Unit 8: Right Triangles & Trigonometry
Homework 4: Trigonometric Ratios &
Finding Missing Sides

The volume of the stone is 1032 cm³.

The volume of the stone can be calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 2.7 cm. Therefore, the volume of the stone is V = 10 x 24 x 2.7 = 648 cm³.

The volume of the water in the container is calculated using the formula V = lwh. Here, l = 10 cm, w = 24 cm, and h = 7 cm. Therefore, the volume of the water in the container is V = 10 x 24 x 7 = 1680 cm³.

The difference between the volume of the water and the volume of the stone is the volume of the water displaced by the stone, which is V = 1680 - 648 = 1032 cm³. Therefore, the volume of the stone is 1032 cm³.

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Answer:

B linear

Step-by-step explanation:

If the rate of change stayed the same then it has to be a straight line so no C or D, and it cant be A be cause there is a rate of change.

Answer : There are 84 different ways that six letters can be grouped from nine letters total.

Now that we have determined that the problem deals with combinations, we can use the formula for combinations to calculate the number of ways that six letters can be grouped from nine letters total. The formula for combinations is:

C(n,k) = n! / (k! * (n-k)!)

Where n is the total number of items, and k is the number of items being chosen. In this case, n = 9 and k = 6. Plugging these values into the formula gives us:

C(9,6) = 9! / (6! * (9-6)!)

C(9,6) = 9! / (6! * 3!)

C(9,6) = 362880 / (720 * 6)

C(9,6) = 362880 / 4320

C(9,6) = 84

Therefore, there are 84 different ways that six letters can be grouped from nine letters total.

Answer: 84.

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The answer is in the attachment given below ...

Thank you :)

By answering the above question, we may state that Multiplying these equation prime factorizations together, we get:

[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]

A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.

then multiply the prime factors together using the laws of exponents.

[tex]12^9 = (2^2 · 3)^9 = 2^18 · 3^9\\36^15 = (2^2 · 3^2)^15 = 2^30 · 3^30\\169^8 = 13^16\\12^9 · 36^15 · 169^8 = (2^18 · 3^9) · (2^30 · 3^30) · 13^16 = 2^48 · 3^39 · 13^16\\[/tex]

(b)

[tex]16^13 = 2^52\\10^7 = 2^7 · 5^7\\81^18 = (3^4)^18 = 3^72\\[/tex]

Multiplying these prime factorizations together, we get:

[tex]16^13 * 10^7 * 81^18 = (2^52) * (2^7 * 5^7) * (3^72) = 2^59 * 3^72 * 5^7[/tex]

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a) The basic formula is [tex]y=v_0t-gt^2/2[/tex]

[tex]9.81m/sec^2 x \ t^2 - (14 m/sec x t) - 60m = 0[/tex]

quadratic equation t= -b+/- √b^2-4ac /2a

t= 14+- √(-14)^2 -4(4.905)(-60)/ 2(4.905) = 5.20 sec

b) [tex]y=v_0t-gt^2/2[/tex]

At max height H, [tex]V_y = 0[/tex]

[tex]Vy^2 = V^2_{0y} - 2g(y-y_0)[/tex]

[tex]0=(14)^2 -2(9.81)(H-60)[/tex]

[tex]H=70m[/tex]

The ball would fall 10m from max height of 70m. set y=0 and H=10m

[tex]y=gt^2/2+H, t = 1.42 \ sec[/tex].

[tex]\bold{Therefore, 5.2 - 1.42 = 3.77 \ sec}[/tex]

The real cube root of 64 is 4.

The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.

the prime factorization using the exponent found in the previous step. We can write the number 64 as:

64 = 2^2 * 2^2 * 2^2

Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:

∛2 = 1.259921...

Step 5: Multiply the factors together to get the final result:

∛64 = ∛(2^2 * 2^2 * 2^2) = ∛2^6 = (∛2)^2 = 1.259921...^2 = 4

Therefore, the real cube root of 64 is 4.

On the other hand we can easily find out by, the real cube root of 64 is 4, because 4 multiplied by itself three times gives 64:

4 * 4 * 4 = 64

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The real cube root of 64 is 4.

What is a Real cube root?

The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.

the prime factorization using the exponent found in the previous step. We can write the number 64 as:

64 = 2² * 2² * 2²

Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:

∛2 = 1.259921...

Step 5: Multiply the factors together to get the final result:

∛64 = ∛(2² * 2² * 2²) = ∛2⁶ = (∛2)² = (1.259921...)² = 4

Therefore, the real cube root of 64 is 4.

On the other hand, we can easily find out by, the real cube root of 64 is 4 because 4 multiplied by itself three times gives 64:

4 * 4 * 4 = 64

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Answer:

P(odd or at most 14)

Answer: (a) 7/27, 0.2593, 25.93%

P(king)

Answer: (d) 13/52

P(spade or heart)

Answer: (b) 1/2

Answer:

115.50

Step-by-step explanation:

Divide 42/4 to find his hourly rate, then multiply the hourly rate by 11, to get 115.50

Answer:

$115.05

Step-by-step explanation:

If he earns $42 in 4 hours than he earns $10.05 in 1 hour

42 / 4 = 10.5

10.5 x 11 = 115.5

The probability of all the defendants being found guilty is 1/16. Answer: 1/16.

