Given the sequence 7, 14, 28, 56, ..., which expression shown would give the tenth term? A. 7^10 B. 7·2^10 C. 7·2^9

For which value of theta is cot (theta) undefined?

sattari [20]

The cotangent function is defined as the ratio between cosine and sine of a given angle, i.e.

$\cot(x) = \frac{\cos(x)}{\sin(x)}$

Since you can't have zero at the denominator, the cotangent function is not defined when the sine is zero.

Let's look at your option:

$\sin(90^\circ) = 1$ , so the cotangent is defined here

$\sin(180^\circ) = 0$ , so the cotangent is not defined here

$\sin(270^\circ) = -1$ , so the cotangent is defined here

$\sin(450^\circ) = \sin(360^\circ+90^\circ)=\sin(90^\circ) = 1$ , so the cotangent is defined here

6 0

3 years ago

Read 2 more answers

Oumou is buying tile for her kitchen. The area of Oumou’s rectangular kitchen, in square feet, can be found by using the express

Jobisdone [24]

The answer is: 15m + 20n

Hope this helped

4 0

3 years ago

Carla is arranging square patches of grass on her rectangular lawn her lawn is 10 yards wide and 3 and 1/2 yards long how many s

Paraphin [41]

Answer:

I don't know if this is correct but wouldn't it be 560?

Step-by-step explanation:

If you have 10 on one side, you divide 10 by 1/4 to get 40. So you need 40 blocks to fill one side, and 3 1/2 on the other only needs 14. 14*40=560.

8 0

2 years ago

I need help in this math number 7,I got the picture here for u to know what to do because I don’t understand the question ppplll

tia_tia [17]

You have to find a common denominator for both fractions. I chose the denominator to be 10, so the 1/2 will become 5/10, and 1/5 will become 2/10.

Subtract 5/10 from 2/10. You will get -3/10.

Answer: -3/10

You can check your answer by solving 1/2-3/10=1/5 to see if it is true. (It is:)

5 0

2 years ago

National Ave gas prices

Musya8 [376]

Question: What equation models the data?
For this question I used a software to calculate the equation. When plotted, we can notice that the points form a parabolic function therefore we needed quadratic regression for this one. The quadratic equation is in the form of $y=A+Bx+Cx^{2}$ where y represents the gas prices, x is the year, and A, B, and C are coefficients. I have found A, B, and C using the software and the equation for the data is:

$y=-0.092+0.587x-0.026x^{2}$

Question: What are the domain and range of the equation?
To find the range of the equation, we just transform the quadratic equation into the form $y=a(x-h)^{2}+k$ . The value for k would be the maximum element in our range, and for the sake of the problem, let's assume that we don't have negative prices.

$y=-0.092+0.587x-0.026x^{2}$
$y+0.092=0.587x-0.026x^{2}$
$y+0.092=-0.026(x^{2}-22.577x)$
$y+0.092-0.026(127.442)=-0.026(x^{2}-22.577x+127.442)$
$y-3.221=-0.026(x-11.289)^{2}$
$y=-0.026(x-11.289)^{2}+3.221$

We can see that 3.221 is the maximum value of the range while zero is the minimum. Thus, we can express the range as { $y|0 \leq y \leq 3.221$ }

For the domain, the number of years can extend infinitely but it will also depend if we want to consider the years where the price will be negative. Thus, let's just find the year when the price would be zero.

$0=-0.026(x-11.289)^{2}+3.221$
$-3.221=-0.026(x-11.289)^{2}$
$123.885=(x-11.289)^{2}$
$+-11.130=x-11.289$

$x=0.159$
$x=22.419$

Anywhere before and after the range of the x values above would result to a negative price therefore we can restrict the domain to those values. However, since x represents the year, we would need to round up the first value and round down the larger value.

Domain: { $x|01 \leq x \leq 22$ }

Question: Do you think your equation is a good fit for the data?
To know whether our equation is a good fit or not, we just look at the value of the correlation coefficient r. We can calculate this manually but in this case I just used a software. According to the software, the value for r is 0.661. This is almost close to a strong correlation which is 0.7 thus we can say that this equation is a good fit.

Question: Is there a trend in the data?
There might be a trend, but it won't be a simple linear one. Since the data initially rose before continuously decreasing, our data would best be described by a quadratic trend. The quadratic trend would be the parabolic equation we just used to model the data.

Question: Does there seem to be a positive correlation, a negative correlation, or neither?
Neither. A positive or negative correlation only applies when we are talking about linear trends, where it's either one variable increases as the other one also increases or the variable decreases as the other one increases. In our case, the price rose and fall as the years increase so there is neither a positive nor a negative correlation.

Question: How much do you expect gas to cost in 2020?
We can answer this question by using the equation that we used to model the data. For this question, we would just need to substitute 20 for x since we want to know the price in 2020 (we have only used the last two digits of the year for the equation) while the answer to this would be the expected price.

$y=-0.092+0.587(20)-0.026(20)^{2}$
$y=-0.092+11.740-10.400$
$y=1.248$

The expected price in 2020 would be 1.248 units.

4 0

3 years ago