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3 years ago

A circle has a radius of 5.4 m.

Mathematics

2 answers:

PolarNik [594]3 years ago

8 0

Yes it is good job !

Sergio039 [100]3 years ago

7 0

$\bf \textit{arc's length}\\\\
s=\cfrac{\pi \theta r}{180}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=5.4\\
\theta =60
\end{cases}\implies s=\cfrac{\pi (60)(5.4)}{180}\implies s=1.8\pi$

yes, it is correct.

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Answer:

$A(-1,-8)$

Step-by-step explanation:

Given

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Translation: 1 left and 3 up

Rotation: 180 degrees

Required

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Taking the exercise one after the other

<em>Represent the function as: (x,y)</em>

Such that

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1 unit left translation means the function becomes (x - 1, y)

2 unit up translation means the function becomes (x - 1, y + 2)

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At this stage, the coordinate becomes

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So;

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$A(1,8) -> A(-1,-8)$

Hence, the new image of A is

$A(-1,-8)$

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3 years ago

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3 years ago

Evaluate the summation of 3 n plus 2, from n equals 1 to 14. 39 49 340 343.

lord [1]

The summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

<h3>How to find the sum of consecutive integers?</h3>

$1 + 2 + 3 + ... + n = \dfrac{n(n+1)}{2}$

<h3>
What are the properties of summation?</h3>

$\sum_{i=r}^s (a \times f(i) + b) = a \times [\: \sum_{i=r}^s f(i)] + (s-r)b$

where a, b, r, and s are constants, f(i) is function of i, i ranging from r to s (integral assuming).

For the given case, the considered summation can be written symbolically as:

$\sum_{n=1}^{14} (3n + 2)$

It is evaluated as;

$\sum_{n=1}^{14} (3n + 2) = 3 \times [ \: \sum_{n=1}^{14} n ] + \sum_{n=1}^{14} 2\\\\\sum_{n=1}^{14} (3n + 2) = 3 \times \dfrac{(14)(14 + 1)}{2} + (2 + 2 + .. + 2(\text{14 times}))\\\\\sum_{n=1}^{14} (3n + 2) = 3 \times 105 + 28 = 343\\$

Thus, the summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

Learn more about summation here:

brainly.com/question/14322177

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