Calculate the surface area of the box 6.5 inches by 6 inches by 2 inches

Solve using algebraic equation: 5sin2x=3cosx (No exponents)

DaniilM [7]

$5\sin2x=3\cos x\iff10\sin x\cos x=3\cos x$

by the double angle identity for sine. Move everything to one side and factor out the cosine term.

$10\sin x\cos x=3\cos x\iff10\sin x\cos x-3\cos x=\cos x(10\sin x-3)=0$

Now the zero product property tells us that there are two cases where this is true,

$\begin{cases}\cos x=0\\10\sin x-3=0\end{cases}$

In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of $\dfrac\pi2$ , so $x=\dfrac{(2n+1)\pi}2$ where $n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}$

which occurs twice in the interval $[0,2\pi)$ for $x=\arcsin\dfrac3{10}$ and $x=\pi-\arcsin\dfrac3{10}$ . More generally, if you think of $x$ as a point on the unit circle, this occurs whenever $x$ also completes a full revolution about the origin. This means for any integer $n$ , the general solution in this case would be $x=\arcsin\dfrac3{10}+2n\pi$ and $x=\pi-\arcsin\dfrac3{10}+2n\pi$ .

6 0

3 years ago

What would the variables for a and b be? 3/x + 5/x^2 = (ax+b)/x^2

allsm [11]

Answer:

a=3,b=5

Step-by-step explanation:

$\frac{3}{x} + \frac{5}{ {x}^{2} } \\ = \frac{3x}{ {x}^{2} } + \frac{5}{ {x}^{2} } \\ = \frac{3x + 5}{ {x}^{2} }$

so as you got it:

$\frac{(ax + b)}{ {x}^{2} } = \frac{3x + 5}{ {x}^{2} } \\ a = 3 \\ b = 5$

4 0

3 years ago

Of the 22 students in the class, 16 of them are boys.

Eddi Din [679]

22 students...16 boys

probability student will be a boy is 16/22 which reduces to 8/11 or 72.7%

6 0

3 years ago

SOMEONE PLEASE HELP ME WITH THIS QUESTION 2.5x - 3 = 2x - 2 I don't get what x is equal to

Luda [366]

Answer:

2

Step-by-step explanation:

Use the property of equality :)

5 0

3 years ago

30 random samples of high school students were asked if they played a sport for their high school. Each sample was 20 students.

Ludmilka [50]

Answer:

a. This option is correct

b. This will be true only if we take the mode as the best representative value

c. This is a correct choice

d. This is not a correct choice

Step-by-step explanation:

Statistics

We are given a dot plot representing 30 random sample proportions of high school students about their sports activities. Based on the data extracted from the plot, we can make some basic conclusions and, less accurately, some predictions.

From the data plot we can see that the following proportions were obtained, along with their absolute frequencies:

0.05 -> 3

0.10 -> 8

0.15 -> 7

0.20 -> 5

0.25 -> 4

0.30 -> 2

Let's select which of the following options are correct

a. A sample proportion of 0.20 means that 4 of 20 high school students responded that they play a sport.

The ratio between the sport playing students to the total of high school students is

$\displaystyle \frac{4}{20}=\frac{1}{5}=0.20$

Thus, this statement is correct.

b. The best prediction for the proportion of all high school students that play a sport is 0.10.

This will be true only if we take the mode as the best representative value for the whole dataset. Personally, I don't like to trust the mode as a good central tendency result, I'd prefer the mean instead.

c. The mean of the 30 sample proportions calculated to the nearest hundredth is 0.16

Computing the mean of the sample proportions

$\displaystyle \bar x=\frac{\sum x_i.f_i}{\sum f_i}$

$\displaystyle \bar x=\frac{0.00\cdot 1+0.05\cdot 3+0.10\cdot 8+0.15\cdot 7+0.20\cdot 5+0.25\cdot 4+0.30\cdot 2}{1+3+8+7+5+4+2}$

$\bar x\approx 0.16$

This is a correct choice

d. The shape of the sample distribution is fairly symmetrical

We can see the distribution if left-skewed because its peak value is not at the mean value. The mode and the mean are fairly different, thus this choice is not correct

5 0

3 years ago

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