How many ways can 8 different gifts be given to 5 diffrent children with each children recieving onegift?

What is the following product? 3sqrt4 times sqrt3

Harman [31]

Answer:

$\sqrt[6]{432}$

Step-by-step explanation:

$\sqrt[3]{4}\cdot\sqrt{3}=4^{\frac{1}{3}}\cdot3^\frac{1}{2}=(2^2)^\frac{1}{3}\cdot3^\frac{1}{2}=(2^\frac{4}{3})^\frac{1}{2}\cdot3^\frac{1}{2}=(2^\frac{4}{3}\cdot3)^\frac{1}{2}=(2^4\cdot27)^\frac{1}{6}=432^\frac{1}{6}=\sqrt[6]{432}$

3 0

3 years ago

The length of a rectangle is 5 yd more than double the width, and the area of the of the rectangle is 42 yd to the second power

yanalaym [24]

Answer:

The answer to your question is l = 12 and w = 7/2 or 3.5

Step-by-step explanation:

Data

length = l

width = w

Area = 42 yd²

Process

1) Write equations that help to solve this problem

Area = length x width = l x w

Length = 2width + 5 or l = 2w + 5

2) Substitution

42 = lw Equation l

l = 2w + 5 Equation ll

42 = (2w + 5)w Substitute equation ll in l

3.- Expand

42 = 2w² + 5w

2w² + 5w - 42 = 0

Solve the equation by factoring

-Multiply 2 by 42

2 x 42 = 84

-Find the prime factors of 84

84 = 2² 3 7

-Find two numbers that added gives +5 using the prime factors

These numbers are +12 and -7

-Substitute the values in the equation

2w² -7w + 12w - 42

-Factor by grouping

w(2w - 7) + 6(2w - 7)

(2w - 7)(w + 6)

-Find w

2w₁ - 7 = 0 w₂ + 6 = 0

w₁ = 7/2 w₂ = -6 This value is discarted because

there are no negative values

-Find l

l = 2(7/2) + 5

l = 7 + 5

l = 12

7 0

3 years ago

a person runs at a constant speed of 9.2 miles per hour for 6 minutes and 30 seconds. How far did they travel in yards.

ipn [44]

Given:

Speed $= \bold{9.2 \ \frac{miles}{hour}}$

$\therefore \\\\$

1-hour= 60 minutes

1-minutes=60 second

So

1-hour= 3600 second

Converting the given time into seconds:

Time= 6 minutes and 30 second

$=\bold{6\times 60 \ second + 30 \ second }\\\\=\bold{360\ second+30\ second}\\\\=\bold{390\ second}\\\\$

When 3600 seconds covers=9.2 miles

Then equation:

$=\bold{\frac{9.2}{3600}}\\\\$

390 seconds covers:

$=\bold{\frac{9.2}{3600}\times 390 \ miles} \\\\$

Let

$\bold{1 \ miles= 1760\ yard}\\\\$

Convert the traveling value into yards:

$=\bold{ \frac{9.2}{3600}\times 390\times 1760}\\\\=\bold{ \frac{9.2}{36}\times 39\times 176}\\\\=\bold{ \frac{9.2}{12}\times 13\times 176}\\\\=\bold{ \frac{9.2}{12}\times 2288}\\\\=\bold{ 9.2\times 190.66}\\\\=\bold{ 1754.072\ yards}\\\\$