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2 years ago

Find the length of the longest object that will fit inside a cylinder that has a radius of 3.25 inches and is 7 inches high.

Mathematics

1 answer:

ra1l [238]2 years ago

6 0

Answer:

9.5 inches

Step-by-step explanation:

The Pythagorean theorem can be used to find the length of the longest linear object of small dimensions that will fit across the space diagonal of the cylinder. The relevant length is that of the hypotenuse of a triangle whose legs are the diameter and height of the cylinder.

... length² = (3.25×2)² +7² = 91.25

... length = √91.25 ≈ 9.55249 ≈ 9.5 . . . inches

_____

Ordinarily, such a number would be rounded up, but that longer length will not fit. Hence it is appropriate to round the number down.

If the object can be curled up, more than 3.2 billion miles of DNA molecule would fit in the space.

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A shop sells sweets where every 3 sweet wrappers can be exchanged for one more sweet. Kelvin has enough money to buy only 19 swe

drek231 [11]

Answer:

Kelvin can get 6 free sweets

6 0

1 year ago

The number of households without a computer at home in 2009 was closest to A)801000 B)1153000 C)1737000 D)3433000 E)4017000

bagirrra123 [75]

Answer:

B) 1153000

Step-by-step explanation:

Given

See attachment

Required

Number of households without computer in 2009

From the attachment, we have:

$n=5170000$ --- survey

$p = 22.3\%$ --- proportion without computer

So, the actual number is:

$Number = p * n$

$Number = 22.3\% * 5170000$

$Number = 1152910$

$Number \approx 1153000$

<em>Hence: (B) is correct</em>

7 0

2 years ago

A parabola with the vertex at (1.5, 12.5) inscribes a segment of length 5 on x-axis. What is the area of the triangle formed by

damaskus [11]

Answer:

20 units²

Step-by-step explanation:

The x-intercepts are symmetrically located around the x-coordinate of the vertex, so are at

1.5 ± 5/2 = {-1, 4}

Using one of these we can find the unknown parameter "a" in the parabola's equation (in vertex form) ...

0 = a(4 -1.5)² +12.5

0 = 6.25a +12.5 . . . . . simplify

0 = a +2 . . . . . . . . . . . divide by 6.25

-2 = a

Then the standard-form equation of the parabola is ...

y = -2(x -1.5)² +12.5 = -2(x² -3x +2.25) +12.5

y = -2x² +6x +8

This tells us the y-intercept is 8. Then the relevant triangle has a base of 5 units and a height of 8. Its area is given by the formula ...

A = (1/2)bh = (1/2)(5)(8) = 20 . . . . units²

5 0

2 years ago

write a slope intercept equation for a line passing through the point (2,-2) that is parallel and perpendicular to the line x=-1

vekshin1

You would need two different lines to complete this as lines cannot be both parallel and perpendicular (these are opposites). The answers would be:

Parallel: x = 2

Perpendicular: y = -2

In order to find these, we first need to see that the original line of x = -1 is a horizontal line. Therefore, any line that is parallel should be horizontal as well. To get a horizontal line through the point (2, -2), the only option is x = 2.

Similarly, with the perpendicular line, if the original line is horizontal, the new line must be vertical. The only vertical line that goes through (2, -2) is y = -2.

5 0

2 years ago

What is the solution for the system of equations {4x−3y=36x−2y=4?

dimaraw [331]

Answer:

x = 1/25

y = 32/25

Step-by-step explanation:

3 0

2 years ago