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ruslelena [56]
4 years ago
8

How do you simplify i²⁹? (If you can't tell, that's the imaginary number i^29).

Mathematics
1 answer:
maria [59]4 years ago
6 0
The imaginary number ' i ' is the square root of -1.

i = √-1
i² = -1
i³ = -√-1
i to the 4th power = +1
i to the 5th power = √-1
etc.

and all the higher powers keep going in the same 4-step cycle.

What's 29 divided by 4 ?
It's 7 with a remainder of 1.

So 29 with all the 4s thrown away is 1, and ' i ' to the 29th power is
the same thing as ' i ' to the 1st power = √-1  or just  plain ' i '.
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Jimmy owns a small engine repair business. The revenue, in dollars, can be modeled by the equation y = 420 + 72x, where x is the
Nataly [62]
I added a screenshot with the complete question.

Answer:
5 hours

Explanation:
We are given that:
Revenue equation:
y = 420 + 72x
Overhead equation:
24x² + 180

We are asked to get the break-even point which is calculated by equating the revenue to the overhead cost.

This can be done as follows:
revenue = overhead cost
420 + 72x = 24x² + 180
24x² + 180 - 420 - 72x = 0
24x² - 72x -240 = 0
(x-5)(x+2) = 0

either: x-5=0 ..........> x = 5 hours (accepted value)
or: x+2=0 .......> x = -2 hours (rejected value as time cannot be negative)

Based on the above:
break-even occurs at 5 hours

Hope this helps :)

4 0
4 years ago
Use the tangent radio to find the missing leg of this right triangle. Estimate your answer to two decimal places.
erica [24]

Answer:

  11.55

Step-by-step explanation:

SOH CAH TOA reminds you ...

  Tan = Opposite/Adjacent

The angle at lower left is the complement of 60°, so is 30°. Then the side x satisfies the equation ...

  tan(30°) = x/20

Multiplying by 20 gives ...

  20·tan(30°) = x ≈ 11.55

8 0
3 years ago
Tim is investigating the relationship between the number of years since a tree was planted and the height of the tree in feet. H
wolverine [178]

Answer: There is not a good prediction for the height of the tree when it is 100 years old because the prediction given by the trend line produced by the regression calculator probably is not valid that far in the future.

Step-by-step explanation:

Years since tree was planted (x) - - - - height (y)

2 - - - - 17

3 - - - - 25

5 - - - 42

6 - - - - 47

7 - - - 54

9 - - - 69

Using a regression calculator :

The height of tree can be modeled by the equation : ŷ = 7.36X + 3.08

With y being the predicted variable; 7.36 being the slope and 3.08 as the intercept.

X is the independent variable which is used in calculating the value of y.

Predicted height when years since tree was planted(x) = 100

ŷ = 7.36X + 3.08

ŷ = 7.36(100) + 3.08

y = 736 + 3.08

y = 739.08

Forward prediction of 100 years produced by the trendline would probably give an invalid value because the trendline only models a range of 9 years prediction. However, a linear regression equation isn't the best for making prediction that far in into the future.

3 0
4 years ago
Does anybody know how to get the 3rd mark ?
Talja [164]

Answer:

Long sides are 1.4 and short sides are 0.7

Step-by-step explanation:

5 0
3 years ago
HELP ME PLEASE! I WILL GIVE BRAINLIEST LOTS OF POINTS
azamat
Number the tables as follows:

1  2
3  4

Eliminate 3 and 4 immediately, because for x = 2 the y values are wrong (3 and 1).

In tables 1 and 2, the input (1) produces the correct output (-1).

So we have to determine which table agrees 100% with the system of equations given.

Comparing tables 1 and 2, row by row, we see that their contents are the same EXCEPT for the first rows.  So focus on determing which of those 2 rows displays values that satisfy both given equations.

First I looked at y=2x-5, and subst. -1 for x.  I got -7, which is correct in table 1 but not in table 2 (where the value would be -13).

Thus, table 1 correct represents the solution of the system of equations.
6 0
3 years ago
Read 2 more answers
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