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BartSMP [9]
3 years ago
14

How do you this question (pre-cal)

Mathematics
1 answer:
Novay_Z [31]3 years ago
4 0

The goal to proving identities is to transform one side into the other. We can only pick one side to transform while the other side stays the same the entire time. The general rule of thumb is to transform the more complicated side (though there may be exceptions to this guideline).

So I'll take the left hand side and try to turn it into \csc^2( B )

One way we can do that is through the following steps:

\frac{\tan(B) + \cot(B)}{\tan(B)} = \csc^2(B)\\\\\frac{\tan(B)}{\tan(B)} + \frac{\cot(B)}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\frac{1}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\cot(B) = \csc^2(B)\\\\1 + \cot^2(B) = \csc^2(B)\\\\1 + \frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)}{\sin^2(B)}+\frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)+cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{1}{\sin^2(B)} = \csc^2(B)\\\\\csc^2(B)=\csc^2(B) \ \ {\Large \checkmark}\\\\

Since we've shown that the left hand side transforms into the right hand side, this verifies the equation is an identity.

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What value of b makes the trinomial below a perfect square x^2-bx+100
Aloiza [94]
1. Perfect square trinomials, are 2nd degree polynomials, of the form          a x^{2} +bx+c so that a \neq 0, b \neq 0, c \neq 0, which can be written as perfect squares.

2. For example (x+1) ^{2} = x^{2} +2x+1
 
(3x-1)^{2}= (3x)^{2}-2(3x)+(-1) ^{2}= 9x^{2}-6x+1    


3. Thus x^{2} +2x+1, 9x^{2}-6x+1 are perfect square trinomials.

4. x^{2} -bx+100= x^{2} -bx+ 10^{2}= (x+10)^{2}   or  (x-10)^{2}

5. In the first case -b=20, so b=-20. In the second case, -b=-20, so b=20.

6. b∈{-20, 20}
6 0
2 years ago
A standard number cube is tossed. Find the following probability. ​P(greater than 4 or odd​)
lorasvet [3.4K]
A standard cube has 6 possible outcomes. But since we want to find P(4+ or odd), the outcomes become more narrow.
So:
6 outcomes -> 1, 2, 3, 4, 5, 6

But we want to find 4+
So:
4+ = 4, 5, 6

We also want to find all odd possibilities.
So:
odd = 1, 3, 5

As you can see, there is a 5 in both the 4+ and the odd numbers so 5 will only be counted once.
P(4+ or odd) = 1, 3, 4, 5, 6

So the probability of having an outcome that is P(4+ or odd) is:
5/6 or 0.8333 or 83.33%

Hope I helped!
8 0
2 years ago
Read 2 more answers
The final scores from the last five games of two basketball teams are given. Jumping Jackrabbits: 70, 65, 72, 80, 73 Leaping Liz
scoundrel [369]

Using the Mean Absolute Deviation(MAD) concept, it is found that:

a) The Jumping Jackrabbits have a MAD of 3.6 and the Leaping Lizards of 6.8.

b) The MAD is lower for the Jumping Jackrabbits then for the Leaping Lizards, hence their scores are more consistent.

<h3>What is the mean absolute deviation of a data-set?</h3>

  • The mean of a data-set is given by the sum of all observations divided by the number of observations.
  • The mean absolute deviation(MAD) of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.
  • The mean absolute deviation represents the average by which the values differ from the mean.

Item a:

For the Jumping Jackrabbits, the mean and MAD are given by:

M = (70 + 65 + 72 + 80 + 73)/5 = 72

MAD = (|70 - 72| + |65 - 72| + |72 - 72| + |80 - 72| + |73 - 72|)/5 = 3.6.

For the Leaping Lizards, the mean and the MAD are given by:

M = (61 + 47 + 70 + 63 + 54)/5 = 59

MAD = (|61 - 59| + |47 - 59| + |70 - 59| + |63 - 59| + |54 - 59|)/5 = 6.8.

The Jumping Jackrabbits have a MAD of 3.6 and the Leaping Lizards of 6.8.

Item b:

The MAD is lower for the Jumping Jackrabbits then for the Leaping Lizards, hence their scores are more consistent.

More can be learned about the Mean Absolute Deviation(MAD) concept at  brainly.com/question/3250070

#SPJ1

4 0
2 years ago
Find the median and the mode of the data.
frosja888 [35]

Answer:

Median: 8

Mode: 7

I believe this is correct.

7 0
2 years ago
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A spaceship traveled 32 million miles. In scientific notation that is _____ miles. 3.2 × 10-7 3.2 × 10-6 3.2 × 106 3.2 × 107
In-s [12.5K]
In scientific notation :
32 million miles is 3.2 x 10 ^7 miles.
7 0
3 years ago
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