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Nikitich [7]
3 years ago
8

Write an explicit formula for An, the nth term of the sequence 7, 42, 252, ...

Mathematics
1 answer:
AlekseyPX3 years ago
3 0

Answer:

Step-by-step explanation:

This is a geometric progression.

Givens

a1 = 7

r = 6

Formula

a_n = a1 * r^(n - 1)

a_n = 7 (6)^(n - 1)

Sample

Try n = 3

a_3 = 7*(6)^(3-1)

a_3 = 7*(6)^2

a_3 = 7 * 36

.a_3 = 252      which is exactly what it should be.

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Show that the equation x^4/2021 − 2021x^2 − x − 3 = 0 has at least two real roots.
andreev551 [17]

The roots of an equation are simply the x-intercepts of the equation.

See below for the proof that \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0} has at least two real roots

The equation is given as: \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}

There are several ways to show that an equation has real roots, one of these ways is by using graphs.

See attachment for the graph of \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}

Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)

From the attached graph, we can see that \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0} crosses the x-axis at approximately <em>-2000 and 2000 </em>between the domain -2500 and 2500

This means that \mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0} has at least two real roots

Read more about roots of an equation at:

brainly.com/question/12912962

6 0
3 years ago
Item 16
alexdok [17]

Answer:

Step-by-step explanation:

Given that the dresser is in shape of a rectangular prism

Note that, a rectangular prism has a shape of a cuboid

So, area of the rectangular prism is same as area of a cuboid

A = (2LB + 2LH + 2BH)

Where

L is length

B is breadth

H is height

Then, given the dimension of the rectangular prism to be

2ft by 2ft by 6ft

Then, you can assume that,

Length L = 2ft

Breadth B = 2ft

Height H = 6ft.

NOTE: you can take you assumption anyhow, there is no standard, you will get the same answer.

Then,

A = (2LB + 2LH + 2BH)

A = (2×2×2 + 2×2×6 + 2×2×6)

A = (8 + 24 + 24)

A = 56 ft²

The total surface area of the dresser is 56ft²

8 0
3 years ago
Read 2 more answers
Which area of this sound wave represents a compression?
Karo-lina-s [1.5K]

Answer:

c

Step-by-step explanation:

idk but im think im sure

4 0
3 years ago
Read 2 more answers
is the square root of 36 real, irrational, rational, integer, whole, natural? can b more than 1 answer
Vaselesa [24]

√36 = plus or minus 6. These results are real, rational, integer, whole and natural, and yes, there can be more than one answer; that's because we're solving a quadratic equation. Note that both 6 and -6, when squared, yield 36.

6 0
3 years ago
Help pls I give a really good rating.
GalinKa [24]

Answer:

Range is 6 and mode is 2

Step-by-step explanation:

Range is the greatest number of the set (7) subtracted by the smallest number of the set(1).

Mode is the most repeated number of the set(2).

<em>Hope this was helpful:)</em>

7 0
3 years ago
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