What are the next three terms of the geometric sequence 32, -16, 8, …?

1 answer:

4 0

To find the common ratio, divide the 2nd term by the first term
-16 / 32 = -0.5....this means u multiply each number by -0.5 to find the next number

8 * -0.5 = -4 <==
-4 * - 0.5 = 2 <==
2 * -0.5 = -1 <==

answer D

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Find the length of side AB Give answer to 3 significant figures

Rina8888 [55]

Answer:

AB = 8.857 cm

Step-by-step explanation:

Here, we are given a right angle $\triangle ABC$ in which we have the following things:

$\angle A = 90 ^\circ\\\angle C = 41 ^\circ\\\text{Side }BC = 13.5 cm$

Side BC is the hypotenuse here.

We have to find the side AB.

Trigonometric functions can be helpful to find the value of Side AB here.

Calculating $\angle B$ :

Sum of all the angles in $\triangle ABC$ is $180^\circ$ .

$\Rightarrow \angle A + \angle B + \angle C = 180^\circ\\\Rightarrow 90^\circ + \angle B + 41^\circ = 180^\circ\\\Rightarrow \angle B = 49^\circ$

We know that cosine of an angle is:

$cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\Rightarrow cos B = \dfrac{AB}{BC}\\\Rightarrow cos 49^\circ = \dfrac{AB}{13.5}\\\Rightarrow AB = 13.5 \times 0.656\\\Rightarrow AB = 8.857 cm$