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3 years ago

What is (6,2) rotation 270

Mathematics

1 answer:

nignag [31]3 years ago

3 0

Given:

The point is (6,2).

To find:

The image of given point after rotation of 270 degrees.

Solution:

Let the given point be P(6,2).

Rotation of 270 degrees means the figure is rotated 270 degrees counterclockwise about the origin. So, the rule of rotation is

$(x,y)\to (y,-x)$

Using this rule, we get

$P(6,2)\to P'(2,-6)$

Therefore, the image of given point is (2,-6).

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A drama club made $3,200 from a school play. Seventy-five percent of that amount came from ticket sales. Identify the values of

aev [14]

Answer: $2400

Step-by-step explanation:

Based on the question above, a will be the percentage of tickets that were sold while b will be tickwt sales. Therefore,

a = 75%

b = 75% × $3,200

= 0.75 × $3200.

= $2400

Based on the information above, the amount of tickets sales is $2400

7 0

3 years ago

A school has 1800 students and 1800 light bulbs, each with a pull cord and all in a row. All the lights start out off. The first

Gnom [1K]

<u>Solution-</u>

A school has 1800 students and 1800 light bulbs, each with a pull cord and all in a row.

As all the lights start out off, in the first pass all bulbs will be turned on.

In the second pass all the multiples of 2 will be off and rest will be turned on.

In the third pass all the multiples of 3 will be off, but the common multiple of 2 and 3 will be on along with the rest. i.e all the multiples of 6 will be turned on along with the rest.

In the fourth pass 4th light bulb will be turned on and so does all the multiples of 4.

But, in the sixth pass the 6th light bulb will be turned off as it was on after the third pass.

This pattern can observed that when a number has odd number of factors then only it can stay on till the last pass.

1 = 1

2 = 1, 2

3 = 1, 3

<u>4 = 1, 2, 4</u>

5 = 1, 5

6 = 1, 2, 3, 6

7 = 1, 7

8 = 1, 2, 4, 8

9 = 1, 3, 9

10 = 1, 2, 5, 10

11 = 1, 11

12 = 1, 2, 3, 4, 6, 12

13 = 1, 13

14 = 1, 2, 7, 14

15 = 1, 3, 5, 15

16 = 1, 2, 4, 8, 16

so on.....

The numbers who have odd number of factors are the perfect squares.

So calculating the number of perfect squares upto 1800 will give the number of light bulbs that will stay on.

As, $\sqrt{1800} =42.42$ , so 42 perfect squared numbers are there which are less than 1800.

∴ 42 light bulbs will end up in the on position. And there position is given in the attached table.

7 0

3 years ago

From compound interest-Class 10.Suntali deposited Rs 9000 altogether in her saving account and fixed deposit account in a bank.S

Katarina [22]

Answer:

Step-by-step explanation:

Step-by-step explanation:

Year 1 - You earn interest on your Principal.

Year 2 - You earn interest on your (Principal + Interest of Year 1).

Year 3 - You earn interest on your (Principal + Interest of Year 1 + Interest of Year 2).

Compound interest is the basis of long-term growth of the stock market. It forms the basis of personal savings plans. Compound interest also affects inflation.

Types of Compound Interest

There are generally two types of compound interest used.

Periodic Compounding - Under this method, the interest rate is applied at intervals and generated. This interest is added to the principal. Periods here would mean annually, bi-annually, monthly, or weekly.

Continuous Compounding - This method uses a natural log-based formula and calculates interest at the smallest possible interval. This interest is added back to the principal. This can be equalled to the constant rate of growth for all natural growth. This figure was born out of physics. It uses Euler’s number which is a famous irrational number which is known to more than 1 trillion digits of accuracy. Euler’s number is denominated by the letter “E”.

Periodic Compound Interest Formula Overview

There are two formulas you can use to calculate compound interest, depending on what result you wish to find out. You can find out the following:

The total value of the deposit.

The total compound interest earned.

Value of the Deposit

Formulas can be a deterrent to many. If you aren’t savvy with math, your eyes turn away from these codes or just skip them altogether. But once it’s explained, it’s pretty simple to understand. To calculate the total value of your deposit, the formula is as follows:

P (1+ i/n)nt

P = Principal invested.

i = Nominal Rate of Interest.

n = Compounding Frequency or number of compounding periods in a year.

t = Time, meaning the length of time the interest is applicable, generally in years.

Simply put, you calculate the interest rate divided by the number of times in a year the compound interest is generated. For instance, if your bank compounds interest quarterly, there are 4 quarters in a year, so n = 4. This result must be multiplied to the power of the deposit period. For example, if your deposit is for 10 years, t = 10. This whole result should be multiplied by the principal you invested. The result generated will equal the total accumulated value of your deposit. You can find out how much your deposit is worth currently after accumulating interest.

Total Compound Interest Earned

To find out how much interest was earned, you can use the following formula for Compound Interest.

P[(1+ i/n))nt-1]

Compound Interest Equation and Calculation

To understand the compound interest equation further, we can break it down in simpler terms. If you decide to invest in a fixed deposit with compound interest, this is how you will earn interest every year.

Period Deposit Balance

Investment P

Year 1 P + iP

Year 2 (P+ iP) + i(P+iP)

To collapse this formula, we can pull out factors of (1+i). Simply substitute iP with (1+i) to get the following:

Period Deposit Balance

3 0

3 years ago

Each employee in a company is either right-handed or left-handed.

sweet [91]

Answer:

Step-by-step explanation:

A = 176368374.8837477463636

5 0

3 years ago

1. The function f(x) = –0.05(x2 – 26x – 120) represents the path coming out of the cannon. If x is the horizontal distance from

LenaWriter [7]

Question 1

f(x) represents the distance of the cannon from the ground

Question 2

When f(x) = 0, there will two values of 'x'. The point on the positive x-axis where the graph crosses represent the point where the cannon hits the ground.

Question 3

Yes, it would. By knowing the spot where the cannon will hit the ground, we can set the net at the spot.

Question 4

f(x) = 0
-0.05 (x² - 26x -120) = 0
x² - 26x - 120 = 0

Question 5

Please refer to the table attached below

Question 6

The value of p and q that gives the correct factors are -30 and 4 since it gives p+q = -26

Question 7

Factorising the equation completely

-0.05 (x² - 26x - 120) = 0
-0.05 (x+4) (x-30) = 0
(x+4) (x-30) = 0

Question 8

Solving the equation

x+4 = 0 and x-30=0
x=-4 and x=30

Question 9

The roots of the equation is x = -4 and x = 30

Question 10

Please refer to the third graph

Question 11

Yes

Question 12

The negative zero means the initial distance of the cannon, where it was fired from

Question 13

The distance between x = -4 and x = 30 is 34 units. If the cannon was fired from the point when x = -4, the cannon will hit the ground again 34 units from the point it was fired from. If Nik put a net 30 units from the firing point, the cannon will fly pass it.

7 0

3 years ago