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lawyer [7]
3 years ago
14

This visual representation shows the sets of real numbers. Classify the number −85. Select all terms that are correct. Venn diag

ram with outer loop labeled capital R, Real Numbers. Inside that loop is another loop divided into two parts. The right part is labeled capital I, Irrational Numbers. The left part is labeled capital Q, Rational Numbers. A loop inside the rational numbers loop is labeled capital Z, Integers. A loop inside the integers loop is labeled capital W, Whole Numbers. A loop inside the whole numbers loop is labeled N, Natural Numbers. Select 2 correct answer(s) Question 6 options: Rational Whole Natural Integer Irrational
Mathematics
1 answer:
Olenka [21]3 years ago
7 0

♡ The Question/Task ♡          

Classify the number -85.

Rational, Whole, Natural, Integer, Irrational.  

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*              

♡ The Answer ♡          

-85 is an integer, and a rational number!

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*              

♡ The Explanation/Step-By-Step ♡          

Natural numbers are <u>positive integers</u> from 1 till infinity, though, nautral numbers don't include zero. Since -85 is a negative number, this wouldn't be a natural number.

A whole number is a set of numbers including <u>all positive integers and 0.</u> Since -85 isn't a positive number, this wouldn't be a whole number.

An irrational number is where any real number that cannot be expressed as the quotient of two integers. Irrational numbers are commonly square roots, too. Although, -85 isn't a square root.

A rational number is where any number that can be written as a ratio, or a fraction, of two integers can be classified as a rational number. Rational numbers are commonly fractions, decimals, negative decimals, etc!

An integer is a whole number that can be positive, negative, or zero. 85 is a whole number, and can be negative, which in this case, is -85. The number we're using. Therefore, -85 is an integer.  

*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*              

♡ Tips ♡          

-No Tips Provided!

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1. Consider the right triangle ABC given below.
lbvjy [14]
#1) 
A) b = 10.57
B) a = 22.66; the different methods are shown below.
#2)
A) Let a = the side opposite the 15° angle; a = 1.35.
Let B = the angle opposite the side marked 4; m∠B = 50.07°.
Let C = the angle opposite the side marked 3; m∠C = 114.93°.
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Explanation
#1)
A) We know that the sine ratio is opposite/hypotenuse.  The side opposite the 25° angle is b, and the hypotenuse is 25:
sin 25 = b/25

Multiply both sides by 25:
25*sin 25 = (b/25)*25
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B) The first way we can find a is using the Pythagorean theorem.  In Part A above, we found the length of b, the other leg of the triangle, and we know the measure of the hypotenuse:
a²+(10.57)² = 25²
a²+111.7249 = 625

Subtract 111.7249 from both sides:
a²+111.7249 - 111.7249 = 625 - 111.7249
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Take the square root of both sides:
√a² = √513.2751
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The second way is using the cosine ratio, adjacent/hypotenuse.  Side a is adjacent to the 25° angle, and the hypotenuse is 25:
cos 25 = a/25

Multiply both sides by 25:
25*cos 25 = (a/25)*25
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The third way is using the other angle.  First, find the measure of angle A by subtracting the other two angles from 180:
m∠A = 180-(90+25) = 180-115 = 65°

Side a is opposite ∠A; opposite/hypotenuse is the sine ratio:
a/25 = sin 65

Multiply both sides by 25:
(a/25)*25 = 25*sin 65
a = 25*sin 65
a = 22.66

#2)
A) Let side a be the one across from the 15° angle.  This would make the 15° angle ∠A.  We will define b as the side marked 4 and c as the side marked 3.  We will use the law of cosines:
a² = b²+c²-2bc cos A
a² = 4²+3²-2(4)(3)cos 15
a² = 16+9-24cos 15
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Take the square root of both sides:
√a² = √1.82
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Use the law of sines to find m∠B:
sin A/a = sin B/b
sin 15/1.35 = sin B/4

Cross multiply:
4*sin 15 = 1.35*sin B

Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin B)/1.35
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Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin B)
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Subtract both known angles from 180 to find m∠C:
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B)  Use the law of sines to find side b:
sin C/c = sin B/b
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Cross multiply:
b*sin 52 = 12*sin 45

Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
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Find m∠A by subtracting both known angles from 180:
180-(52+45) = 180-97 = 83°

Use the law of sines to find side a:
sin C/c = sin A/a
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Cross multiply:
a*sin 52 = 12*sin 83

Divide both sides by sin 52:
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Answer:

See verification below

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To obtain the required form, extract a factor in both the numerator and denominator:

\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)

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