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3 years ago

2,3,1,-2,-3, ....

Mathematics

2 answers:

My name is Ann [436]3 years ago

7 0

The sum of the fust 20 terms in the sequence is 5 because williamwu309 said so

Andreyy893 years ago

5 0

Well, the best way to solve this is maybe just to find a pattern, so 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, so we find out that it repeats and the sum is 0 every 6 terms! Now that we know this, We can just find out the last two digits, which are 2 and 3. So $2 + 3 =$ 5, which is our answer

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a regular rectangular pyramid has a base and lateral faces that are congruent equilateral triangles. it has a lateral surface ar

Margarita [4]

A pyramid is regular if its base is a regular polygon, that is a polygon with equal sides and angle measures.
(and the lateral edges of the pyramid are also equal to each other)

Thus a regular rectangular pyramid is a regular pyramid with a square base, of side length say x.

The lateral faces are equilateral triangles of side length x.

The lateral surface area is 72 cm^2, thus the area of one face is 72/4=36/2=18 cm^2.

now we need to find x. Consider the picture attached, showing one lateral face of the pyramid.

by the Pythagorean theorem:

$h= \sqrt{ x^{2} - (x/2)^{2}}= \sqrt{ x^{2}- x^{2}/4}= \sqrt{3x^2/4}= \frac{ \sqrt{3} }{2}x$

thus,

$Area_{triangle}= \frac{1}{2}\cdot base \cdot height\\\\18= \frac{1}{2}\cdot x \cdot \frac{ \sqrt{3} }{2}x\\\\ \frac{18 \cdot 4}{ \sqrt{3}}=x^2$

thus:

$x^2 =\frac{18 \cdot 4}{ \sqrt{3}}= \frac{18 \cdot 4 \cdot\ \sqrt{3} }{3}=24 \sqrt{3}$ (cm^2)

but $x^{2}$ is exactly the base area, since the base is a square of sidelength = x cm.

So, the total surface area = base area + lateral area = $24 \sqrt{3}+72$ cm^2

Answer: $24 \sqrt{3}+72$ cm^2

4 0

3 years ago

Find the circumferences of both circles

nika2105 [10]

Answer:

Both circles

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

These two scalene triangles are similar with a scale of 4:5. What is true about these figures?

disa [49]

Alright, lets get started.

Lets check each possible answer one by one.

We will start from option B.

BC is from small triangle and its corresponding side is DF, so its ratio will be $\frac{4}{5}$ not $\frac{5}{4}$ as given in option. Hence option B is incorrect.

For option C,

Angle a° and angle f° are not similar angles, if they were similar, then only their ratio will be 1 otherwise not 1. Hence option C is incorrect.

For option D,

Angle c° and angle f° are similar angles so, their ratio will be $\frac{c}{f} = 1$ . Hence option D is incorrect.

Now option A,

ED and AB are corresponding sides. ED is from bigger triangle and AB is from smaller triangle. Their ratio will be $\frac{ED}{AB} = \frac{5}{4}$ . Hence option A is correct answer.

Hope it will help :)

6 0

3 years ago

Read 2 more answers

When an integer is subtracted from 5 times the next consecutive integer, the difference is 17. Find the value of the greater int

Mars2501 [29]

Answer:

Step-by-step explanation:

5(x + 1) -x = 17 Distribute the 5

5x + 5 - x = 17 Combine like terms

4x + 5 = 17 Subtract 5 from both sides

4x = 12 Divide both sides by 4

x = 3

Three is the smaller integer and 4 is the greater integer.

5 0

1 year ago

Please help due today

alisha [4.7K]

77.) x= {-5, 6}
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83.) x= {-7, -3}
84.) x= {-√85 +9 /2, √85 -9 /2}

6 0

3 years ago