All categories

3 years ago

Search cos jk and tan jk knowing that sin jk = 8/3

Mathematics

1 answer:

aleksley [76]3 years ago

3 0

Answer:

cosjk = √55 i/3

tanjk = 8/√55 i

Step-by-step explanation:

Given

sin jk = 8/3

According to SOH CAH TOA

Sin theta = opposite/hypotenuse = 8/3

Opposite = 8

hypotenuse = 3

Get the adjacent using the pythagoras theorem

hyp² = opp²+adj²

adj² = hyp² - opp²

adj² = 3² - 8²

adj² = 9-64

adj² = -55

adj = √-55

adj = √55 i (i = √-1)

Get cosjk

cosjk = adj/hyp

cosjk = √55 i/3

Get tanjk

tanjk = opp/adj

tanjk = 8/√55 i

You might be interested in

Least

Alex73 [517]

Answer:

we don't have the full answer sry.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The table below shows the typical hours worked by employees at a company. A salaried employee makes $67,000 per year. Hourly emp

nadezda [96]

First, we must calculate the weekly pay of an employee that is paid a fixed amount. Given that there are 52 weeks in a year, the weekly pay for a regularly paid employee is: 67,000 / 52 = $1,288.46 Now, we calculate the number of hours an employee that is paid hourly works per week: 0 + 10 + 8 + 8 + 7 + 6.5 + 4.5 = 44 So this employee is paid: 25 x 40 + 37.5 x 4 = $1,150 Therefore, it is recommended that a new employee goes for the salaried pay since the weekly earnings are greater in this option. The answer is C<span>.</span>

7 0

3 years ago

Read 2 more answers

A boat traveled 128 kilometers in

AlekseyPX

Answer:

The Distance cover by boat in 2 hours and 15 minutes is 72 km

Step-by-step explanation:

Given as :

The Distance cover by boat = 128 kilometer

The time taken is 4 hours

As , Distance = Speed ×Time

So , Speed = $\frac{Diastance}{Time}$

Or, Speed = $\frac{128 km}{4 hours}$

∴ Speed = 32 km per hour

Now, again The boat travel 2 hours and 15 minutes further with speed 32 kmph

So, Time2 = 2 + $\frac{15}{60}$

Or, Time2 = 2 + $\frac{1}{4}$

I.e Time2 = $\frac{9}{4}$ hours

Again , Distance = Speed ×Time

So , Distance = 32kmph × $\frac{9}{4}$ hours

I.e Distance = $(\frac{32\times 9}{4})$ = 72 kilometer

Hence The Distance cover by boat in 2 hours and 15 minutes is 72 km Answer

5 0

3 years ago

Anyone know how to do this??

Ghella [55]

Answer:

csc²(x)

Step-by-step explanation:

csc(x) = 1/sin(x)

sin²(x) + cos²(x) = 1

=> cos²(x) = 1 - sin²(x)

cos(2x) = cos²(x) - sin²(x) = (1 - sin²(x)) - sin²(x) =

= 1 - 2×sin²(x)

=> 2×sin²(x) = 1 - cos(2x)

sin²(x) = 1/2×(1-cos(2x))

=> 1 - cos(2x) = 2×(1/2×(1-cos(2x)) = 2×sin²(x)

=> 2 / (1-cos(2x)) = 2 / (2×sin²(x)) = 1/sin²(x) =

= 1/sin(x) × 1/sin(x) = csc(x)×csc(x) = csc²(x)

6 0

3 years ago

The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, al

Valentin [98]

Answer:

a) $p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 0$

Alternative hypothesis: $\mu_y -\mu_x$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679$

The next step is calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Now we can calculate the p value, since we have a left tailed test the p value is given by:

$p_v =P(t_{(9)}$

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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

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

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

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

$-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469$

$-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069$

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0

3 years ago