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Zepler [3.9K]
3 years ago
7

ethan ate 4/8 of the sandwich.Andy ate 1/2 of the sandwich. the sandwiches were the same size whose sandwich had more equal part

s
Mathematics
1 answer:
son4ous [18]3 years ago
6 0
Ethan ate 1/2 of it and had more equal parts.
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Write a word phrase for and algebraic expression 3x+10
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Three multiplied by a number plus ten.
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2. The number of atoms of a particular chemical element is modelled by
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9514 1404 393

Answer:

  a) 600

  b) see below

  c) 1.26 hours

Step-by-step explanation:

a) The value of y when x=0 is the coefficient of the exponential term:

  y = 600·3^(-0) = 600·1 = 600

There were 600 atoms to start.

__

b) see attached for a graph

__

c) The graph shows 150 atoms at t = 1.26, about 1.26 hours after the start of time counting.

If you want to find that value algebraically, substitute for y and solve for x. Logarithms are involved.

  150 = 600·3^(-x)

  150/600 = 3^(-x)

  log(1/4) = -x·log(3)

  x = -log(1/4)/log(3) = log(4)/log(3) ≈ 1.2618595

After about 1.26 hours, there were 150 atoms.

6 0
3 years ago
A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is ce
lubasha [3.4K]
<h2>Answer:</h2>

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

<h2>Step-by-step explanation:</h2>

The origin of the coordinate system is the center of the circle. So we have an angle that measures 5\pi/12=75^{\circ}. so the x-coordinate and y-coordinate can be found, by using trigonometry as follows:

x=20cos(5\pi/12)=5\sqrt{6}-5\sqrt{2} \\ \\ Arranging:\\ \\x=5(-\sqrt{2}+\sqrt{6}) \\ \\y=20sin(5\pi/12)=5\sqrt(6)+5\sqrt{2} \\ \\ Arranging:\\ \\y=5(\sqrt{2}+\sqrt{6})

Finally, the exact value of the position of the rider after the carousel rotates 5\pi/12 radians is:

\boxed{(5(-\sqrt{2}+\sqrt{6}),5(\sqrt{2}+\sqrt{6}))}

3 0
2 years ago
Express the series using sigma notation. 2 - 6 + 18 – 54 + 162 ...
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2-6+18-54+162+\cdots=2(-3)^0+2(-3)^1+2(-3)^2+2(-3)^3+2(-3)^4+\cdots
=\displaystyle2\sum_{n=0}^\infty(-3)^n
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3 years ago
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