<span>Each penny is 0.75 inches in diameter
0.061 inches thick
If pennies has a diameter of 6 inches and a height of 11.5 inches
Cylinder: Diameter-6 in/ Height 11.5 in
V=3.14(r²)h
3.14(3²) (11.5)
3.14*9 (11.5)
Volume=324.99
Pennies
Diameter-0.75 in/ Height .061
V=3.14(r²)h
3.14(.375²)(0.061)
3.14*.140625 (.061)
4415625*.061
Volume=0.0269353125
324.99/0.0269353125= 12,065
pennies(approximately)
12,065 Pennies can fit in the cylinder
hope this helps</span>
Answer:
D
Step-by-step explanation:
It’s correct
Step-by-step explanation:
Let √x - 1/√x = a
Squaring both the sides,
x + 1/x - 2 = a^2
Putting the value,
3–2√2 + 1/(3–2√2) - 2 = a^2
a^2 = 1 - 2√2 + 1/(3–2√2)
= [(3–2√2) (1–2√2) + 1] / 3–2√2
= {3 - 8√2 + 9} / 3–2√2
= [12 - 8√2] / 3–2√2
Rationalising both the sides
= {(12 - 8√2)(3+2√2)} ÷ (9–8)
= 36 + 24√2 - 24√2 + 16(2)
= 36 - 32
=> 4
a^2 = 4
a = √4
a = 2, -2
So,
√x - 1/√x = a = 2, -2.
Answer:
(4,3)
Step-by-step explanation:
The orthocenter of a triangle is the point of intersection of the altitudes of the triangle .
The vertices are:
A(-2,5), B(6,5), and C(4,-1)
Slope of (6,5), and (4,-1) is
Slope of altitude through A is
The equation of the altitude through A is
The slope of A(-2,5), B(6,5) is zero because it is a horizontal line.
The equation of altitude through (4,-1) will be the vertical line x=4.
This implies that,
Hence the orthocenter is (4,3)
The area here is 2 triangles and 3 rectangularso the total area is the sum of all areas area of triangle = 0.5 * base * height = 0.5 * 4 * 3 = 6 ft^2 the area of the rectangular 1 = 5 * 7 = 35 ft^2 the area of rectangular 2 = 4 * 7 = 28 ft^2 the area of rectangular 3 = 3 * 7 = 21 ft^2 so the total surface area = 2(6) + 35 + 28 + 21 = 96 ft^2