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3 years ago

Evaluate the expression for the given value of the variable. d=75 2d+−45d−−−−−√3=

Mathematics

1 answer:

Ahat [919]3 years ago

3 0

Answer:

The expression for the given value of the variable d=75 is, 135

Step-by-step explanation:

Given the expression:

$2d+\sqrt[3]{-45d}$ ....[1]

We have to find the value for the given expression when d = 75

Substitute the value of d in [1] we have

$2(75)+\sqrt[3]{-45(75)}$

⇒ $150+\sqrt[3]{-3375}$

⇒ $150-15$

Simplify:

⇒ $135$

Therefore, the expression for the given value of the variable d=75 is, 135

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Exercise 1: The length of the unknown leg is 4 inches.

Exercise 3: The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

Step-by-step explanation:

Exercise 1:

Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:

$y = \sqrt{l^{2}-x^{2}}$ (1)

Where:

$l$ - Hypotenuse, in inches.

$x$ - Known leg, in inches.

$y$ - Unknown leg, in inches.

If we know that $l = 11\,in$ and $x = 10\,in$ , then the length of the unknown leg is:

$y = \sqrt{21}$

Since 4 is the least whole number closest to $\sqrt{21}$ , then we conclude that the length of the unknown leg is 4 inches.

Exercise 3:

The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:

$x + y > l > x-y$ (2)

Where:

$x$ - Greater side, in inches.

$y$ - Lesser side, in inches.

$l$ - Missing side, in inches.

If we know that $x = 8\,in$ and $y = 6\,in$ , then we have the following range of missing sides:

$14\,in > l > 2\,in$

The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

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Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:

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Possible choices: 4 inches, 6 inches.

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Possible choices: 5 inches, 6 inches.

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Possible choices: 5 inches.

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Possible choices: None.

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Possible choices: 5 inches.

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Nitella [24]

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I will assume this is a rectangular prism since it isn't specified.

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That is the definition of a irrational number, A rational number must be able to be written as a ratio of 2 integers. The denominator cannot be 0, because that would make the number undefined

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