.
source from: https://www.purplemath.com/modules/quadform.htm
your welcome!
Answer:
The new volume is 3n^2+2n inches greater.
Step-by-step explanation:
Volume of a cube = s^3 where s is side of cube
Original volume = n^3
Volume of a Rectangular Prism = LBH
New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n
DIfference = New- original = 3n^2+2n
Answer:
(B) ![\displaystyle \frac{W(3.1) - W(2.9)}{0.2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BW%283.1%29%20-%20W%282.9%29%7D%7B0.2%7D)
General Formulas and Concepts:
<u>Calculus</u>
Limits
Derivatives
- The definition of a derivative is the slope of the tangent line.
Derivative Notation
Instantaneous Rates
- Tangent Line:
![\displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D)
Step-by-step explanation:
Since we are trying to find a <em>rate</em> at which W(t) changes, we must find the <em>derivative</em> at <em>t</em> = 3.
We are given 2 close answer choices that would have the same <em>numerical</em> answer but different <em>meanings</em>:
- (A)
![\displaystyle \lim_{t \to 3} W(t)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bt%20%5Cto%203%7D%20W%28t%29)
- (B)
![\displaystyle \frac{W(3.1) - W(2.9)}{0.2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BW%283.1%29%20-%20W%282.9%29%7D%7B0.2%7D)
If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the <em>rate</em> at which the volume would be changing and it is not a derivative.
If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a <em>derivative</em> at <em>t</em> = 3, and a derivative tells us what <em>rate</em> something is changing.
∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when <em>t</em> = 3.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e