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3 years ago

9. Evaluate the ceiling function for the given value.

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

8 0

Given:

A. f(x) = ⌈x⌉; x = −7.4

B. g(x) = ceiling (x, 0.50); x = 21.27

To find:

The values of ceiling function for the given value.

Solution:

We have,

f(x) = ⌈x⌉; x = −7.4

Here, f(x) is a ceiling function, so we need to find the nearest next integer value because if m < x ≤ n, then ⌈x⌉ = n, where m and n are integers.

Now,

f(-7.4) = ⌈-7.4⌉

f(-7.4) = -7

Therefore, the value of f(x) is -7 at x=-7.4.

g(x) = ceiling (x, 0.50); x = 21.27

Here, g(x) is a ceiling function with 0.50, so we need to find the nearest next multiple of 0.50 because if m < x ≤ n, then ⌈x⌉ = n, where, m and n are multiples of 0.50.

Now,

g(21.27) = ceiling (21.27, 0.50)

g(21.27) = 21.50

Therefore, the value of g(x) is 21.50 at x=21.27.

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ANSWER FAST ITS URGENT

Vlad1618 [11]

Answer:

9) 6.3 units

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10) m=6√3, n=6

12) 330.6 ft

Step-by-step explanation:

1) The Pythagoras Theorem says that, the square of the hypotenuse is the sum of the squares of the two shorter legs.

Let the missing side, which is the hypotenuse be x.

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${x}^{2} = {2}^{2} + {6}^{2}$

${x}^{2} = 4 + 36$

${x}^{2} = 40$

$x = \sqrt{40}$

$x = 6.3$

The missing side is 6.3 units to the nearest tenth.

2) This is an isosceles right triangle.

This implies that, the two legs are equal.

$n = 6 \sqrt{2}$

The hypotenuse can be found using Pythagoras Theorem.

${m}^{2} = {(6 \sqrt{2} )}^{2} + {(6 \sqrt{2} )}^{2}$

${m}^{2} = 36(4)$

$m = \sqrt{36 \times 4} = 6 \times 2 = 12$

3) The side lengths of 30°-60°-90° are in the ratio, 2x,x√3,x

From the diagram, the hypotenuse is 12, therefore the other two legs are

$n = \frac{1}{2} (12) = 6$

and

$m = 6 \sqrt{3}$

4) The height of the monument is 115 feet, the hypotenuse is 350.

By Pythagoras Theorem,

${x}^{2} + {115}^{2} = {350}^{2}$

${x}^{2} = {350}^{2} - {115}^{2}$

${x}^{2} = 109275$

$x = \sqrt{109275} = 330.6 ft$

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What is the area of this polygon?

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Another name for 23 ten thousand is: Two hundred thirty thousand

And another name also is: 230 Thousands

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