Answer:
The solutions are a₁ = -4/19 i, a₂ = 4/19 i and a₃ = -1/4
Step-by-step explanation:
Given the equation 76a³+19a²+16a=-4, for us to solve the equation, we need to find all the factors of the polynomial function. Since the highest degree of the polynomial is 3, the polynomial will have 3 roots.
The equation can also be written as (76a³+19a²)+(16a+4) = 0
On factorizing out the common terms from each parenthesis, we will have;
19a²(4a+1)+4(4a+1) = 0
(19a²+4)(4a+1) = 0
19a²+4 = 0 and 4a+1 = 0
From the first equation;
19a²+4 = 0
19a² = -4
a² = -4/19
a = ±√-4/19
a₁ = -4/19 i, a₂ = 4/19 i (√-1 = i)
From the second equation 4a+1 = 0
4a = -1
a₃ = -1/4
P(TTTTT)=P(T)*P(T)*(PT)*P(T)*P(T)
P(TTTTT)=(P(T))^5
P(T)=1/2 so
P(TTTTT)=(1/2)^5
P(TTTTT)=1/32
P(TTTTT)=3.125%
Answer:
Step-by-step explanation:
If Daniel does 1/9 of the job in one hour
let x = Paul's rate
Paul does 1/x of the job in one hour
They both do the job in 4.95hrs
(1/9)(4.95) + (1/x)(4.95) = job completion
multiply both sides by 9x
(9x)(1/9)(4.95) + (9x)(1/x)(4.95) = 9x(1)
4.95x + 9*4.95 = 9x
4.95x + 44.55 = 9x
9x - 4.95x = 44.55
4.05x = 44.55
x = 44.55/4.05
x = 11 hours i.e time it takes for Paul to pick the 40 bushels alone
9514 1404 393
Answer:
7. 91 m²
8. 56 in²
9. 105 in²
10. 135 m²
Step-by-step explanation:
The formula for the area of a triangle is ...
A = 1/2bh
where b is the base length, and h is the height perpendicular to the base.
The formula for the area of a trapezoid is ...
A= 1/2(b1 +b2)h
where b1 and b2 are the lengths of the parallel bases, and h is the perpendicular distance between them. Note that this formula is virtually identical to the triangle formula, with the triangle 'b' being replaced by (b1+b2).
__
Fill in the numbers and do the arithmetic. The result is shown in the attachment. (We have used the triangle formula for all, with b1+b2 being used for 'b' to find the area of the trapezoids.)
7. A = 1/2(14 m)(13 m) = 91 m²
8. 56 in²
9. A = 1/2(14 +16 in)(7 in) = 105 in²
10. 135 m²
