Given that sin(x)
A. 4
B.
11
NEF=
7
11
C. 11
7
D. 11
4
=
7
11'
find cos (90-x).

Answers

Answer 1

The value of cos (90 - x ) = sin (x) = 7/11.

option B.

What is the value of cos (90 - x)?

In trigonometry identity, we know that sin(x) = opposite / hypotenuse. Therefore, we can draw a right triangle with an angle x and opposite side 7 and hypotenuse 11.

Using the Pythagorean theorem, we can find the adjacent side of the triangle:

adjacent² = hypotenuse² - opposite²

adjacent² = 11² - 7²

adjacent² = 120

adjacent = √(120)

adjacent = 2 √(30)

Now, we can use the definition of cosine to find cos(90 - x):

cos(90 - x) = sin(x)

Therefore, cos(90 - x) = 7/11.

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Related Questions

A cylinder fits perfectly inside a box. The width of the cylinder is 3 feet, and the space between
the cylinder and the box is filled with 15 gallons of oil, taking up 75% of the space. What is the
height of the box in feet?

Answers

The height of the box must be at least 2.9111 feet.

Define volume of the cylinder

The volume of the cylinder is given by the formula V = πr²h, where r is the radius of the cylinder and h is its height.

Since the width of the cylinder is 3 feet, the radius is 1.5 feet.

The volume of the oil is 15 gallons, which is equivalent to 0.2 cubic feet. We know that this volume of oil takes up 75% of the space between the cylinder and the box, so the total space between the cylinder and the box is 0.2 / 0.75 = 0.2667 cubic feet.

Since the cylinder fits perfectly inside the box, the volume of the box is equal to the volume of the cylinder plus the space between the cylinder and the box. Therefore, we have:

Volume of box = Volume of cylinder + Volume of oil

Volume of box = πr²h + 0.2667

Substituting the values we have:

Volume of box = π(1.5)²h + 0.2667

Volume of box = 7.0686h + 0.2667

To find the height of the box, we need to isolate h. We know that the volume of the box must be greater than or equal to the volume of the cylinder, so we can set up the inequality:

Volume of box ≥ Volume of cylinder

πr²h + 0.2667 ≥ πr²(3)

h + 0.0889 ≥ 3

h ≥ 2.9111

Therefore, the height of the box must be at least 2.9111 feet.

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Part B What is the recursive formula for the sequence 8, 10, 12.5, 15.625

Answers

Answer:

Step-by-step explanation:

The given sequence can be written as:

a_1 = 8

a_2 = 10

a_3 = 12.5

a_4 = 15.625

To find the recursive formula, we need to find the common ratio (r) between consecutive terms:

r = a_2 / a_1 = 10 / 8 = 1.25

r = a_3 / a_2 = 12.5 / 10 = 1.25

r = a_4 / a_3 = 15.625 / 12.5 = 1.25

Since the common ratio is constant, we can use the formula for a geometric sequence to find the recursive formula:

a_n = r * a_{n-1}

Substituting r = 1.25 and a_1 = 8, we get:

a_n = 1.25 * a_{n-1}

Therefore, the recursive formula for the given sequence is:

a_n = 1.25 * a_{n-1}, with a_1 = 8.

A 5 m ladder reaches 4.7 m up a wall. What angle does the ladder make with the wall?

Answers

The ladder makes an angle of approximately 19.94 degrees with the wall.

Calculating the angle of the ladder up on the wall

We can use trigonometry to solve for the angle between the ladder and the wall.

Let's call the angle we're looking for "theta" (θ). We can use the cosine function, which is defined as the ratio of the length of the adjacent side to the length of the hypotenuse side of a right triangle, to solve for theta:

cos(θ) = opposite/adjacent

So we have:

cos(θ) = 4.7/5

We can use a calculator to solve for theta:

cos(θ) = 0.94

Take the arc cos

θ ≈ 19.94 degrees

Therefore, the ladder makes an angle of approximately 19.94 degrees with the wall.

Answers

The correct inequality that represents the statement "One half of a number decreased by 3 is at most -5" is option C) x ≤ -4.

What is an inequality?

Let's start by defining a variable for the number we are trying to find. Let's call it "x".

"One half of a number" can be represented as (1/2)x.

"Decreased by 3" means we need to subtract 3 from (1/2)x. So, "one half of a number decreased by 3" can be represented as:

(1/2)x - 3

Now, the problem says that this expression is "at most -5". "At most" means that the expression can be equal to -5 or any number less than -5. We can represent this as:

(1/2)x - 3 ≤ -5

To simplify this inequality, let's add 3 to both sides:

(1/2)x ≤ -2

Multiplying both sides by 2 (to eliminate the fraction) gives:

x ≤ -4

Therefore, the correct inequality that represents the statement "One half of a number decreased by 3 is at most -5" is option C) x ≤ -4.

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16. Find the difference 4/9 - ⅖

17. Find the quotient 2/9 / ⅚

18. Write each terminating decimal as a quotient of integers. (a) 0.437 (b) 8.2

19. Use the method below to decide whether each rational number would yield a repeating or a terminating decimal.
(Hint: Write in lowest terms before trying to decide.)

Terminating decimal - if the only prime factor of the denominator is 2 or 5 or both.
Repeating decimal - if a prime other than 2 or 5 appears in the prime factorization of the denominator.
Example: 24/75 can be simplified to 8/25 by dividing 3 into both the numerator and the denominator. Next, factor the denominator 25 using prime factors: 25 = 5x5, the only prime factor of the denominator is 5 in this case, so the original fraction is a Terminating decimal
(a) 8/15
Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(b) 8/35 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(c) 13/125 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(d) 3/24 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(e) 22/55 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

(f)) 24/75 Is the fraction simplified? (Yes/No) If not, simplify the fraction.
Does the simplified denominator contain factors other than 2 or 5? (Yes/No)
Is it a terminating or repeating decimal? (Terminating/Repeating)

Answers

1 ) Finding the difference 4/9 - ⅖:

We require a common denominator to subtract fractions. The least frequent multiple of 9 and 5 in this example is 45. So we'll recast both fractions with 45 as the denominator:

[tex]\frac{4}{9} = \frac{20}{45} \\\frac{2}{5} = \frac{18}{45}[/tex]

Now we can subtract:

[tex]\frac{20}{45} - \frac{18}{45} = \frac{2}{45}[/tex]

Therefore, the difference between 4/9 and ⅖ is 2/45.

How will you find if the fraction is terminating or repeating?

Examine the prime factors of the denominator when the fraction is in its simplest elementary form to determine if it will have a terminating or repeating decimal. The decimal will end if they are made up of 2s and/or 5s.

2) calculating the quotient 2/9 / ⅚:

Fractions are divided by multiplying the first fraction by the reciprocal of the second fraction. So:

2/9 ÷ ⅚ = 2/9 x 6/5

Before multiplying, we can simplify:

2/9 x 6/5 = 12/45

And here's another example:

12/45 = 4/15

As a result, the quotient of 2/9 56 is 4/15.

3) Writing each terminating decimal as an integer quotient:

(a) 0.437 = 437/1000

(b) 8.2 = 82/10 = 41/5

4) Choosing whether each rational number will result in a repeated or terminating decimal:

(a) 8/15