All categories

3 years ago

Someone help me with this

Mathematics

1 answer:

Jet001 [13]3 years ago

7 0

2a. 14,9; 2b. 15,4; 2c. 30,8; 3. 32

For 2a., you have to set it up like this: csc 48° = 20⁄x [OR sin 48° = ˣ⁄20]. Then you would have to isolate the variable by getting rid of the denominator. The cosecant function has an extra step because you will get xcsc 48° = 20. As stated, isolate the variable; this time, divide by csc 48°. This is what 20 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

For 2b., you have to set it up like this: sec 39° = ˣ⁄12 [OR cos 39° = 12⁄x. Then you would have to isolate the variable by getting rid of the denominator. The cosine function has an extra step because you will get xcos 39° = 12. As stated, isolate the variable; this time, divide by cos 39°. This is what 12 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

For 2c., you have to set it up like this: cot 64° = 15⁄x [OR tan 64° = ˣ⁄15]. Then you would have to isolate the variable by getting rid of the denominator. The cotangent function has an extra step because you will get xcot 64° = 15. As stated, isolate the variable; this time, divide by cot 64°. This is what 15 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

Now, for 3., it is unique, but similar concept. In this exercise, we are solving for an angle measure, so we have to use inverse trigonometric ratios. So, we set it up like this: cot⁻¹ 1⅗ = m<x [OR tan⁻¹ ⅝ = m<x]. We simply input this into our calculator and we get 32,00538321°. When rounded to the nearest degree, we get 32°.

WARNING: If you use a graphing calculator, you have to input it uniquely because most graphing calculators do not have the inverse trigonometric ratios programmed in their systems. This is how you would write this: tan⁻¹ 1⅗⁻¹. You set 1⅗ to the negative first power, ALONG WITH the inverse tangent function, because without it, your answer will be thrown off. Since Cotangent and Tangent are multiplicative inverses of each other, that is the reason why the negative first power is applied ALONG WITH the inverse tangent function.

**NOTE: 1⅗ = 8⁄5

Take into consideration:

sin θ = O\H

cos θ = A\H

tan θ = O\A

sec θ = H\A

csc θ = H\O

cot θ = A\O

I hope this helps you out alot, but if you are still in need of assistance, do not hesitate to let me know and subscribe to my channel [username: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

You might be interested in

Installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. If the

VikaD [51]

Answer:

(a). $1465.42

(b). $214.58

Step-by-step explanation:

We have been given that installment Buying TV Town sells a big screen smart HDTV for $600 down and monthly payments of $30 for the next 3 years. The interest rate is 1.25% per month on the unpaid balance.

(a) To find the cost of the TV, we will use monthly payment formula.

$R=\frac{Pi}{1-(1+i)^{-n}}$ , where,

R = Periodic payment,

P = Loan amount,

i = Monthly interest rate in decimal form,

n = Number of total payments.

$n=3\times 12=36$

$1.25\%=\frac{1.25}{100}=0.0125$

$30=\frac{P*0.0125}{1-(1+0.0125)^{-36}}$

$30=\frac{0.0125P}{1-(1.0125)^{-36}}$

$30=\frac{0.0125P}{1-0.6394091578134724264}$

$30=\frac{0.0125P}{0.3605908421865275736}$

$10.817725265595827208=0.0125P$

$0.0125P=10.817725265595827208$

$P=\frac{10.817725265595827208}{0.0125}$

$P=865.41802124766617664$

$P\approx 865.42$

We know that total cost of TV would be equal to down payment plus amount of loan that is:

$865.42+600=1465.42$

Therefore, the total cost of the TV would be $1465.42.

(b). First of all, we need to find total amount paid in 3 years by multiplying amount of each monthly payment by 36 (3 years equal to 36 months).

$\$30\times 36=\$1080$

To find the total amount of interest paid, we will subtract amount of loan from total payment.

$\$1080-\$865.42=\$214.58$

Therefore, the total amount paid in interest would be $214.58.

8 0

4 years ago

Plz help me out !!!!!!

pshichka [43]

Answer:

There are 1,679,616 ways to answer the test

Step-by-step explanation:

Here, we want to get the number of ways to answer the test

From the question, we have that there are 8 questions, with each having 6 possible answers

Hence, the total number of answers to pick from is 8 * 6 = 48

We are to pick 6 out of this total 48, with 1 option per question

So in the first, we are picking 1 out of 6

The number of ways here is;

6 C 1 = 6 ways

The next, we have 6 ways also , up to the 8th question

So, the total number of ways will be;

6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 6^8 =

1,679,616

3 0

3 years ago

What is the main idea of passage?

AlladinOne [14]

What passage? I don’t see

5 0

3 years ago

Read 2 more answers

0=4X-7Y what is the value of x and y but not 0

Irina18 [472]

Solving for X we get:
$X=\frac{7Y}{4}$
Solving for Y, we get:
$Y=-\frac{4X}{7}$

8 0

3 years ago

According to the Public Health Service (PHS), the optimal concentration of fluoride in public water supplies is 0.70 mg/L. Suppo

ASHA 777 [7]

Answer:

Alicia conclude that the mean fluoride level is less than or equal to the PHS recommendation.

Step-by-step explanation:

We are given that the Public Health Service (PHS), the optimal concentration of fluoride in public water supplies is 0.70 mg/L.

Alicia tests the water from 60 randomly selected residences and finds that the mean fluoride concentration is 0.79 mg/L, with a standard deviation of 0.36 mg/L.

Let $\mu$ = population mean fluoride level

SO, Null Hypothesis, $H_0$ : $\mu \leq$ 0.70 mg/L {means that the mean fluoride level is less than or equal to the PHS recommendation}

Alternate Hypothesis, $H_a$ : $\mu$ > 0.70 mg/L {means that the mean fluoride level is significantly higher than the PHS recommendation}

The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{{\frac{s}{\sqrt{n} } } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean fluoride concentration = 0.79 mg/L

s = sample standard deviation = 0.36 mg/L

n = sample of residences = 60

So, test statistics = $\frac{0.79-0.70}{{\frac{0.36}{\sqrt{60} } } }$ ~ $t_5_9$

= 1.94

P-value of the test statistics is given to us as 0.03.

The decision rule based on p-value is given by;

If the P-value of test statistics is more than the level of significance, then we will not reject our null hypothesis as it will not fall in the rejection region.

If the P-value of test statistics is less than the level of significance, then we will reject our null hypothesis as it will fall in the rejection region.

Now, here the P-value is 0.03 which is clearly higher than the level of significance of 0.01, so we will not reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean fluoride level is less than or equal to the PHS recommendation.

5 0

3 years ago