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2 years ago

Find the first term and the explicit formula a12=1/32 and r=1/2

Mathematics

1 answer:

Alexxx [7]2 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

$a_{n}$ = a $(r)^{n-1}$

where a is the first term and r the common ratio

Given $a_{12}$ = $\frac{1}{32}$ and r = $\frac{1}{2}$ , then

a $(\frac{1}{2}) ^{11}$ = $\frac{1}{32}$ , that is

$\frac{a}{2^{11} }$ = $\frac{1}{32}$

$\frac{a}{2048}$ = $\frac{1}{32}$ ( cross- multiply )

32a = 2048 ( divide both sides by 32 )

a = 64 ← first term

Thus the explicit formula is

$a_{n}$ = 64 $(\frac{1}{2}) ^{n-1}$

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Martha's mom is making party bags for all of her guests. She has 24 green gumballs and 33 blue gumballs. If she splits them even

Dmitry_Shevchenko [17]

Answer:

3 bags

Step-by-step explanation:

Suppose there are

bags of candy.

If the

blue gumballs are to be split evenly with no leftovers among the

bags, then

must divide evenly into

If the

green gumballs are to be split evenly with no leftovers among the

bags, then

must divide evenly into

To get the largest number of bags (

must be the Greatest Common Divisor of

and

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7 0

2 years ago

More math help pls. :)

Step2247 [10]

By using trigonometric relations, we will see that x = 9.97°.

<h3>How to find the missing angle?</h3>

First, we need to find the bottom cathetus of the smaller triangle, we will use the relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus).

Where:

θ = 26°
Adjacent cathetus = k
Opposite cathetus = 55ft.

Replacing that we get:

Tan(26°) = 50ft/k

Solving this for k, we get:

k = 55ft/tan(26°) = 112.8 ft

Now, we can see that the longer triangle adds 200ft to this cathetus, so now we will have:

angle = x
opposite cathetus = 55ft
adjacent cathetus = 112.8ft + 200ft = 312.8ft.

Then we have:

Tan(x) = (55ft/312.8ft)

Using the inverse tangent function in both sides, we get:

x = Atan(55ft/312.8ft) = 9.97°

If you want to learn more about right triangles, you can read:

brainly.com/question/2217700

6 0

1 year ago

BRAINLIESTTT ASAP!! PLEASE HELP ME :)

Tju [1.3M]

Answer:

Choice C.

Step-by-step explanation:

A parallelogram is a quadrilateral with two pairs of opposite parallel sides.

There is a theorem that states that opposite sides of a parallelogram are congruent.

In this case, sides AB and CD are opposite sides.

Sides BC and AD are opposite sides.

Side CD is opposite side AB, so they are congruent.

Answer:

Choice C.

CD = AB; Opposite sides of parallelograms are congruent.

5 0

2 years ago

Which statement is true?

SVEN [57.7K]

Answer:

$y=log_{1} x$ is not a logarithmic function because the base is equal to 1.

Step-by-step explanation:

A logarithmic function is of the form: $y=log_{b}x$

For a logarithmic function to exist, we must fulfill certain conditions. The conditions are

i. The base, $b$ , is greater than 0. ${b>0)$

ii. The base, $b$ , is not equal to 1. $(b\ne 1)$

iii. $x$ must be greater than 0. $(x>0)$

Now, if we observe all the choices given, we conclude that the third choice is correct as the base there is 1. If base is equal to 1, then it violates the definition of logarithmic functions. So, the correct choice is:

$y=log_{1} x$ is not a logarithmic function because the base is equal to 1.

6 0

2 years ago

Read 2 more answers

What is a whole number

Vlada [557]

Answer:

Whole numbers are positive numbers (this includes 0) that do not have decimals or fractions to them.

Example:

1, 2, 3, 4, 5,etc are all whole numbers, because they are positive and do not have decimals or fractions

1.25 would not be a whole number, because although it is positive, it has a decimal.

8 0

2 years ago