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Ivan
3 years ago
5

HELP PLZ

Mathematics
1 answer:
Lera25 [3.4K]3 years ago
3 0

Answer:

the answer is 28 for A the answer for B is -5 for A, 15 for B, and -6 for C

Step-by-step explanation:

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Show that cos(3x) = cos3(x) − 3 sin2(x)cos(x). (Hint: Use cos(2x) = cos2(x) − sin2(x) and the cosine sum
otez555 [7]

<u>Step-by-step explanation:</u>

To prove:

\cos 3x=\cos^3x-3\sin^2 x\cos x

Identities used:

\cos(A+B)=\cos A\cos B+\sin A\sin B      ......(1)

\sin 2A=2\sin A\cos A        ........(2)

\cos 2A=\cos^2A-\sin^2 A     .......(3)

Taking the LHS:

\Rightarrow \cos 3x=\cos (x+2x)

Using identity 1:

\Rightarrow \cos (x+2x)=\cos x\cos 2x-\sin x\sin 2x

Using identities 2 and 3:

\Rightarrow \cos x(\cos ^2x-\sin^2 x)-\sin x(2\sin x\cos x)\\\\\Rightarrow \cos^3x-\sin^2x\cos x-2\sin^2 x\cos x\\\\\Rightarrow \cos^3x-3\sin^2x\cos x

As, LHS = RHS

Hence proved

4 0
3 years ago
Daniel buys a video game for $48.50. He must pay 6% sales tax. How much tax must Daniel pay?
dolphi86 [110]
If you add 6% your answer would be $<span>51.41 hope it helps <3</span>
4 0
3 years ago
Read 2 more answers
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard devia
gtnhenbr [62]

Answer:

n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547

So the answer for this case would be n=22547 rounded up to the nearest integer

Step-by-step explanation:

Let's define some notation

\bar X represent the sample mean

\mu population mean (variable of interest)

\sigma=58.2 represent the population standard deviation

n represent the sample size  

ME =1 represent the margin of error desire

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be \alpha=0.01 and the critical value z_{\alpha/2}=2.58, replacing into formula (b) we got:

n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547

So the answer for this case would be n=22547 rounded up to the nearest integer

3 0
3 years ago
A closed box with a square base is to have a volume of 85. 75 cm^3. the material for the top and bottom of the box costs ​$3.00
tiny-mole [99]

We can create two equations here:

(1) Volume = area of square * height of box

85.75 = s^2 h

(2) Cost = 3 * area of square + 1.5 * area of side box

C = 3 s^2 + 1.5 s h

 

From (1), we get:

h = 85.75 / s^2

 

Combining this with (2):

C = 3 s^2 + 1.5 s (85.75 / s^2)

C = 3 s^2 + 128.625 s-

 

Taking the 1st derivative and equating dC/ds = 0:

dC/ds = 6s – 128.625 / s^2 = 0

Multiply all by s^2:

6s^3 – 128.625 = 0

6s^3 = 128.625

s = 2.78 cm

 

So h is:

h = 85.75 / s^2 = 85.75 / (2.78)^2

h = 11.10 cm

 

So the dimensions are 2.78 cm x 2.78 cm x 11.10 cm

 

The total cost now is:

C = 3 (2.78)^2 + 1.5 (2.78) (11.10)

C = $69.47

8 0
3 years ago
For each quadrilateral work out<br> The sizes of angles a b c and d <br> The value of a + b + c + d
Vika [28.1K]

Answer:

A) (i) a = 95° (180 - 85), b = 85° (180 - 95), c = 85° (180 - 95), d = 95° (180 - 85)

A) (ii) a = 103° (180 - 77), b = 77° (180 - 103), c = 103° (180 - 77), d = 77° (180 - 103)

B) (i) 95 + 85 + 85 + 95 = 360°

B (ii) 103 + 77 + 103 + 77 = 360°

Tip: Angles on a straight line add to 180°

Hope this helps!

7 0
2 years ago
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