Given that a cylinder has a height of 6 meters and a diameter that is 6 times the measure of the height, to determine, using 3.14 for pi, which of the following can be used to calculate the volume of the cylinder, the following calculation must be done, knowing that the volume of a cylinder is determined by multiplying Pi by the height by the radius squared, and that the diameter of a circle is twice its radius:

3.14 x 6 x (6x3) ^ 2 = X

18.84 x 18 ^ 2 = X

18.84 x 324 = X

6,104.16 = X

Therefore, the volume of the cylinder is 6,104.16 square meters.

3 0

3 years ago

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find the value of "a" and "b" for which the limit exists both as x approaches 1 and as x approaches 2:

lbvjy [14]

Answer:

a = 4

b = -2

Step-by-step explanation:

If the given function is continuous at x = 1

$\lim_{x \to 1^{-}} f(x)=(x+1)$

$=2$

$\lim_{x \to 1^{+}} f(x)=ax+b$

$=a+b$

$\lim_{x \to 1} f(x)=ax+b$

$=a+b$

And for the continuity of the function at x = 1,

$\lim_{x \to 1^{-}} f(x)=\lim_{x \to 1^{+}} f(x)=\lim_{x \to 1} f(x)$

Therefore, (a + b) = 2 -------(1)

If the function 'f' is continuous at x = 2,

$\lim_{x \to 2^{-}} f(x)=ax+b$

$=2a+b$

$\lim_{x \to 2^{+}} f(x)=3x$

$=6$

$\lim_{x \to 2} f(x)=3x$

$=6$

Therefore, $\lim_{x \to 2^{-}} f(x)=\lim_{x \to 2^{+}} f(x)=\lim_{x \to 2} f(x)$

2a + b = 6 -----(2)

Subtract equation (1) from (2),

(2a + b) - (a + b) = 6 - 2

a = 4

From equation (1),

4 + b = 2

b = -2

3 0

3 years ago

A child is laying on the ground relaxing and looking up at a plane that is passing by. If the plane’s altitude is 33,500 feet an

murzikaleks [220]

Answer:

about 76.2°

Step-by-step explanation:

The geometry can be modeled by a right triangle with the given dimensions being the side opposite the angle (height = 33,500 ft) and the side adjacent to the angle (8,200 ft). The fact that you know these two sides suggests the inverse of the tangent function may be useful.

Tan = Opposite/Adjacent

tan(angle) = (33,500/8,200)

angle = arctan (335/82) ≈ 76.246°

The angle of elevation is about 76.2°.

3 0

3 years ago