Math and Arithmetic

The area of a circle can be calculated using the formula ( A = \pi r^2 ), where ( r ) is the radius. Given that the radius is 7 inches, the area is ( A = \pi (7^2) = \pi \times 49 ). Therefore, the area is approximately ( 153.94 ) square inches when using ( \pi \approx 3.14 ).

It is: 100/2 = 50

5 fifths are in a whole (1). 75 fifths are in 15.

The bending moment (M) in a beam can be calculated using the formula ( M = \frac{F \cdot d}{4} ) for a simply supported beam with a central load, where ( F ) is the load applied and ( d ) is the distance from the support to the point of application. For more complex structures, the bending moment can be determined using the moment-area method or by applying equations of static equilibrium. Additionally, for uniform distributed loads, the formula can be expressed as ( M = \frac{w \cdot L^2}{8} ), where ( w ) is the load per unit length and ( L ) is the length of the beam.

The supplement of an angle is found by subtracting the angle from 180 degrees. For a 135-degree angle, the supplement is calculated as 180 - 135, which equals 45 degrees. Therefore, the supplement of a 135-degree angle is 45 degrees.

0

2900

5.5

5

To compare any decimals

0.01 & 0.020

Bring both decimals to the same number of decimal places by inserting suffix zeroes.

Hence

0.010 & 0.020 ( 3 d.p in this case)

Drop the decimal point

0010 & 0020

Drop the prefix zeroes

10 & 20

I think you will agree that 20 > 10

Hence kit follows that 0.020 > 0.01

NB THis method is good for camparing any decimals.

e.g. 0.0009 & 0.0079

In this case 4 d.p.

00009 & 00079

9 & 79

79 > 9

Hence

0.0079 > 0.0009

3.625 = 3625/1000, which can be simplified.

a negative x a negative= a positive, a positive x a positive= a positive, a negative x a positive= a negative, and a positive x a negative= a negative. Same thing with division. a negative divided by a negative= a positive, a positive divided by a positive= a positive, a negative divided by a positive= a negative, and a positive divided by a negative is a negative. U see?

For all x not equal to 0, -x/x = -1

There are NO inches in 3 x 5 , because you have NOT given the units.

However, assuming it is 3 inches X 5 inches , then the answer is ' 15 SQUARE inches.

The answer is NOT in inches(linear) but ''Square inches(area)'. NOT inches^(2) ( Inches squared).

12.835

'3' is HundredTHS . ( Note the 'THS'.

Column names are

'1' is Tens

'2' is Units

Decimal point

'8' is Tenths

'3' is Hundredths ( as above)

'5' is Thousandths.

NB All decimal digits have '---THS' in the name.

No, 93, 120, and 303 are not rectangular numbers. A rectangular number, also known as a pronic number, is the product of two consecutive integers (n(n+1)). The numbers 93, 120, and 303 do not fit this definition as they cannot be expressed as the product of two consecutive integers.

3n X 3n = = 36

Hence

(3n)^(2) = 36 = 6^(2)

Square root both sides

3n = 6

n = 2

-33

4x-23x = -19

By LONG MULTIPLICATION .

223

X 23

4460 ( 223 X 20)

+669 ( 223 X 3)

5129 The answer ( NB 20 + 3 = 23).

This is the Trig. Identity .

Sin( A + B) = SinACosB + CosASinB.

Hence

Sin55Cos35 + Cos555Sin35 =

Sin(55 + 35) = Sin(90) = 1

Verification

If you take the various Sin & Cos values and multiply then add, they will answer to '1'.

Hence./

(0.819153..)(0.819152...) +(0.573576...)(0,573586...) =

0.67100999 + 0.328989 = 0.99995... ~ 1. as required.

To calculate counts per second (CPS) of a radioactive material, first measure the total number of decay events detected over a specific time interval using a radiation detector. Then, divide the total count by the duration of the measurement in seconds. For example, if you detect 300 counts in 60 seconds, the CPS would be 300 counts / 60 seconds = 5 CPS. This value represents the activity of the radioactive material in terms of detected decay events per second.

Running 1500 meters in under 4 minutes (a “sub-4 mile” level effort, though slightly shorter) is an elite performance. It requires world-class speed, endurance, and years of structured training. For reference, the first man to break 4 minutes for the mile was Roger Bannister in 1954 — and a 1500m under 4:00 is still extremely competitive at read more ln.run/iGgSx

To add 7.56 liters and 1854 milliliters, first convert 7.56 liters to milliliters: 7.56 L = 7560 mL. Then, add the two amounts together: 7560 mL + 1854 mL = 9414 mL. Therefore, 7.56 L plus 1854 mL equals 9414 mL.

The constant term in a mathematical equation or expression typically represents a fixed value that does not change with the variables involved in the problem. In the context of a specific problem, it may indicate a starting point, initial condition, or baseline value that influences the outcome. Understanding the constant term helps to clarify how it interacts with the variable components and can provide insight into the overall behavior of the equation.