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3 months ago

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Use the geometric definition of the cross product and the properties of the cross product to make the following calculations. (a

) ((i⃗ +j⃗ )×i⃗ )×j⃗ = (b) (j⃗ +k⃗ )×(j⃗ ×k⃗ ) = (c) 4i⃗ ×(i⃗ +j⃗ ) = (d) (k⃗ +j⃗ )×(k⃗ −j⃗ ) =

1 answer:

tester [12.3K]3 months ago

6 0

Answer:

Step-by-step explanation:

We understand that

$\vec{i}\times \vec{j}=\vec{k}$

$\vec{j}\times \vec{k}=\vec{i}$

$\vec{k}\times \vec{i}=\vec{j}$

(a) $\left [ \left ( \hat{i}+\hat{j}\right )\times \hat{i}\right ]\times \hat{j}$

$=\left [ \hat{i}\times \hat{i}+\hat{j}\times \hat{i}\right ]\times \hat{j}$

$=\left [ 0-\hat{k}\right ]\times \hat{j}$

$=\hat{i}$

(b) $\left ( \hat{j}+\hat{k}\right )\times \left ( \hat{j}\times \hat{k}\right )$

$=\left ( \hat{j}+\hat{k}\right )\times \left ( \hat{i}\right )$

$=\hat{k}+\hat{j}$

(c) $4\hat{i}\times \left ( \hat{i}+\hat{j}\right )$

$=4\hat{i}\times \hat{i}+4\hat{i}\times \hat{j}$

$=0+4\hat{k}$

(d) $\left ( \hat{k}+\hat{j}\right )\times \left ( \hat{k}-\hat{j}\right )$

$=\hat{k}\times \hat{k}-\hat{k}\times \hat{j}+\hat{j}\times \hat{k}-\hat{j}\times \hat{j}$

$=0+\hat{i}+\hat{i}-0$

$=2\hat{i}$

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3 months ago

A large washer has an outer radius of 10mm and a hole with a diameter of 14mm. What is the area of the top surface of the washer

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Answer:

The top surface area of the washer equals 160.14 square millimeters.

Step-by-step Explanation:

The washer's top surface forms an annulus, characterized by an outer radius of 10 mm and an inner radius of 7 mm (obtained since the hole's diameter is 14 mm and the radius is half the diameter).

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3 months ago

Read 2 more answers

PATS, PETE AND KOFFI ANNUAL SALARIES AGGREGATE TO 200,000.00 A YEAR PETE MAKES $11000.00 MORE THAN KOFFI AND PAT MAKES $1000.00

zzz [12365]

Respuesta:

El salario mensual de Koffi: $3500 ($42000 anuales)

Salario mensual de Pete: $4416.7 ($53000 anuales)

Salario mensual de Pat: $8750 ($105000 anuales)

Explicación paso a paso:

Sea x el salario anual de Pat

Sea y el salario anual de Pete

Sea z el salario anual de Koffi

Según el enunciado, sus salarios anuales suman $200000 es decir, x + y + z= $200000

Pete gana $11000 más que Koffi anualmente, lo que significa que y = $11000 + z

Pat gana $1000 menos que el doble (×2) del salario anual de Pete, es decir, x = 2y - $1000

Así, tenemos 3 ecuaciones:

(1)..... x + y + z= $200000

(2).... y = $11000 + z

(3).... x = 2y - $1000

Primero, sustituimos y en la ecuación (3), es decir,

x = 2(11000 + z) - 1000

x = 22000 + 2z - 1000

x = 21000 + 2z............ (4)

Luego incorporamos las ecuaciones (4) y (2) en la ecuación (1) para encontrar z:

x + y + z = 200000

21000 + 2z + 11000 + z + z = 200000

4z + 32000 = 200000

4z = 200000 - 32000

4z = 168000

z = 42000

Así que z (salario anual de Koffi) es de $42000.

Para conocer y, sustituimos z en la ecuación (2).

y = 11000 + z

y = 11000 + 42000

y = 53000

Por lo tanto, y (salario anual de Pete) es de $53000

Para hallar x, sumamos $42000 y $53000, y restamos de $200000 es decir, 42000 + 53000 = 95000

200000 - 95000 = 105000

Por lo tanto, x (salario anual de Pat) es de $105000.

Para obtener el salario mensual de cada individuo, dividimos su salario anual entre 12:

Koffi (z) = 42000/12 = $3500

Pete (y) = 53000/12 = $4416.7

Pat (x) = 105000/12 = $8750

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Answer:

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Detailed breakdown:

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2 months ago

The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to cover the block entirely wit

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Response:

Total paper needed is 57 cm²

Detailed explanation:

Provided information

slant height b = 4 cm

base side h = 3 cm

block height h1 = 2 cm

Solution

The surface area of a right square pyramid is determined by summing the areas of all four triangular faces expressed as

area = 4 × Area of Triangles

area = 4 × $\frac{bh}{2}$

area = 4 × $\frac{4\times 3}{2}$

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Also,

the surface area of the box includes the area of its four side faces plus the base

area = 4 × ( h × h1 ) + h²

area = 4 × ( 3 × 2 ) + 3²

area = 24 + 9

area = 33 cm²

Thus, the total paper required is = 24 + 33

therefore, the total paper needed equals 57 cm²

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1 month ago