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3 years ago

Find the common ratio of the sequence 90, 60, 40, 80/3 What is the common ratio?

Mathematics

1 answer:

Trava [24]3 years ago

6 0

Answer:

2/3

Step-by-step explanation:

<em>Common ratio = next term/previous term</em>

<u>Sequence:</u>

90, 60, 40, 80/3

<u>Common ratio:</u>

60/90 = 2/3

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20 POINTS! PLEASE HELP

aleksandrvk [35]

The standard form of the equation of the parabola with a focus at (- 3, 2) and directrix at y = 4 is - 4 · (y - 3) = (x + 3)².

<h3>How to determine the standard form of the equation of the parabola</h3>

In accordance with the information presented in the statement, we find a parabola whose axis of symmetry is parallel to the y-axis. The location of the vertex is the midpoint of the segment between the focus and a point of the directrix.

V(x, y) = 0.5 · (- 3, 4) + 0.5 · (- 3, 2)

V(x, y) = (- 3, 3)

The distance between the focus with respect to the vertex (p) is:

D(x, y) = F(x, y) - V(x, y)

D(x, y) = (- 3, 2) - (- 3, 3)

D(x, y) = (0, - 1)

Which a distance equal to - 1.

The standard form of the equation of the parabola is based on this model:

4 · p · (y - k) = (x - h)² (1)

Where (h, k) are the coordinates of the vertex.

If we know that (h, k) = (- 3, 3) and p = - 1, then the standard form of the equation of the parabola is:

- 4 · (y - 3) = (x + 3)²

The standard form of the equation of the parabola with a focus at (- 3, 2) and directrix at y = 4 is - 4 · (y - 3) = (x + 3)².

<h3>Remark</h3>

The statement has typing and orthographical mistakes. Correct form is presented below:

<em>What is the standard form of the equation of the parabola with a focus at (x, y) = (- 3, 2) and directrix at y = 4.</em>

To learn more on parabolas: brainly.com/question/21685473

#SPJ1

7 0

2 years ago

A trigonometry student stands 25 meters from a building and measures the angle of elevation to the top of the building as 30â°.

kozerog [31]

Using the slope concept, it is found that the angle measurement has to be within 1.2º of 30º.

<h3>What is a slope?</h3>

The slope is given by the <u>vertical change divided by the horizontal change</u>, and it's also the tangent of the angle of depression.

In this problem, considering the horizontal distance and the actual angle, the following equation is applied to find the actual height:

$\tan{30^\circ} = \frac{h}{25}$

$h = 25\tan{30^\circ}$

h = 14.43.

For an error of 5%, the bounds of h are as follows:

$h_{min} = 0.95 \times 14.43 = 13.71$

$h_{max} = 1.05 \times 14.43 = 15.15$

Hence, the angles will be given by:

$\tan^{\alpha} = \frac{13.71}{25}$

$\alpha = \tan^{-1}{\left(\frac{13.71}{25}\right)}$

$\alpha = 28.8$

$\tan^{\alpha} = \frac{15.15}{25}$

$\alpha = \tan^{-1}{\left(\frac{15.15}{25}\right)}$

$\alpha = 31.2$

Hence the angle measurement has to be within 1.2º of 30º.

More can be learned about the slope concept at brainly.com/question/18090623

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2 years ago

Which of the following is an si base unit for measuring length<br> inch<br> gram<br> meter<br> mole

erik [133]

I believe the correct answer from the choices listed above is the third option. It would be meter that is a si base unit for measuring length. <span>The basic unit of length in the metric system; it was originally planned so that the circumference of the Earth would be measured at about forty million </span>meters<span>.</span>

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3 years ago

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The value of my tens digit is 50 and the value of my ones digit is 4

Elina [12.6K]

The answer is to this question is 54

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4 years ago

The main goal of a personal budget is to

bezimeni [28]

Answer:

have income be greater than expenses