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3 years ago

8

Let V be the volume of the pyramid of height 11 whose base is a square of side length 6. Find a formula for the area A of the ho

rizontal cross section at a height y.

1 answer:

Rainbow [258]3 years ago

7 0

Answer:

Base area = 36

Volume of the pyramid = 132

Step-by-step explanation:

Volume of a pyramid = Base Area × Height/3

Base area = Length × Length (since base of the pyramid is a square)

Given the side length of the square = 6

Base area = 6×6

Base area = 36

Given height of pyramid =11

Volume of the pyramid = 36×11/3

Volume of the pyramid = 12×11

Volume of the pyramid = 132

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vekshin1

Answer:

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Step-by-step explanation:

From the graph, we see that when y = 2, x is either +1 or -1

Also,when y = 1, x = +2 or -2

Thus,we can say that;

y = (-x) + 3 or -(x - 3)

So, we can write this in absolute value form as; y = -|x| + 3

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3 years ago

Kyle Lowry earned $31.2 million in US dollars playing for the Toronto Raptors during the 2018–2019 season. How much was he earni

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3 years ago

What is the sum of the geometric series

Sergio039 [100]

Answer: 2343 / 256

Explanation

I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.

1) Adding the terms:

4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0

= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =

= 2343 / 256

2) Using the formula:

n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0

Here n - 1 = 4 => n = 5

r = 3/4

A = 3

Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =

= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =

= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256

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3 years ago

Write a real world scenario that matches the following equation. 15+3h=30 Then solve for the equation

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3 years ago

La potencia que se obtiene de elevar a un mismo exponente un numero racional y su opuesto es la misma verdadero o falso?

malfutka [58]

Answer:

Falso.

Step-by-step explanation:

Sea $d = \frac{a}{b}$ un número racional, donde $a, b \in \mathbb{R}$ y $b \neq 0$ , su opuesto es un número real $c = -\left(\frac{a}{b} \right)$ . En el caso de elevarse a un exponente dado, hay que comprobar cinco casos:

(a) <em>El exponente es cero.</em>

(b) <em>El exponente es un negativo impar.</em>

(c) <em>El exponente es un negativo par.</em>

(d) <em>El exponente es un positivo impar.</em>

(e) <em>El exponente es un positivo par.</em>

(a) El exponente es cero:

Toda potencia elevada a la cero es igual a uno. En consecuencia, $c = d = 1$ . La proposición es verdadera.

(b) El exponente es un negativo impar:

Considérese las siguientes expresiones:

$d' = d^{-n}$ y $c' = c^{-n}$

Al aplicar las definiciones anteriores y las operaciones del Álgebra de los números reales tenemos el siguiente desarrollo:

$d' = \left(\frac{a}{b} \right)^{-n}$ y $c' = \left[-\left(\frac{a}{b} \right)\right]^{-n}$

$d' = \left(\frac{a}{b} \right)^{(-1)\cdot n}$ y $c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{(-1)\cdot n}$

$d' = \left[\left(\frac{a}{b} \right)^{-1}\right]^{n}$ y $c' = \left[(-1)^{-1}\cdot \left(\frac{a}{b} \right)^{-1}\right]^{n}$

$d' = \left(\frac{b}{a} \right)^{n}$ y $c = (-1)^{n}\cdot \left(\frac{b}{a} \right)^{n}$

$d' = \left(\frac{b}{a} \right)^{n}$ y $c' = \left[(-1)\cdot \left(\frac{b}{a} \right)\right]^{n}$

$d' = \left(\frac{b}{a} \right)^{n}$ y $c' = \left[-\left(\frac{b}{a} \right)\right]^{n}$

Si $n$ es impar, entonces:

$d' = \left(\frac{b}{a} \right)^{n}$ y $c' = - \left(\frac{b}{a} \right)^{n}$

Puesto que $d' \neq c'$ , la proposición es falsa.

(c) El exponente es un negativo par.

Si $n$ es par, entonces:

$d' = \left(\frac{b}{a} \right)^{n}$ y $c' = \left(\frac{b}{a} \right)^{n}$

Puesto que $d' = c'$ , la proposición es verdadera.

(d) El exponente es un positivo impar.

Considérese las siguientes expresiones:

$d' = d^{n}$ y $c' = c^{n}$

$d' = \left(\frac{a}{b}\right)^{n}$ y $c' = \left[-\left(\frac{a}{b} \right)\right]^{n}$

$d' = \left(\frac{a}{b} \right)^{n}$ y $c' = \left[(-1)\cdot \left(\frac{a}{b} \right)\right]^{n}$

$d' = \left(\frac{a}{b} \right)^{n}$ y $c' = (-1)^{n}\cdot \left(\frac{a}{b} \right)^{n}$

Si $n$ es impar, entonces:

$d' = \left(\frac{a}{b} \right)^{n}$ y $c' = - \left(\frac{a}{b} \right)^{n}$

(e) El exponente es un positivo par.

Considérese las siguientes expresiones:

$d' = \left(\frac{a}{b} \right)^{n}$ y $c' = \left(\frac{a}{b} \right)^{n}$

Si $n$ es par, entonces $d' = c'$ y la proposición es verdadera.

Por tanto, se concluye que es falso que toda potencia que se obtiene de elevar a un mismo exponente un número racional y su opuesto es la misma.

3 0

3 years ago