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Misha Larkins [42]
2 years ago
12

Formula for the geometric sequence 1/2, 1, 2, 4

Mathematics
1 answer:
zmey [24]2 years ago
5 0

Answer:

a_{n} = \frac{1}{2} (2)^{n-1}

Step-by-step explanation:

the nth term of a geometric sequence is

a_{n} = a₁ (r)^{n-1}

where a₁ is the first term and r the common ratio

here a₁ = \frac{1}{2} and r = \frac{a_{2} }{a_{1} } = \frac{1}{\frac{1}{2} } = 2 , then

a_{n} = \frac{1}{2} (2)^{n-1}

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A 30-foot ladder was put up against a building. The ladder makes a 64° angle with the ground. How high up
miv72 [106K]

Answer:

height = 26.96 feet

Step-by-step explanation:

sin 64° = height/30

0.8988 = height/30

height = 26.96 feet

7 0
2 years ago
Lines that appear to be tangent are tangent. Find the value of each variable.
galina1969 [7]

Tangent secant theorem which in this case says

6² = x (x + x) = 2x²

36 =  2x²

18 = x²

x = 3√2

Answer: x = 3√2

4 0
3 years ago
Michael had $64 on his Paycheck monday morning. He earned +2 for completing his brainbreakfast but lost $1 for talking. What is
andrezito [222]

Answer:

$65

Step-by-step explanation:

64+2=66

66-1=65

6 0
3 years ago
Read 2 more answers
The height of a triangle is 4 sqrt 3 . What is the perimeter of the equatorial triangle?
Karo-lina-s [1.5K]

The perimeter of the equatorial triangle is 24 units

<h3><u>Solution:</u></h3>

Given that,

An equilateral triangle has an height equal to 4 \sqrt{3}

The triangle is shown below

From Triangle ABC in the shown figure AD =4 \sqrt{3}

Let the sides of the equilateral triangle be ‘a’

AB = BC = a

Since, it is an equilateral triangle we get,

BD = DC = a ÷ 2

Now, using Pythagoras Theorem in Triangle ABD,

The Pythagorean theorem is this: In a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

\mathrm{AB}^{2}=\mathrm{BD}^{2}+\mathrm{AD}^{2}

\begin{array}{l}{a^{2}=\left(\frac{a}{2}\right)^{2}+(4 \sqrt{3})^{2}} \\\\ {a^{2}-\left(\frac{a}{2}\right)^{2}=(4 \sqrt{3})^{2}}\end{array}

\frac{4 a^{2}-a^{2}}{4}=16 \times 3

\begin{array}{l}{\frac{3 a^{2}}{4}=16 \times 3} \\\\ {3 a^{2}=192} \\\\ {a^{2}=192 \div 3=64}\end{array}

a = 8

Hence, the three sides of the triangle are 8 units each

In equilateral traingle, length of all three sides of triangle are equal

So, Perimeter = 3 \times (Length of each side of triangle)

Perimeter = 3 \times 8 = 24

Thus the perimeter of the equatorial triangle is 24 units

7 0
3 years ago
The sale price of ground beef at a local grocery store is $1.49 for the first pound and $1.09 for each additional pound. Which f
cricket20 [7]

Answer:

y=1.09x+0.4

Step-by-step explanation:

Let's assume that the price of beef stays the same for every pound of beef (the first pound is also $1.09)

Then, the equation would be, it y was the cost, and x was pounds:

y=1.09x

But, the price of beef is not the same for the first pound.

The first pound costs an extra 1.49-1.09=0.4 dollars a pound, so we will add that to the equation.

y=1.09x+0.4

6 0
3 years ago
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