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3 years ago

Find the unkown angle of a triangle

Mathematics

1 answer:

REY [17]3 years ago

6 0

Step-by-step explanation:

Find

Triangle A(because there are two triangles)

take 28°+39°=67°

an angle is 180° in total so you take

180°-67°=113°

Angle x = 113°

Angle y = 67°

Triangle B

64°+67° = 131°

180°-131°=49°

Angle z =49°

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3 years ago

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3 years ago

1..A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 26

statuscvo [17]

Answer:

See below for answers and explanations (along with a graph attached)

Step-by-step explanation:

Part A

The amplitude of a sinusoidal function is half the distance between the maximum and the minimum. It is given to us that the distance from the highest and lowest point is 6 feet, so our amplitude is 6/2 = 3 feet

Part B

The graph's function would be in the form of $y=acos(bx+c)+d$ where $a$ is the amplitude, $\frac{2\pi}{b}$ is the period, $-\frac{c}{b}$ is the phase/horizontal shift, and $d$ is the average/midline.

We already know our amplitude of $a=3$ from part A.

Since our period is given to us as 26 seconds, then we can use the equation $\frac{2\pi}{b}=26$ to find $b$ , which happens to be $b=\frac{\pi}{13}$ .

Since the cosine function starts at its maximum and we want it to start at the average where the bottle travels up, we would need to use the cofunction identity $sin(x)=cos(x-\frac{\pi}{2})$ which shifts the cosine graph $\frac{\pi}{2}$ units to the right. This means that $c=-\frac{\pi}{2}$ , making our phase shift $-\frac{c}{b}=-\frac{-\frac{\pi}{2}}{\frac{\pi}{13}}=6.5$ , or 6.5 feet to the right

Our average/midline would be $d=12$ as given as the average height by the problem.

Therefore, the function is $f(x)=3cos(\frac{\pi}{13}x-\frac{\pi}{2})+12$

Part C

Using our determined function from Part B, by looking at its graph, we see that the bottle will reach its lowest height of 9 feet after 19.5 seconds (see attached graph).

5 0

2 years ago

Read 2 more answers

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

Kruka [31]

Answer:

$6.76-2.01\frac{2.55}{\sqrt{50}}=6.03$

$6.76+2.01\frac{2.55}{\sqrt{50}}=7.49$

The 95% confidence interval would be given by (6.03;7.49)

Step-by-step explanation:

Notation

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=50 represent the sample size

Solution

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

We can calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=6.76$

The sample deviation calculated $s=2.55$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=50-1=49$

We assume a standard confidence level of 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that $t_{\alpha/2}=2.01$

Now we have everything in order to replace into formula (1):

$6.76-2.01\frac{2.55}{\sqrt{50}}=6.03$

$6.76+2.01\frac{2.55}{\sqrt{50}}=7.49$

The 95% confidence interval would be given by (6.03;7.49)

3 0

3 years ago

2. Express the number 1750 as a product of prime factors of the form: p * qr * s

Artyom0805 [142]

9514 1404 393

Answer:

1750 = 2 · 5³ · 7

Step-by-step explanation:

It is often helpful to start with divisibility rules when finding prime factors of a small composite number.

The least-significant digit is even, so we know 2 is a factor.

1750/2 = 875

The least significant digit is 5, so we know 5 is a factor.

875/5 = 175

175/5 = 35

35/5 = 7

7 is a prime number, so we're done.

The factorization is ...

1750 = 2 · 5³ · 7

4 0

3 years ago

Find the unkown angle of a triangle​

Find the unkown angle of a triangle