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inn [45]
2 years ago
8

Given f(x) = 2 sin x, find the exact value of f (7pi/6) in simplest form with a rational denominator.​

Mathematics
1 answer:
IrinaVladis [17]2 years ago
6 0

Answer:

           \bold{f(\frac{7\pi}6)=-1}

Step-by-step explanation:

f(\frac{7\pi}6)=2\sin(\frac{7\pi}6)=2\sin(\frac{7\pi}6)=2\sin(\pi+\frac{\pi}6)=-2\sin(\frac{\pi}6)=-2\cdot\frac12=-1

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Let g be the function given by g(x)=√ 1−sin2x. Which of the following statements could be false on the interval 0≤x≤π ?
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Answer:

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Step-by-step explanation:

yesirskiii\

6 0
2 years ago
If 45% of a number, n, is 225, what is 74% of n?<br><br> A. 185<br> B. 298<br> C. 370<br> D. 406
Stolb23 [73]

Answer:

C

Step-by-step explanation:

4 0
3 years ago
100 points!!! Pre calculus. I need helpppppppppp
Fantom [35]

Answer:

We have function,

y = 3 - 6 \sin {}^{} (2x +  \frac{\pi}{2} )

Standard Form of Sinusoid is

y =  - 6 \sin(2x +  \frac{\pi}{2} )  + 3

Which corresponds to

y = a \sin(b(x + c))  + d

where a is the amplitude

2pi/b is the period

c is phase shift

d is vertical shift or midline.

In the equation equation, we must factor out 2 so we get

y =  - 6(2(x +  \frac{\pi}{4} )) + 3

Also remeber a and b is always positive

So now let answer the questions.

a. The period is

\frac{2\pi}{ |b| }

\frac{2\pi}{ |2| }  = \pi

So the period is pi radians.

b. Amplitude is

| - 6|  = 6

Amplitude is 6.

c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.

So using that<em> rule, our range is [6+3, -6+3]= [9,-3] So our range</em> is [-3,9].

D. Plug in 0 for x.

3 - 6 \sin((2(0) +  \frac{\pi}{2} )

3 - 6 \sin( \frac{\pi}{2} )

3 - 6(1)

3 - 6

=  - 3

So the y intercept is (0,-3)

E. To find phase shift, set x-c=0 to solve for phase shift.

x +  \frac{\pi}{4}  = 0

x =  -  \frac{\pi}{4}

Negative means to the left, so the phase shift is pi/4 units to the left.

f. Period is PI, so use interval [0,2pi].

Look at the graph above,

6 0
2 years ago
How many square inches are 9 cubes with a 1 inch edge
ki77a [65]
Add it up then you will get answer

4 0
3 years ago
Extreme cold and hot temperatures are known to affect the operation of electronic components. Winter is approaching and you are
Musya8 [376]

Answer:

A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

Test statistic(Z) = 2.31

P-value = 0.0104

Step-by-step explanation:

Step 1

Null hypothesis: The average damaging temperature of nine iPods is 5°F

Alternate hypothesis: The average damaging temperature of nine iPods differs from 5°F

Step 2

Mean=5°F, Sd=3, df=n-1=9-1=8

The t-value corresponding to 8 degrees of freedom and 95% confidence level (5% significance level) is 2.306

Confidence Interval(CI) = (mean + or - t×sd/√n)

CI = (5 + 2.306×3/√8) = 5 + 6.918/2.828= 5+2.45=7.45°F

CI = (5 - 2.306×3/√8) = 5-2.45 = 2.55°F

Z = (sample mean - population mean)/(sd÷√n) = (5-2.55)/(3÷√8) = 2.45/1.061 = 2.31

Step 3

Using the standard distribution table, the cumulative area to the left of Z = 2.31 is 0.9896

P-value = 1 - 0.9896 = 0.0104

Step 4

Conclusion: A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F

7 0
3 years ago
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