All categories

3 years ago

These are the first six terms of a sequence starting with a1 = 80:

Mathematics

1 answer:

Nikitich [7]3 years ago

6 0

Answer:

$a _{n} = a( {r}^{n - 1} ) \\ a _{n} = 80(2 {}^{n - 1} ) \\ a _{n} = \frac{80. {2}^{n} }{ {2}^{ 1} } \\a _{n} = 40( {2}^{n} ) \\ a _{n} = ( {2}^{3} \times 5)( {2}^{n} ) \\ a _{n} = 5( {2}^{n + 3} )$

You might be interested in

URGENT HELP!!!!<br> Picture included

natka813 [3]

Answer:

Length (L) = 72 feet

Step-by-step explanation:

From the question given above, the following data were obtained:

Period (T) = 9.42 s

Pi (π) = 3.14

Length (L) =?

The length of the pendulum can be obtained as follow:

T = 2π √(L/32)

9.42 = (2 × 3.14) √(L/32)

9.42 = 6.28 √(L/32)

Divide both side by 6.28

√(L/32) = 9.42 / 6.28

Take the square of both side

L/32 = (9.42 / 6.28)²

Cross multiply

L = 32 × (9.42 / 6.28)²

L = 72 feet

Thus, the Lenght is 72 feet

5 0

3 years ago

If a number is an element of the set of real

kvasek [131]

Answer:

Option (A)

Step-by-step explanation:

A set of real numbers is a combination of both rational and irrational numbers.

But the elements in the sets of rational and irrational numbers will be different.

In short, rational and irrational number sets are the two subsets of real numbers.

Hence, the number is an element of either the set of rational numbers or the set of irrational numbers.

Option (A) is the correct option.

3 0

3 years ago

There are a total of 91 students in a drama club and a yearbook club. The drama club has 19 more students than the yearbook club

abruzzese [7]

Step-by-step explanation:

91-19=72

72/2=36

36+19=55=Drama Club students

36 =Yearbook Club Students

8 0

4 years ago

A potential energy function is given by U = A x3 + B x2 − C x + D . For positive parameters A, B, C, D this potential has two eq

Ivenika [448]

Answer:

7.8655

Step-by-step explanation:

Given the functionl

$U=Ax^3+Bx^2-cx+D$

Where,

$A=1.45J/m^3\\B=2.85J/m^2\\c= 1.7J/m\\D=0.6J$

We have, replacing,

$U=1.45x^3+2.85x^2-1.7x+0.6$

We need to derivate and verify for stable equilibrum that,

$\frac{d^2 U}{dx^2}>0$

Then,

$U'(x) = 4.32x^2+5.7x-1.7$

Roots in,

$x_1=-1.57008\\x_2=0.250636$

We obtain U"(x), then we have

$\frac{d^2U}{dx}=8.64x+5.7$

For $x=-1.57, U"(x)=-7.86549$ Unestable

For $x=0.250636 U"(x)=7.8655>0$ Stable

7 0

3 years ago

A researcher is interested in studying crime rates in each state. To do so, he records the number of violent crimes that occur p

Lesechka [4]

Answer:

A. Data

Step-by-step explanation: <em>Data is a term used to describe facts, information or statistics that are collected together in order for it to be used as a reference or for analysis.</em>

An effective data collection is one of the most important aspects in research,experiments or statistics as it helps to guarantee a reliable and effective outcome.

Data collection should be done in such a way that it helps to solve the problem which is being studied or handled.

3 0

3 years ago