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2 years ago

When you divide a whole number by a decimal less than 1, the quotient is greater than the whole number. why?

2 answers:

7 0

100 divided by 4 = 25
100 divided by a lesser number than 4, say 2, = 50 
100 divided by an even lesser number than 4, say 1, = 100. 

Notice the pattern. Each time we divide by a lesser number, the quotient (the answer) gets larger and larger 

Dividing by 1 already equals a quotient that is EQUAL to the original number we are dividing. 

Thus, for the pattern to continue, the quotient must become greater than the number. 

100 divided by an even lesser number than 1, say .5 = 200.

Viktor [21]2 years ago

4 0

Well if you get back to the definition of a division, diving X by Y is finding out how many Ys you can have in a X.

It is clear that you will have more than X times Y if Y is less than 1 since dividing X by 1 is exactly X.

If you think of 10 and 1, you can divide 10 in exactly 10 portions of 1.
But you can divide it into 100 portions of 0,1.
And 100 is bigger than 10 of course.
Hope this helps.

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A soccer ball kicked by a Real Madrid midfielder leaves the player's foot at a speed of 48 mph at an angle θ above the horizonta

kodGreya [7K]

<h2>For maximum range, θ = π/4 </h2>

Step-by-step explanation:

Consider the vertical motion of ball,

We have equation of motion v = u + at

Initial velocity, u = u sin θ

Final velocity, v = -u sin θ

Acceleration = -g

Substituting

v = u + at

-u sin θ = u sin θ - g t

$t=\frac{2usin\theta }{g}$

This is the time of flight.

Consider the vertical motion of ball till maximum height,

We have equation of motion v² = u² + 2as

Initial velocity, u = u sin θ

Acceleration, a = -g

Final velocity, v = 0 m/s

Substituting

v² = u² + 2as

0² = u²sin² θ + 2 x -g x H

$H=\frac{u^2sin^2\theta }{2g}$

This is the maximum height reached,

Consider the horizontal motion of ball,

Initial velocity, u = u cos θ

Acceleration, a =0 m/s²

Time, $t=\frac{usin\theta }{g}$

Substituting

s = ut + 0.5 at²

$s=ucos\theta \times \frac{2usin\theta }{g}+0.5\times 0\times (\frac{2usin\theta }{g})^2\\\\s=\frac{2u^2sin\theta cos\theta}{g}\\\\s=\frac{u^2sin2\theta}{g}$

This is the range.

For maximum range

sin 2θ = 1

2θ = π/2

θ = π/4

For maximum range, θ = π/4

8 0

2 years ago

in the diagram below, <AFB = <EFD. if m<EFD = (5x+6)°, m<DFC = (19x-15)°, and m<EFC = (17x+19)°, find m<AFE

NeX [460]

Answer:

m<AFE = 128°.

Step-by-step explanation:

Step 1: Find the value of x

Angle EFD + Angle DFC = Angle EFC

5x + 6 + 19x - 15 = 17x + 19

24x - 9 = 17x + 19

7x = 28

x = 4

Step 2: Find all angles

Angle AFB=Angle EFD= 5x + 6

5(4) + 6 = 26°

Angle DFC = 19x - 15

19(4) - 15 = 61°

Step 3: Find angle AFE

Line BD is a straight line and all angles on a straight line are equal to 180°.

Angle AFB + Angle AFE + Angle EFD = 180°

26 + BFC + 26 = 180°

BFC = 180 - 52

BFC = 128°

Therefore, m<AFE is equal to 128°.

3 0

2 years ago

The keyless entry system in some cars uses a 4-digit keypad. There are 10 possible digits, and the digits can be repeated. How m

Len [333]

This item can be answered through the concept of fundamental principles of counting. In the first of the four digits, there are 10 possible digits. The same with all the other 3 places or digits of the code. That is,
n = 10 x 10 x 10 x 10
Giving us the answer of 10,000. Thus, there are 10,000 possible keys for the keyless entry.

8 0

2 years ago

Read 2 more answers

2x-10/4=3x −10 −1 2 11

evablogger [386]

Answer:

Step-by-step explanation:

$\dfrac{2x-10}{4}=3x\qquad\text{multiply both sides by 4}\\\\2x-10=12x\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\-10=10x\qquad\text{divide both sides by 10}\\\\-1=x\to x=-1$

6 0

2 years ago

A local pizzeria offers 15 toppings for their pizzas and you can choose any 3 of them for one fixed price. How many different ty

Shtirlitz [24]

Answer:

455 or 680, depending

Step-by-step explanation:

If we assume the three choices are different, then there are ...

15C3 = 15·14·13/(3·2·1) = 35·13 = 455

ways to make the pizza.

___

If two or three of the topping choices can be the same, then there are an additional ...

2(15C2) +15C1 = 2·105 +15 = 225

ways to make the pizza, for a total of ...

455 + 225 = 680

different types of pizza.

There is a factor of 2 attached to the number of choices of 2 toppings, because you can have double anchovies and tomato, or double tomato and anchovies, for example, when your choice of two toppings is anchovies and tomato.

_____

nCk = n!/(k!(n-k)!)

6 0

2 years ago