Answer:
Step-by-step explanation:
Let <em>m</em> represent the amount of months that has passed.
Paulo started out with 20 coins.
Each month, he adds four more coins to his collection.
Therefore, the amount of coins added after <em>m</em> months will be given by 4<em>m</em>.
So, the amount of coins Paulo has total after <em>m</em> months can be given by:
We want to know when Paulo will have "more than" 50 coins in his collection. Therefore, we will use the "greater than" sign. Thus, our inequality will be:
1/2 + 4 ≤ 16
four more = +4
half a number = 1/2
at most means less or greater which is ≤
Answer: aₙ = 3 + 4ⁿ⁻¹
So the formula would be:
<u>aₙ = 3 + 4ⁿ⁻¹</u>
Where a₁ = 3
Common Ratio (r) = 4
And n = the term number that needs to be found out
Step-by-step explanation:
<u>Let's check if the answer is right:</u>
To find the 1st number in the term we can substitute 1 in for n in the equation:
a₁ = 3 + 4¹⁻¹
a₁ = 3 + 4⁰
a₁ = 3 + 1
a₁ = 4
And if going back and checking the first number in the sequence given is indeed 4, therefore this equation is correct
Hope this helps!
Answer:
a.
b. x ≠ -5 (Vertical asymptote) and x ≠ 5 (Hole)
Step-by-step explanation:
Factor the numerator (Grouping):
Two numbers that multiply to -30 and add to -7 = -3 and 10
Factor the denominator (Difference of Two Squares):
=
Factored Expression:
(x - 5) can be factored out of top and bottom as a hole-
Variable Restrictions:
Denominator ≠ 0
Vertical asymptote at x = -5 ⇒ x ≠ -5
Answer:
The dimension of the cardboard is 34 cm by 34 cm by 17 cm.
Step-by-step explanation:
Let the dimension of the cardboard box be x cm by y cm by z cm.
The surface area of the cardboard box without lid is
f(x,y,z)= xy+2xz+2yz.....(1)
Given that the volume of the cardboard is 19,652 cm³.
Therefore xyz =19,652
......(2)
putting the value of z in the equation (1)
The partial derivatives are
To find the dimension of the box set the partial derivatives and .Therefore
.......(3)
and
.......(4)
Now putting the x in equation (3)
⇒y=34 cm
Then =34 cm.
Putting the value of x and y in the equation (2)
=17 cm.
The dimension of the cardboard is 34 cm by 34 cm by 17 cm.