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2 years ago

7

Curved surface of a cone of slant height 20 cm and base radius 14 cm is ____. * 1 point 280 sq.cm 2080 sq.cm 1496 sq.cm 880 sq.c

m

1 answer:

valkas [14]2 years ago

7 0

Answer:

880 cm²

Step-by-step explanation:

Given that :

Curved surface area of a cone : πrl

r = base Radius = 14 cm

l = slant height = 20 cm

Hence,

Curved surface area = π * 14 * 20

Curvwd surface are = π * 14 * 20

Curved surface area = 879.64594 cm²

Curved surface area = 880 cm²

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3 years ago

Arianna cycles for 3 hours at a speed of 40 mph. what distance did she travel

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A steel cargo container is shaped like a cube measuring 5.2 ft on each edge how much steel is needed to make this container? Sho

bearhunter [10]

Answer:

162.24 ft

Step-by-step explanation:

So you first find the area of one side.

5.2 x 5.2 = 27.4

Then you times it by 6, because a cube has 6 sides.

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3 years ago

What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of <span>the first 51 consecutive odd positive integers, so:

</span> $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
<span>and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

</span> $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$
<span>
Then:

</span> $a_{n} = a_{1} + (n-1)d$
<span>
So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

</span> $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$
<span>
Therefore, we need to find:
</span> $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

4 0

3 years ago

Find the 75th term of the arithmetic sequence -17, -13, -9....

Sphinxa [80]

Answer:

The 75th term of the arithmetic sequence -17, -13, -9.... is:

$a_{75}=279$

Step-by-step explanation:

Given the sequence

$-17, -13, -9....$

An arithmetic sequence has a constant difference 'd' and is defined by

$a_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$-13-\left(-17\right)=4,\:\quad \:-9-\left(-13\right)=4$

The difference between all the adjacent terms is the same and equal to

$d=4$

The first element of the sequence is:

$a_1=-17$

now substitute $d=4$ and $a_1=-17$ in the nth term of the sequence

$a_n=a_1+\left(n-1\right)d$

$a_n=4\left(n-1\right)-17$

$a_n=4n-21$

Now, substitute n = 75 in the $a_n=4n-21$ sequence to determine the 75th sequence

$a_n=4n-21$

$a_{75}=4\left(75\right)-21$

$a_{75}=300-21$

$a_{75}=279$

Therefore, the 75th term of the arithmetic sequence -17, -13, -9.... is:

$a_{75}=279$

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3 years ago