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dlinn [17]
3 years ago
15

Which expression represents the second partial sum for

Mathematics
2 answers:
NeTakaya3 years ago
6 0

Answer:

S_{2} = 3\cdot \left(\frac{1}{2} \right)^{0} + 3\cdot \left(\frac{1}{2} \right)^{1}

Step-by-step explanation:

The first partial sum is:

S_{1} = 3\cdot \left(\frac{1}{2} \right)^{0}

The second partial sum is:

S_{2} = 3\cdot \left(\frac{1}{2} \right)^{0} + 3\cdot \left(\frac{1}{2} \right)^{1}

Which represents the option A.

NeTakaya3 years ago
4 0

Answer:

option A

Step-by-step explanation:

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3 years ago
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3 years ago
Find the longer leg of the triangle.
Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

  • The length of the hypotenuse (the side opposite to the right angle) is given.
  • The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let \text{Opposite} denotes the length of the side opposite to the 30^{\circ} acute angle, and \text{Adjacent} be the length of the side next to this 30^{\circ} acute angle.

\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}.

Similarly,

\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}.

The longer leg in this case is the one adjacent to the 30^{\circ} acute angle. The answer will be 3.

There's a shortcut to the answer. Notice that \sin{30^{\circ}} < \cos{30^{\circ}}. The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the 30^{\circ} angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship \sin{\theta} < \cos{\theta} holds for all acute angles? (That is, 0^{\circ} < \theta?) It turns out that:

  • \sin{\theta} < \cos{\theta} if 0^{\circ} < \theta;
  • \sin{\theta} > \cos{\theta} if 45^{\circ} < \theta;
  • \sin{\theta} = \cos{\theta} if \theta = 45^{\circ}.

4 0
3 years ago
Read 2 more answers
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