- - = = = B. Fill in the blanks. 2. 52mºn4 = 13mºn = 1. 18x3 = 6x = 3. – 40a3b2 = 8ab2 = 4. -14(x – y)2 = 7(x – y)2 = 5. 56(a – b)2 (b – c) (c – a)4 = (-28)(a - b)(b – c)? (c – a)) = C. Carry out the following division: 1. 7x²y2 z2: 14xyz 2. 56X’y_ z3= (–14xyzz) D. Divide the given polynomial by the given monomial: 1. (10x - 25) = 5 2. (12a4 – 10a– 8a%) = 2a2 E. Work out the following division: - 1. (10x – 25) = (2x - 5) 2. 10y(6y + 21) = 5(2y + 7) -
Answers
Answer:
Step-by-step explanation: Given determinant \triangle =\begin{vmatrix}a-b &b-c &c-a \\b-c &c-a &a-b \\c-a &a-b &b-c \end{vmatrix}=0
Applying the rows addition R_{1} \rightarrow R_{1}+R_{2} then we have;
\triangle =\begin{vmatrix}a-c &b-a &c-b \\b-c &c-a &a-b \\-(a-c) &-(b-a) &-(c-b) \end{vmatrix}=0
=-\begin{vmatrix}a-c &b-a &c-b \\b-c &c-a &a-b \\(a-c) &(b-a) &(c-b) \end{vmatrix}=0
So, we have two rows R_{1} and R_{2} identical hence we can say that the value of determinant = 0
Therefore \triangle = 0.
Answer:
yt
Step-by-step explanation:
inches 1 MGD = 1.55 cfs 1 grain / gal = 17.1 mg/L 1 minute = 60 seconds
1 yard = 3 feet 1 cu. yd. = 27 cu. ft. 1 gram = 1,000 mg 1 hour = 60 minutes
1 meter = 3.28 feet 1 cu. ft. = 7.48 gal 1 kg = 1,000 gram 1 day = 1,440 min
1 mile = 5,280 feet 1 gal = 8.34 lbs 1 liter = 1,000 ml 1% = 10,000 mg/L
1 sq. ft. = 144 sq. in. 1 cu. ft. = 62.4 lbs 1 gal = 3.785 liters 1 mg/l = 1 ppm
1 acre = 43,560 sq. ft. 1 kg = 2.2 lbs 1 psi = 2.31 ft. of water head 1 hp= 0.746 kW
1 acre-ft. = 43,560 cu. ft. 1 lb. = 454 g 1 ft. of water head = 0.433 psi 1 hp = 33,000 ft. lbs/min
1 acre-ft. = 325,829 gallons 1kW = 1,000 Watts
Legend: L = length W = width H = height R = radius D = diameter π = 3.14 g = gram
Alkalinity Concepts
Phenolphthalein Alkalinity, mg/L as CaCO3 = (Titrant Volume A, ml) (Acid Normality) (50,000)
Sample Volume, ml
Total Alkalinity, mg/L as CaCO3 = (Titrant Volume B, ml) (Acid Normality) (50,000)
Sample Volume, ml
Alkalinity Relationships: Alkalinity, mg/l as CaCO3
Result of
Titration
Bicarbonate
Alkalinity as
CaCO3
Carbonate
Alkalinity as
CaCO3
Hydroxide
Alkalinity as
CaCO3
P = 0 T 0 0
P < ½ T T – 2P 2P 0
P = ½ T 0 2P 0
P > ½ T 0 2(T – P) 2P – T
P = T 0 0 T
Key: P – phenolphthalein alkalinity; T – total alkalinity
Area, Circumference and Volume
Area, square feet (ft2
)
Circle: A = 3.14 x R2
or A = 0.785 x D2
Cylinder, (total outer surface area): A = (2 x 3.14 x R2
) + 3.14 x D x H or A = (2 x 0.785 x D2
) + (3.14 x D x H)
Cylinder (pipe): A = 3.14 x D x L
Square or Rectangle: A = L x W
Circumference (Perimeter), linear feet
Circle = 3.14 x D
Rectangle = (2 x L) + (2 x W)
Volume, cubic feet (ft3
):
Cylinder: V = 3.14 x R2 x H or V = 0.785 x D2 x H
Rectangle: V = L