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3 years ago

Given the following geometric sequence find the common ratio {0.45, 0.9, 1.8}

Mathematics

1 answer:

Fofino [41]3 years ago

3 0

Answer:

Given the following geometric sequence, find the common ratio. {0.45, 0.9, 1.8, ...} 0.45 0.9 2

Given the following geometric sequence {0.45, 0.9, 1.8, ...}, the common ratio is 2. The common ratio = 1.8/0.9 = 0.9/0.45 = 2

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elena55 [62]

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3 years ago

You deposit $5000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years?

Rasek [7]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}$

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5 0

3 years ago

The sector of a circle shown to the left has its center at point OO. The arc XYZXYZ has length 10.810.8, and the central angle X

BARSIC [14]

Answer: Length of the radius of the sector is 6 units.

Step-by-step explanation:

Since we have given that

Length of an arc = 10.8

Radian of a central angle = 1.8

First we convert radian into degrees,

$1\ radian= 57.295779513\textdegree\\\\1.8\ radians=1.8\times 57.3\textdegree\\\\1.8\ radians=103.14\textdegree$

As we know the formula for "Length of an arc":

$\text{Length of an arc}=\frac{\theta}{360\textdegree}\times 2\pi r\\\\10.8=\frac{103.14}{360\textdegree}\times 2\times \frac{22}{7}\times r\\\\10.8=1.8r\\\\r=\frac{10.8}{1.8}\\\\r=6$

Hence, Length of the radius of the sector is 6 units.

3 0

3 years ago

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 to the length of its hypotenuse? CHECK A

8_murik_8 [283]

Answer:

A. √3 : 2

D. 3√3 : 6

Step-by-step explanation:

In a triangle described as 30°-60°-90° triangle, the base angles are 90° and 60°

The side with angles 90° and 60° is the shortest leg and can be represented by 1 unit

The hypotenuse side is assigned a value twice the shorter leg value, which is 2 units

From Pythagorean relationship; the square of the hypotenuse side subtract the square of the shorter leg gives the square of the longer side

This is to say if;

The given the shorter leg = 1 unit

The hypotenuse is twice the shorter leg= 2 units

The longer leg is square-root of the difference between the square of the hypotenuse and that of the shorter leg

$=2^2-1^2\\\\=4-1=3\\\\\\b^2=3\\\\\\b=\sqrt{3}$

where the longer leg is represented by side b in the Pythagorean theorem, the hypotenuse by c and the shorter leg by a to make;

$a^2+b^2=c^2$

<u>Hence the summary is</u>

a=shorter leg= 1 unit

b=longer leg = √3 units

c=hypotenuse=2 units

The ratio of longer leg to its hypotenuse is

=√3:2⇒ answer option A

This is the same as 3√3:6 ⇒answer option D because you can divide both sides of the ratio expression by 3 and get option A

$=3\sqrt{3} :6\\\\\\\frac{3\sqrt{3} }{3} :\frac{6}{3} \\\\\\=\sqrt{3} :2$

Answers are :option A and D

4 0

3 years ago

HELP PLEASE!

Anna [14]

Answer: y= -7

Step-by-step explanation:

Zero slope are horizontal lines. Horizontal lines have the equation Y= a number. That number is the y value of the point.

5 0

3 years ago