The factorization of the expression of 43x³ + 216y³ is
(7x + 6y)(49x² - 42xy + 36y²)
Step-by-step explanation:
The sum of two cubes has two factors:
1. The first factor is ![\sqrt[3]{1st}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B1st%7D)
+ ![\sqrt[3]{2nd}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2nd%7D)
2. The second factor is ( )² - ( ) ( ) + ( )²
Ex: The expression a³ + b³ is the sum of 2 cubes
The factorization of a³ + b³ is (a + b)(a² - ab + b²)
∵ The expression is 343x³ + 216y³
∵ ![\sqrt[3]{343x^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B343x%5E%7B3%7D%7D)
= 7x
∵ ![\sqrt[3]{216y^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B216y%5E%7B3%7D%7D)
= 6y
∴ The first factor is (7x + 6y)
∵ (7x)² = 49x²
∵ (7x)(6y) = 42xy
∵ (6y)² = 36y²
∴ The second factor is (49x² - 42xy + 36y²)
∴ The factorization of 43x³ + 216y³ is (7x + 6y)(49x² - 42xy + 36y²)
The factorization of the expression of 43x³ + 216y³ is
(7x + 6y)(49x² - 42xy + 36y²)
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Answer:
(a) 
(b) 100
Step-by-step explanation:
Solving (a):
Given
Shape: Rectangle
Required
Calculate the perimeter.
Area is calculated as:
Where
and 
Substitute 64.8 for Area
Make L the subject:
Perimeter is calculated as:
Substitute 64.8/W for L
To solve further, we take the derivative of P and set it to 0, afterwards.
Set to 0
Collect Like Terms
Cross Multiply:
Divide through by 2
Take square roots
Recall that:
So:
The perimeter is:
Solving (b):
Given
((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)
Required
Solve
So, the expression becomes:
((1 Group of 
) and (1 group of 
))/(6 groups of 
)
This gives:
((1 Group of 
) and (1 group of 
))/(6 groups of 
)
Group means product, so the expression becomes:
And, as used here means addition
Simplify:
Answer: The answer is 30%.
Step-by-step explanation: Given that there is a group of 10 light users and 10 heavy users. We are to find the probability that exactly 3 of the 20 users are HIV positive.
We have the following four possible cases -
(i) All 3 are light users.
(ii) 1 is a light user and 2 are heavy users.
(iii) 2 are light users and 1 is a heavy user.
(iv) All 3 are heavy user.
Since there is a 45% chance of a light user to be HIV positive and 55% chance of a heavy user to be HIV positive, so the required probability is given by
Thus, the probability is 30.
Answer:
Step-by-step explanation:
The formula of a midpoint between two points A(x₁, y₁) and B(x₂, y₂):
We have the points (3, 17) and (-14, -8).
Substitute:
In ΔABC,
tanA = a/b
∴ a = b×tanA = 12×1/√3 = 6.928 ~ 6.93 m
