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3 years ago

Find the nth term for the sequence 30 27 24 21

2 answers:

7 0

Find the multiplication by subtracting the second term from the first term
27 - 30 = -3, so the multiplication table is -3x.
Now find the deviation of the first term in this sequence from the first term of the original -3x table
30 - -3 = 33
So you're adding 33 to the terms to get the sequence given
Final equation is:
-3n + 33

patriot [66]3 years ago

5 0

Assuming that the 30 is term #1 ..... The 'n'th term of the series is. T(n) = 33 - 3n or 3 (11 - n).

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A sector of a circle makes a 127° angle at its centre. If the arc of the sector has length 36 mm, find

Veseljchak [2.6K]

Answer:

Approximately $68.5\; \rm mm$ .

Step-by-step explanation:

Convert the angle of this sector to radians:

$\begin{aligned}\theta &= 127^{\circ} \\ &= 127^{\circ} \times \frac{2\pi}{360^{\circ}} \\ &\approx 2.22\end{aligned}$ .

The formula $s = r\, \theta$ relates the arc length $s$ of a sector of angle $\theta$ (in radians) to the radius $r$ of this sector.

In this question, it is given that the arc length of this sector is $s = 36\; \rm mm$ . It was found that $\theta = 2.22$ radians. Rearrange the equation $s = r\, \theta$ to find the radius $r$ of this sector:

$\begin{aligned} r&= \frac{s}{\theta} \\ &\approx \frac{36\; \rm mm}{2.22} \\ &\approx 16.2\; \rm mm\end{aligned}$ .

The perimeter of this sector would be:

$\begin{aligned}& 2\, r + s \\ =\; & 2 \times 16.2\; {\rm mm} + 36\; {\rm mm} \\ =\; & 68.5\; \rm mm\end{aligned}$ .

8 0

3 years ago

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis. What is the volume of the figure?

Luden [163]

Given:

A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis.

To find:

The volume of the figure.

Solution:

Points A(0,0) and C(0,9) lies on the y-axis. Length of AC is 9 units.

Points A(0,0) and B(6,0) lies on the x-axis. Length of AB is 6 units.

If a triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis, then it will form a cone with radius 6 units and height 9 units.

Volume of a cone is

$V=\dfrac{1}{3}\pi r^2h$

where, r is radius of the base and h is vertical height of the cone.

Putting r=6 and h=9, we get

$V=\dfrac{1}{3}\pi (6)^2(9)$

$V=\pi (36)(3)$

$V=108\pi$

Therefore, the volume of the figure is $108\pi$ sq. units.

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3 years ago

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boyakko [2]

Answer: 1/7

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