Answer:
28.7 meters
Step-by-step explanation:
Draw a diagram. Let's say d is the distance between the anchor and the bottom of the tower, h is the height of the tower, and x is the length of the wire.
Using trigonometry, we can write two equations for the height of the tower:
h = d tan 65°
h = (d + 25) tan 35°
Setting these equal, we can solve for d.
d tan 65° = (d + 25) tan 35°
d tan 65° = d tan 35° + 25 tan 35°
d (tan 65° − tan 35°) = 25 tan 35°
d = 25 tan 35° / (tan 65° − tan 35°)
d ≈ 12.12
Now we can find x:
cos 65° = d / x
x = d / cos 65°
x ≈ 28.7
The wire is approximately 28.7 meters long.
38 yd is the area of that shape
You are solving for the variable (c).
Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS (Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction)
First, subtract 8 from both sides
4c + 8 (-8) = 20 (-8)
4c = 20 - 8
4c = 12
Next, to fully isolate the variable (c), divide 4 from both sides
(4c)/4 = (12)/4
c = 12/4
c = 3
3 is your answer for c.
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Answer:
7. $8123.79
8. 0.012 g
Step-by-step explanation:
It often pays to follow directions. The attachment shows the use of a TI-84 graphing calculator to find the answers.
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You will notice that the answer to problem 8 does not agree with any of the offered choices. The time period of 22.8 years is 12 times the half-life of the substance, so there will be (1/2)^12 = 1/4096 of the original amount remaining. The time periods corresponding to the amounts shown range from 1.37 years to 16.4 years.
For half-life problems, I find it convenient to use the decay factor (0.5^(1/half-life)) directly, rather than convert it to e^-k. If you do convert it to the form ...
e^(-kt)
the value of k is (ln(2)/half-life), about 0.3648143056.
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For multiple choice problems where the choices make no sense, I like to suggest you ask your teacher to show you how to work the problem. (Alternatively, use the "Report this question" or "Ask a tutor" button sometimes provided.)
Answer: We have an odd number of pennies.
Step-by-step explanation:
So we have N pennies.
When we wan to divide the N pennies into groups of 2, we have a penny left over.
This means that N is not divisible by 2.
The problem is that there are infinite natural numbers that are not divisible by two, this is the set of odd numbers.
And remember that an odd number can be written as:
N = 2*k + 1.
where k is an integer.
Then we want to divide this by 2 (divide N into groups of 2)
we have:
N/2 = (2*k + 1)/2 = 2*k/2 + 1/2 = k + 1/2.
So we have k groups of 2 pennies, and a penny leftover that we can not divide into two.