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3 years ago

9

Can someone help me with my last question.

1 answer:

jek_recluse [69]3 years ago

8 0

Given:

Volume of the cone = 23,942.5 cubic cm

Radius of the cone = 25 cm

The value of π ≈ 3.14

To find:

The height of the cone

Solution:

Volume of the cone formula:

$$V=\frac{1}{3} \pi r^2h$

Substitute the given values.

$$\frac{1}{3} \times 3.14 \times 25^2\times h=23942.5$

$$\frac{1}{3} \times 3.14 \times 625\times h=23942.5$

$$654.17\times h=23942.5$

Divide by 654.17 on both sides.

$$\frac{654.17\times h}{654.17} =\frac{23942.5}{654.17}$

$h=36.6$ cm

The height of the cone is 36.6 cm.

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5 0

3 years ago

Prove that the product of any two consecutive natural numbers is even.

Vitek1552 [10]

Answer with Step-by-step explanation:

Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'

Thus the product of the 2 numbers is given by

$Product=n(n+1)\\\\$

We know that the sum of 'n' consecutive natural numbers starting from 1 is

$S_n=\frac{n(n+1)}{2}\\\\\therefore n(n+1)=2\times S_n............(i)$

Thus from equation 'i' we can write

$Product=2\times S_n$

As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.

6 0

3 years ago

2x + 4 = 3(x – 2) + 1<br> simplify

Rudik [331]

2x + 4 = 3(x - 2) + 1
2x + 4 = 3x - 6 + 1
2x + 4 = 3x - 5
9 = x
So x = 9

7 0

3 years ago

Express these numbers in standard form: 1) 35.18 * 1000000; 2) 0.00000235 / 1000000

Julli [10]

Equivalent of fractions using decimals

5 0

3 years ago

write a linear equation that intersects y=x^2 at two points. Then write a second linear equation that intersects y=x^2 at just o

Liula [17]

We know that $y = x^2$ is a parabola, concave up, with vertex in the origin $(0,0)$

So, we may use three horizontal lines for our purpose: any horizontal line above the x axis will intersect the parabola twice. The x axis itself intersects the parabola once on the vertex, while any horizontal line below the x axis won't intercept the parabola.

Here's the examples:

The horizontal line $y = 4$ intercepts the parabola twice: the system $y = x^2,\ y = 4$ is solved by $x^2=4 \implies x = \pm 2$
The horizontal line $y=0$ intercepts the parabola only once: the system is $y=x^2,\ y=0$ which yields $x^2=0\implies x=0$ which is a repeated solution
The horizontal line $y=-5$ intercepts the parabola only once: the system is $y=x^2,\ y=-5$ which yields $x^2=-5$ which is impossible, because a squared number can't be negative.

5 0

3 years ago