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Aliun [14]
2 years ago
12

What will be the first negative term in the sequence 87,84,81​

Mathematics
1 answer:
o-na [289]2 years ago
8 0

Answer:

a₃₁

Step-by-step explanation:

The terms have a common difference between consecutive terms, that is

d = 84 - 87 = 81 - 84 = - 3

This indicates the sequence is arithmetic with nth term

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 87 and d = - 3 , then

a_{n} = 87 - 3(n - 1) = 87 - 3n + 3 = 90 - 3n

To find when a_{n} < 0 , solve

90 - 3n < 0 ( subtract 90 from both sides )

- 3n < - 90

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity, then

n > 30

Thus the 31st term will be the first negative term

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the length of the rectangle is twice its width. write and solve a system of linear equations to find the length L and width W of
xz_007 [3.2K]

Answer:

2 ( m + 2 m)  = 36 is the required linear equation

Length of the rectangle is 12 ft and width =  6 ft

Step-by-step explanation:

Let the width of the rectangle = m ft.

So, the length of the rectangle = 2m  ft.

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Now, PERIMETER OF THE RECTANGLE = 2(LENGTH + WIDTH)

⇒2 ( m + 2m)  = 36

or, 2 x 3m  = 36

⇒ 6m  = 36  , or m  = 36/6

⇒ m  =6 ft

So, the Width of the rectangle;  =  m = 6 ft

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A certain triangle has a 30° angle and a 60° angle. Which must be a true
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Find the equation of the ellipse with the following properties:
steposvetlana [31]

Answer: The equation of an ellipse:

(

x

−

h

)

2

a

2

+

(

y

−

k

)

2

b

2

=

1

;

a

>

b

Has vertices at

(

h

±

a

,

k

)

Has foci at

(

h

±

√

a

2

−

b

2

,

k

)

Use the vertices to write 3 equations:

k

=

4

[1]

h

−

a

=

−

6

[2]

h

+

a

=

10

[3]

Use equations [2] and [3] to solve for h and a:

2

h

=

4

h

=

2

a

=

8

Use the focus to write another equation:

8

=

h

+

√

a

2

−

b

2

Substitute values for h and a:

8

=

2

+

√

8

2

−

b

2

6

=

√

64

−

b

2

36

=

64

−

b

2

b

2

=

64

−

36

b

2

=

28

b

=

√

28

Substitute the values into the standard form:

(

x

−

2

)

2

8

2

+

(

y

−

4

)

2

(

√

28

)

2

=

1

5 0
3 years ago
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