We know that this is a geometric sequence. Keep in mind that in a geometric sequence, the next term is found by shamelessly multiplying it by "some number", namely the "common ratio".
therefore, if you divide any "next term" by the "previous term", the quotient will just be that "some number", thus, if 1.5 ÷ 7.5 will give it to us, and is, yeap, you guessed it, is 2.
you can check say 3 ÷ 1.5 or 6 ÷ 3, you'll see it.
so, we know the common ratio is 2, and the first term is 0.75, so
The volume of the cylinder is V = πr<span>²h.
For a circumscribed cylinder, we know that in a circumscribed cylinder, the height of a cylinder is twice of its radius as shown in the figure. So,
V = </span>πr²(2r) = 2πr<span>³
</span>Finally,
1458π = 2πr³
r³ = 729
r = 9 cm
That is the answer. Hope this helps <span>✌️</span>☺️✌️
Answer:
192
Step-by-step explanation:
the length of a leg on a 45-45-90 triangle given the hypotenuse is half the length of the hypotenuse times sqrt(2)
hypotenuse = 10
10/2 =5
so the answer should be 5sqrt(2), which I don't see as a choice
The answer is 80 square meters.
The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.
The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.
After renovations, square garden becomes rectangular.
One side is doubled in length:
a₁ = 2a
The other side is decreased by three meters.
b₁ = a - 3
The new area is 25% than the original square garden:
A₁ = A + 25%A =
= A + 25/100·A
= A + 1/25·A
= a² + 1/25·a²
= <span>a² + 0.25·a²
</span> = 1.25·a²
If the starting equation is:
A₁ = a₁ · b₁
Thus, the equation is:
1.25a² = 2a·(<span>a - 3)
</span>1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a
<span>Therefore, the equation that could be used to determine the length of a side of the original square garden is:
</span><u>2a² - 6a = </u><span><u>1.25a²</u></span>
Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0
From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8
If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80
Therefore, the area of the new rectangle garden is 80 square meters.
