Find the mean and range. 20 14 29 39 33 25 19 35

Mathematics

2 answers:

Maksim231197 [3]3 years ago

7 0

Mean: 26.75
Range: 25

egoroff_w [7]3 years ago

4 0

Count:8Sum:214Mean:26.75Median:27Mode:20, 14, 29, 39, 33, 25, 19, 35

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To solve the equation 5sin(2x)=3cosx, you should rewrite it as___.

galina1969 [7]

Answer:

Step-by-step explanation:

We want to solve the equation:

$5\sin(2x)=3\cos(x)$

To do so, we can rewrite the equation.

Recall the double-angle for sine:

$\sin(2x)=2\sin(x)\cos(x)$

By substitution:

$5\left(2\sin(x)\cos(x)\right)=3\cos(x)$

Distribute:

$10\sin(x)\cos(x)=3\cos(x)$

We can subtract 3cos(x) from both sides:

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

And factor:

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

Hence, our answer is A.

*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0, and we cannot divide by 0. Hence, we should subtract and then factor.

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3 years ago

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The 13th term of a geometric sequence is 16, 384 and the first term is 4. What is the common ratio?

AleksAgata [21]

Answer:

$\large \boxed{2}$

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.

$\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}$