Letters
If ABC is congruent to DEF
Then angle A = angle D
angle B = angle E
angle C = angle F
Sides:
AB = DE
BC = EF
AC = DF
Area of a circle equation:
A=(3.14)r^2
40(3.14)=(3.14)*r^2
40=r^2
r= square root of 40
simplified radius is 2 times root 10
(See the photo I attached for the work)
Answer:
47/100
Step-by-step explanation:
47 -> 0.47 47/100 = 0.47
Answer:
![s\approx17531](https://tex.z-dn.net/?f=s%5Capprox17531)
Step-by-step explanation:
When considering a curve defined by a function f(x) and its respective derivative f'(x) that are continuous in an interval [a, b], the length s of the arc delimited by a and b is given by the equation:
![s=\int\limits^a_b {\sqrt{1+(f'(x))^2} } \, dx](https://tex.z-dn.net/?f=s%3D%5Cint%5Climits%5Ea_b%20%7B%5Csqrt%7B1%2B%28f%27%28x%29%29%5E2%7D%20%7D%20%5C%2C%20dx)
First, let's find the derivate of y(x):
![y'(x)=3\sqrt{x}](https://tex.z-dn.net/?f=y%27%28x%29%3D3%5Csqrt%7Bx%7D)
Replacing the derivate in the previous equation:
![s=\int\limits^a_b {\sqrt{1+((3\sqrt{x}) ^2} } \, dx=\int\limits^a_b {\sqrt{1+9x} } \, dx](https://tex.z-dn.net/?f=s%3D%5Cint%5Climits%5Ea_b%20%7B%5Csqrt%7B1%2B%28%283%5Csqrt%7Bx%7D%29%20%5E2%7D%20%7D%20%5C%2C%20dx%3D%5Cint%5Climits%5Ea_b%20%7B%5Csqrt%7B1%2B9x%7D%20%7D%20%5C%2C%20dx)
Substitute u=1+9x and du=9x, so:
![s= \frac{1}{9} \int\limits^a_b u^{1/2} \, du](https://tex.z-dn.net/?f=s%3D%20%5Cfrac%7B1%7D%7B9%7D%20%5Cint%5Climits%5Ea_b%20u%5E%7B1%2F2%7D%20%20%5C%2C%20du)
The antiderivative of
is:
![s=\frac{2u^{3/2} }{27}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B2u%5E%7B3%2F2%7D%20%7D%7B27%7D)
u=1+9x, so:
![s=\frac{2(1+9x)^{3/2} }{27}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B2%281%2B9x%29%5E%7B3%2F2%7D%20%7D%7B27%7D)
Evaluating the antiderivative at the limits:
![s=\frac{2(1+9x)^{3/2} }{27} \left \{ {{b=432} \atop {a=31}} \right. =\frac{2(3889)^{3/2} }{27}-\frac{2(325)^{3/2} }{27} =17530.82988\approx17531](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B2%281%2B9x%29%5E%7B3%2F2%7D%20%7D%7B27%7D%20%5Cleft%20%5C%7B%20%7B%7Bb%3D432%7D%20%5Catop%20%7Ba%3D31%7D%7D%20%5Cright.%20%3D%5Cfrac%7B2%283889%29%5E%7B3%2F2%7D%20%7D%7B27%7D-%5Cfrac%7B2%28325%29%5E%7B3%2F2%7D%20%7D%7B27%7D%20%3D17530.82988%5Capprox17531)
Since she donates 25%, take 25% and multiply it by 1,200
![.25 * 1,200 = 300](https://tex.z-dn.net/?f=.25%20%2A%201%2C200%20%3D%20300)
or,
![\frac{1}{4} * 1,200 = 300](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%2A%201%2C200%20%3D%20300)