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3 years ago

How can you solve multiplication fast with no calculator?

1 answer:

4 0

You study as much of the times tables as possible and once you have that information stored in your Brain, you use mental math. You can write it down on paper but that’s pretty time consuming if you go at a slow pace.

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Suppose that light travels from water to another substance, with an angle of Incidence of 10.0º and an angle of refraction of 14

SVEN [57.7K]

The index of the refraction is 0.898 and the index of the refraction is less than one which is unreasonable because the speed of the light can't be more than c.

<h3>What is refraction?</h3>

The phenomenon bending of a wave as it crosses from one medium to another is said to be refraction. The difference in density is the cause of the bending.

Refraction is a term that is used to describe the phenomenon of refraction."The change in direction of a wave traveling through one medium to another is known as refraction."

From the Snell's law:

nsinФ = n'sin∅

We have n' = 1.33, ∅ = 10.0°, Ф = 14.9°

nsin110.0° = 1.33×sin14.9°

n = 0.898

Because the speed of light cannot be greater than c, the index of refraction is less than one, which is illogical.

It is illogical to assume that the angle of refraction is excessively large in relation to the angle of incidence.

Thus, the index of the refraction is 0.898 and the index of the refraction is less than one which is unreasonable because the speed of the light can't be more than c.

Learn more about the refraction here:

brainly.com/question/17156275

#SPJ1

4 0

1 year ago

Using the graphing function on your calculator, find the solution to the system

stealth61 [152]

Answer:

It has infinite solutions.

D. More than 1 solution

Step-by-step explanation:

$\left \{ {{3y - 9x = -6} \atop {5y - 15x = -10}} \right.$

$\left \{ {{3y(-5) - 9x(-5) = -6(-5)} \atop {5y(3) - 15x(3) = -10(3)}} \right.$

$\left \{ {{-15y +45x = 30} \atop {15y - 45x = -30}} \right.$

$0+0=0$

$5y = 15x - 10\\y = 3x - 2$

$3(3x-2) - 9x = -6$

$0=0$

8 0

2 years ago

Can someone help please?

Dimas [21]

Ok I think this may be right but I hope this helps!

3 0

2 years ago

There are 30 total cards. 10 are yellow. What are the chances that you pull 2 yellow cards.

d1i1m1o1n [39]

Answer: 20

Step-by-step explanation:

3 0

2 years ago

I recently (yesterday) took the AMC 10A, can anyone help me with this problem?

lianna [129]

First, we claim that $\frac{10^n-1}{9}$ is the $n-$ digit number with all digits equal to one.

Note that $10^n$ is a one followed by $n$ zeroes, so subtracting one gives $n$ nines. Divide that number by nine and you get $n$ ones, completing the proof.

Therefore, we have that $A_n = a \frac{10^n - 1}{9}$ , $B_n = b \frac{10^n-1}{9}$ , and $C_n = c \frac{10^{2n} - 1}{9}$ .

Let $x = 10^n$ . Then, we have:

$c \frac{x^2-1}{9} - b \frac{x-1}{9} = (a \frac{10^n - 1}{9})^2 = a^2 \frac{x^2 - 2x + 1}{81}$ .

Multiplying by $81$ gives:

$9c(x^2-1) - 9b(x-1) = a^2 (x^2-2x+1)$

Now, note that $x=1$ is not a valid input, since $10^n = 1$ requires $n=0$ , so we safely divide by $x-1$ to get:

$9c(x+1) - 9b = a^2(x-1)$

$9cx + 9c - 9b = a^2x - a^2$

$x(9c-a^2) = 9b-9c-a^2$

Because this is now a linear equation in $x$ , it has either zero, one, or infinitely many solutions. Obviously, we need the latter to occur, which happens when $9c=a^2$ and $9b-9c-a^2 = 0$ , since the coefficient of $x$ must cancel to zero and thus the RHS must equal zero as well.

Since $9c = a^2$ , we must have $a = 3 \sqrt{c}$ . Since $a$ must be a multiple of three, we plug in values. If $a = 9$ , we get $c = 9$ and thus $9b - 162 = 0$ , which is impossible. So $a = 9$ doesn't work.

With $a = 6$ , $c = 4$ , and thus $9b-72=0$ , so $9b=72$ , so $b=8$ . This gives $6+8+4=18$ as one possibility.

With $a = 3$ , $c = 1$ , and thus $9b - 18 = 0$ , so $b = 2$ . This obviously is worse.

We've gone through all the cases and the two possibilities are $2$ and $18$ , so our answer is $\boxed{18}$ .

8 0

3 years ago