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3 years ago

PLEASE HELP ME PLEASE (10 mins)

Mathematics

1 answer:

NeX [460]3 years ago

5 0

Answer:

Step-by-step explanation:

1) When the sector is cut out, the remaining sector would be used to form the cone. The angle subtended by this sector would be

360 - 60 = 300°

The length of the arc of this sector would represent the circumference of the circular base of the conical hat.

Radius of the circle = diameter/2 = 20/2 = 10 inches

Formula for length of arc = #/360 × 2πr

Where

# is the subtended angle

Therefore,

Length of arc = 300/360 × 2 × 3.14 × 10 = 52.3 inches

circumference of the circular base of the conical hat = 52.3 inches

2) the surface area = πrl

Where

l represents the slant height

the radius of the circle would become l.

To determine the radius of the cone, we would apply, we would make use of the circumference of the circular base.

Circumference = 2πr

52.3 = 2 × 3.14 × r

r = 52.3/6.28 = 8.33 inches

Surface area = 3.14 × 8.33 × 10 = 262 inches²

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Read 2 more answers

Find two consecutive even integers whose sum is 14

bagirrra123 [75]

Let x = small number
Let y = large number
Because they are consecutive even numbers,they must have a difference of 2:
y-x=2
y=2+x

Eqn 1: x+(2+x)=14

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3 years ago

the sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger

Reil [10]

<h2>Answer:</h2>

$x\geq 3 \ and \ x+1 \geq 4$

<h2>Step-by-step explanation:</h2>

The question in this problem is:

<em>The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger. What are the numbers?</em>

<em />

First of all, let's name the first variable $x$ which is the smaller number. Accordingly, the lager number will be $x+1$ given that those numbers are consecutive. On the other hand<em> at most </em>conveys the idea of an inequality, which is:

$\leq \\ which \ means \ less \ than$

So:

1. The sum of 2 consecutive integers can be written as:

$v+(v+1)$

2. Nine times the smaller and 5 times the larger can be written as:

$9v-5(v+1)$

Finally, the whole statement:

The sum of 2 consecutive integers is at most the difference between nine times the smaller and 5 times the larger:

$x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\$

$x+(x+1) \leq 9x-5(x+1) \\ \\ x+x+1\leq 9x-5x-5 \\ \\ 2x+1 \leq 4x-5 \\ \\ 6 \leq 2x \\ \\ \frac{6}{2} \leq \frac{2x}{2} \\ \\ 3 \leq x \\ \\ x\geq 3 \\ \\ and \\ \\ x+1 \geq 4$

The two numbers are:

$x\geq 3 \ and \ x+1 \geq 4$

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3 years ago