Step-by-step explanation:
the volume of any pyramid is
base area × height / 3
so, since we know the base area (a square with 23 mm side length), the only trick we need to do is to get the inner height (straight up in the middle from the base area to the top of the pyramid).
because this is a regular pyramid (the top of the pyramid is right above the middle of the base area), we can use Pythagoras for right-angled triangles
c² = a² + b²
with c being the Hypotenuse (the baseline of the triangle opposite of the 90° angle) and in our case the outer height along a side area triangle (24 mm).
the legs of that right-angled triangle are half of a base area side length (remember, the top of the pyramid is right over the middle of the base area square) and the inner height to the top.
so, we have
24² = 12.5² + height²
height² = 24² - 12.5² = 576 - 156.25 = 419.75
height = 20.48780125... mm
so, the volume of the pyramid is then
23² × 20.48780125... / 3 = 3,612.682287... mm³ ≈
≈ 3,612.7 mm³
The slope is (8-2)/(0-2)=-3
the y intercept is 8
the equation is y=-3x+8
the area to the left is shaded, and the line is solid, so y
-3x+8
Answer:
10
Step-by-step explanation:
sadasdasdasd
Answer:
18
Step-by-step explanation:
Remark
This is one of those questions that can throw you. The problem is that do you include the original rectangle or not. The way it is written it sounds like you shouldn't
However if you don't the question gives you 2 complex answers. (answers with the sqrt( - 1) in them.
Solution
Let the width = x
Let the length = x + 5
Area of the rectangle: L * w = x * (x + 5)
Area of the smaller squares (there are 2)
Area = 2*s^2
x = s
Area = 2 * x^2
Area of the larger squares = 2 * (x+5)^2
Total Area
x*(x + 5) + 2x^2 + 2(x + 5)^2 = 120 Expand
x^2 + 5x + 2x^2 + 2(x^2 + 10x + 25) = 120 Remove the brackets
x^2 + 5x + 2x^2 + 2x^2 + 20x + 50 = 120 collect the like terms on the left
5x^2 + 25x + 50 = 120 Subtract 120 from both sides.
5x^2 + 25x - 70 = 0 Divide through by 5
x^2 + 5x - 14 = 0 Factor
(x + 7)(x - 2) = 0 x + 7 has no meaning
x - 2 = 0
x = 2
Perimeter
P = 2*w + 2*L
w = 2
L = 2 + 5
L = 7
P = 2*2 + 2 * 7
P = 4 + 14
P = 18
6035 =
6000 + 30 + 5
So I would say 3's value is tenths.
