Athome Tuition: March 2014

Monday, March 31, 2014

Unit Conversions - Temperature

To start with, have a look at the table below to learn the common temperature conversions.

Now let’s get to the harder part; converting temperature values from Celsius to Fahrenheit and vice versa using the formula below:

C is Celsius
F is Fahrenheit
K is Kelvin
C = 5/9F-32
F = 9/5C+32
C = K - 273
K = C + 273

Are you ready to try your hand at solving? Look at the following examples and see if you can solve it using the formula.

Convert 87 degrees Celsius to Fahrenheit. C = 87
F = ?
F = 9/5 * 87 + 32
= 188.6 F
Now check your answer by converting it back to Celsius:
C = 5/9 * 188.6 -32
= 87 C

Convert 276 degrees Fahrenheit to Celsius F = 276
C = ?
C = 5/9 * 276 – 32
C = 135.5 C
            Now check your answer by converting it back to Fahrenheit:
            F = 9/5 * 135.5 + 32
            = 276 F
The boiling point of water is 100 degrees C. What is this value in Kelvin? C = 100
k = ?
k = 100 + 273
= 373 k

Try these questions

The temperature in Abu Dhabi is 68 degrees Fahrenheit, and 17 degrees Celsius below zero in Montreal. What is the difference in temperature between the two cities?

Answer: 37 degrees C
First convert 68 F to C
C = 5/9 * 68-32
C = 20
Second, find the difference:
20 – (-17) = 37 degrees C difference

Convert the following to Kelvin a) 0o C = ___
Answer: 0 + 273 = 273 k
b) -50o C = ___
Answer: -50 + 273 = 223 k
c) 90o C = ___
Answer: 90 + 273 = 363 k
d) -20o C = ___
Answer: -20 + 273 = 253 k

Jessie is suffering from hyperthermia, with her body temperature reading at 104 degrees F. What does this read in the Celsius scale?

Answer:
C = 5/9F-32
= 5/9 * 104-32
= 40 degrees centigrade

Convert the following to Celsius a) 130 F = ___
Answer: 5/9 * 130-32
= 54.4 C
b) 198 F = ___
Answer: 5/9 * 198-32
= 92.22 C
c) 90 F = ___
Answer: 5/9 * 90-32
= 32.22 C
d) 231 F
Answer: 5/9 * 231-32
= 110.6 C

Thursday, March 27, 2014

Unit conversions – Liquids and Volume

Look at the table below and memorize the metric conversions of all units used to measure length.

Common Volume Conversion Factors
1 cubic centimeter =	1000 cubic millimeter
1 cubic decimeter =	1000 cubic centimeter
1 cubic meter =	1000 cubic decimeter
1 liter / litre =	.001 cubic meter
1 liter / litre =	10 deciliter
1 deciliter =	10 centiliter
1 centiliter =	10 milliliter
1 cubic foot =	1728 cubic inches
1 cubic yard =	27 cubic feet
1 fluid minims =		61.61152 cu mm
1 fluid drams =		60 minims
1 fluid ounces =		8 fluid drams
1 pint (pt) =		16 fluid ounces
1 gills (gi) =		0.25 pint
1 quart (qt) =		2 pint
1 gallon (gal) =		4 quart
1 oil barrel =		42 gallons

In order to convert metric units into English units and other units of measurements, we will use the conversion factors stated above. Notice that we always use 1 unit of the length to be converted. Once this is known, the conversion factor, we can then use this to multiply against a unit we wish to be converted.

REMEMBER

When going from a large unit to a small unit, you multiply.

When going from a small unit to a large unit, you divide.

There is another way of converting units. It is often called the long way because you need to arrange the values to make a ratio and proportion equation. For example:

If 1 gallon = 4 quarts, how many gallons will there be in 20 quarts?

Answer:

(1 gallon / 4 quarts) = (x gallons / 20 quarts)
1 gallon x 20 quarts = 4 quarts
X = 5 quarts
Today, the price is 3.4 AED/liter. If Jessie filled up her car with 40 deciliter quarts of gasoline, (a) what is the volume she purchased in liters? (b) how much did she pay for this?

Answer:

(a) Convert dL to L

(1 L / 10 dL) = (x / 40)
(40 / 10) = 4 L

b) (3.4 AED / L) = (x / 4)

3.4 x 4 = x
13.6 AED = x
A pint of beer costs $8. Jack and his four friends bought 3 pints each. (a) How many quarts of beer did they consume in total? (b) How much did they pay in total?

Answer:

Total pint consumed = 12 pints

a) (1 pint / 2 quarts) = (12 / x) x = 12 x 2
x = 24 quarts

b) 12 x 8 = $96

Try these questions

A cough syrup has a dosage of 250 mg/5 mL of the prescribed antibacterial. The doctor calls for 750mg to be taken twice daily. What is the total volume to be taken?

Answer: 30 mL

Explanation:

Use ratio and proportion first to find out the volume of one dose:
(250 mg/5 mL) = (750 mg / x mL)
x mL = 15 mL
Twice daily: 15 mL x 2 = 30 mL total volume to be taken
During renovation, the two painters used up 1/3 of the 10 pint red paint. How many fluid ounces of red paint were used up?

Answer: 53.28 fluid ounce

Explanation:

1/3 x 10 pint = 3.33 pint
Convert pint to fluid ounce
1 pint = 16 fluid ounces
(1 pint / 16 fluid ounces) = (3.33 pint / x)
X= 16 fluid ounces x 3.33 pint
X = 53.28 fluid ounce
The sum of the lengths of all sides of a cube is 8 cm. What is its volume? (Volume = l x w x h).

Answer: 2 cm

Explanation:

Since a cube has 12 sides, we get:
12e = 8
e = 8/12 or 2/3
Therefore, its volume is: e3
(2/3) x (2/3) x (2/3) =1.99 or 2 cm.

Jessie diluted 3L of mango puree with 4340 mL of distilled water. What is the resulting volume of the mixture in mL?

Answer: 7340 mL

Explanation:

Convert L to mL
(1 L / 1000 mL) = (3L / x mL)
X = 3000 mL
Add the two volumes:
3000 mL + 4340 mL = 7340 mL

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Tuesday, March 25, 2014

Verifying Trigonometric Identities

VERIFYING TRIGONOMETRIC IDENTITIES

http://www.athometuition.com/VerifyingTrigonometric.php

The fundamental identities are used to establish additional relationships among trigonometric functions. The fundamental identities consist of reciprocal identities, quotient identities, and Pythagorean identities.

Example 1

Verify the identity:

Solution:
An often used strategy in verifying identities is to write the expression in terms of sine and cosine alone.
The left side is more complicated so we start working with this side.

Example 2
Verify the identity:

Solution:

Another way to verify an identity is to work separately with both sides and show that the two sides are identical to the same expression. This method is used when working on one side alone does not seem to work.
We start working with the left side.