All categories

3 years ago

The surface area of the cone is 43.75π cm2. What is the slant height of the cone? with a radius o 5 cm

1 answer:

3 0

The surface area of the cone is calculated through the equation,
A = πr² + πrl
where r is the radius and l is the slant height. Substituting the known values to the equation,
43.75π = π(5 cm)² + π(5 cm)(l)
l is 3.75 cm. Thus, the slant height of the cone is 3.75 cm.

You might be interested in

What is the value of x in the equation 2x+3y=36 when y is 6

Andrew [12]

2x + 3*6 = 36

2x = 36-18

2x = 18

x = 9

4 0

2 years ago

Read 2 more answers

A soccer team won only 10 of their first 30 games. How many of their remaining 20 games will they have to win to have a .500 rec

jeka94

Answer: 5 games

Step-by-step explanation: A .500 record means that the soccer team won half of their games ( that's how I interpret it). Since they are going to play 30 games, they need to win half of 30 or 15 games to have that record. 15-10 = 5. So, they need to win 5 more games to have a .500 record.

8 0

1 year ago

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

Angelina_Jolie [31]

We call:

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

 $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
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:

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

Then:

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

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:

 $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$

Therefore, we need to find:
 $a_{k} = a_{51}$

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

(-0.75+6)-1(2.5x+-1.9

fenix001 [56]

Simplifying

(0.75x + 6) + -1(2.5x + -1.9) = 0

Reorder the terms:

(6 + 0.75x) + -1(2.5x + -1.9) = 0

Remove parenthesis around (6 + 0.75x)

6 + 0.75x + -1(2.5x + -1.9) = 0

Reorder the terms:

6 + 0.75x + -1(-1.9 + 2.5x) = 0

6 + 0.75x + (-1.9 * -1 + 2.5x * -1) = 0

6 + 0.75x + (1.9 + -2.5x) = 0

Reorder the terms:

6 + 1.9 + 0.75x + -2.5x = 0

Combine like terms: 6 + 1.9 = 7.9

7.9 + 0.75x + -2.5x = 0

Combine like terms: 0.75x + -2.5x = -1.75x

7.9 + -1.75x = 0

Solving

7.9 + -1.75x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.9' to each side of the equation.

7.9 + -7.9 + -1.75x = 0 + -7.9

Combine like terms: 7.9 + -7.9 = 0.0

0.0 + -1.75x = 0 + -7.9

-1.75x = 0 + -7.9

Combine like terms: 0 + -7.9 = -7.9

-1.75x = -7.9

Divide each side by '-1.75'.

x = 4.514285714

Simplifying

x = 4.514285714

5 0

3 years ago

Read 2 more answers

What is the greatest possible decimal that can be rounded to 8.03?

Allushta [10]

It would have to be rounded down
8.0349999999999........ is the greatest one
because the 4 rounds down, and every 9 after that doesn't affect the rounding, but it does add a small amount to the number

the number is less than 8.035

8.0349999999999........

6 0

3 years ago