Answer: 145 cans
Step-by-step explanation:
arithmetic sequence
aₙ = a₁ + (n-1).r
aₙ → last term
a₁ → 1st term
n → quantity of terms
r → common difference
a₁ = 1 (one can at the top)
aₙ₋₁ = 25
aₙ = 28
To find out How many cans are in the entire display, we need the SUM of the arithmetic sequence: S = (a₁+aₙ)n/2
∴
S = (1+28).n/2
n = ?
aₙ = a₁ + (n - 1).r
r = 28 - 25 = 3
28 = 1 + (n - 1).3
27 = (n - 1).3
27/3 = (n - 1)
9 = n - 1
n = 9 + 1 = 10
S = (1+28).n/2
S = (1+28).10/2 = 29.10/2 = 29.5 = 145
Answer:
<u>Step 1: Determine why circle 1 is similar to circle 2</u>
The reason why circle 1 is similar to circle 2 is that they both expand at the same rate. While x grows larger, both circle 1 and circle 2 grow at a proportional rate. Circle 2 grows is 5 times bigger than circle 1 given any value 5.
<u>When x = 3:</u> circle 1 = 6 and circle 2 = 30
<u>When x = 10:</u> circle 1 = 20 and circle 2 = 100
The vertex is x and the y intercept is 2
*see attachment for the diagram
Answer:
A. 178 units²
Step-by-step explanation:
Surface area of the figure = (surface area of the square pyramid + surface area of the square prism) - 2(base area of the square pyramid)
✔️Surface area of the square pyramid = s² + 2*s*l
Where,
s = side length of square base (w) = 6 units
l = slant height = ?
Use Pythagorean theorem to find l
l = √((w/2)² + y²)
l = √((6/2)² + 5²) = √(9 + 25)
l = √34
l ≈ 5.8 units
Surface area of the square pyramid = 6² + 2*6*5.8 = 105.6 units²
✔️Surface area of square prism:
SA = 2a² + 4ah
Where,
a = w = 6 units
h = x = 3 units
Substitute
SA = 2(6²) + 4*6*3
= 72 + 72
= 144 units²
✔️base area of the square pyramid = s²
s = w
Base area = 6²
Base area = 36 units²
✅Surface area of the figure = (surface area of the square pyramid + surface area of the square prism) - 2(base area of the square pyramid)
Surface area of the figure = (105.6 + 144) - 2(36)
= 249.6 - 72
= 177.6
≈ 178 units²
9514 1404 393
Answer:
23) x = ±3i, ±√2
26) x = 4/3, (-2/3)(1 ± i√3)
Step-by-step explanation:
23) Put in standard form to make factoring easier.
x^4 +7x^2 -18 = 0
(x^2 +9)(x^2 -2) = 0 . . . . factors in integers
Using the factoring of the difference of squares, you can continue to get linear factors in complex and irrational numbers:
(x -3i)(x +3i)(x -√2)(x +√2) = 0
x = ±3i, ±√2
___
26) This will be the difference of cubes after you remove the common factor.
81x^3 -192 = 0
3(27x^3 -64) = 0
(3x -4)(9x^2 +12x +16) = 0 . . . . . factor the difference of cubes
The complex roots of the quadratic can be found using the quadratic formula.
x = (-12 ±√(12^2 -4(9)(16)))/(2(9)) = (-12 ±√-432)/18 = -2/3 ± √(-4/3)
Then the three solutions to the equation are ...
x = 4/3, (-2/3)(1 ± i√3)