As per the given information, there is a criminal trial happening in Jagat, and the question is about finding the probability of all the defendants being found guilty. Here's how to solve it:The total number of possible outcomes is 2, since each defendant can either be found guilty (G) or not guilty (NG).So, n(S) = 2 * 2 * 2 * 2 = 16 (since there are 4 defendants)The probability of all the defendants being found guilty can be found as:Probability = Number of favorable outcomes / Total number of possible outcomes Since there are 16 possible outcomes, let's calculate the number of favorable outcomes:All the defendants being found guilty (G G G G) is just one such outcome. Hence, the number of favorable outcomes is 1.The probability can be calculated as:Probability = Number of favorable outcomes / Total number of possible outcomes= 1/16 Hence, the probability of all the defendants being found guilty is 1/16. Answer: 1/16.

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The correct statement is a=b implies that ac=bc.

If the real numbers a and b are such that a=b, then their values are equal.

The result of adding c to both sides of the formula a=b is:

a+c = b+c

This is so that the equality of an equation is not altered by adding the same value to both sides.

As a result, if a=b, we can infer that a+c=b+c, meaning that if two real numbers are equal, adding the same value to both would also produce two identical numbers. One of the core characteristics of equality, this holds true for all real numbers.

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The answer will be as follows after answering the supplied question As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is the location of one of the points and m is the line's slope.

We may use the slope formula to calculate the slope:

m = (y2 - y1) / (x2 - x1) (x2 - x1)

where the coordinates of the two points are (x1, y1) and (x2, y2).

m = (5 - (-3)) / (3 - (-1)) = 8 / 4 = 2

As a result, the slope of the line is 2. We can now use one of the two locations to get the equation of the line. Let's take (-1, -3) as an example:

y - (-3) = 2(x - (-1))

y + 3 = 2(x + 1)

y + 3 = 2x + 2

y = 2x - 1

As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.

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Answer:

(3h+4)(2h+3)

Step-by-step explanation:

6h^2 + 8h + 9h + 12h

(6h^2+8h) + (9h+12h)

2h(3h+4) + 3(3h+4)

(3h+4)(2h+3)

Answer:

(3h+4) (2h+3)

Step-by-step explanation:

i hope this helps

Answer: Answers below

Step-by-step explanation:

1. $15.64

2. 5370.28 Yen

3. 13425.70 Yen

4. $100

5. 67128.51 Yen

6.$782.08

Answer: 1: 15 2: 5370 3:13400 4: 160 5: 67100 6: 780

Step-by-step explanation: These are rounded to the nearest 100th

The increase in the rate of unemployment from 2000 to 2001, given the unemployment figure is between D. 0. 46 % and 0. 49 %.

First, find the rate of unemployment in 2000 to be :

= Unemployment number / Total labor force x 100 %

= 3, 503, 917 / 25, 554, 417  x 100 %

= 13.71  %

The rate of unemployment in 2001 was :

= 3, 745, 300 / 26, 416, 800 x 100 %

= 14. 18 %

The increase in the rate of unemployment is:

= 14. 18 - 13. 71

= 0. 47 %

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Answer:

    m∠4 = 133°

Step-by-step explanation:

Given m∠7 = 37°

Since m∠7 ≅ m∠6 [Vertically opposite angles]

and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]

Therefore, 47°+ m∠4 = 180°

m∠4 = 180 - 47

       = 133°

Answer:

8.09017

calculations

The solution to the differential equation is:

$$v(t)=\frac{V_0+kCe^{-Ct}}{1+kCe^{-Ct}}$$
Where $V_0$ is the initial velocity and $C$ is the proportionality constant. The limiting velocity of the falling body as $t \to \infty$ is: $$v_{\infty}=\frac{V_0}{1+kC}$$

The instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t: v ( t ) = d d t x ( t ) . v ( t ) = d d t x ( t ) . Like average velocity, instantaneous velocity is a vector with dimension of length per time.

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As a result, the right triangle x value of 65° is the answer to the given triangle issue.

Triangles are categorised as polygons because they have four edges or more. Its shape is simple and symmetrical. The characters ABC make a square angle that is a triangle. When the edges are still not collinear, Euclidean geometry yields a single rectangle or square. Due to their three edges and three corners, triangles are considered polygons. The corners of a triangle are where its three edges meet. Angles in a trapezoid add up to 360 °.

Here,

Given:

Triangle is 90 degrees because of its right orientation.

The total of the triangle's angles is 180 degrees.

Thus,

=> x + 25° + 90° = 180°

=> x + 115° = 180°

=> x = 180° -115°

=> x = 65°

Thus, the value of x is 65°.

As a result, the answer to the provided triangle problem is

Right triangle's x number is 65 degrees.

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On answering the provided question, we have got that 3.3 is the average  equation result after rolling the dice ten times.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

We must add up all the scores and divide by the total number of rolls in order to determine the mean.

The total of every score is:

1 + 1 + 2 + 2 + 3 + 1 + 4 + 2 + 5 + 4 + 6 + 2 = 33

There are ten rolls in total.

The mean is as a result:

mean = total scores / total rolls = 33 / 10 = 3.3

3.3 is the average result after rolling the dice ten times.

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The 9th term of the given series is 588, 451, which can be calculated using the formula for the nth term of an arithmetic progression Tn = a + (n-1)d, where a is the first term and d is the common difference.

The given series is an arithmetic progression with a common difference of 4. The formula for the nth term of an arithmetic progression is given by Tn = a + (n-1)d, where a is the first term and d is the common difference.

Therefore, for the given series, a = 1 and d = 4.

Substituting these values in the above formula, we get

T9 = 1 + (9-1)4

 = 1 + 32

 = 33

Now, adding 33 to each of the terms of the given series, we get

1 + 33 = 34

5 + 33 = 38

25 + 33 = 58

125 + 33 = 158

Therefore, the required 9th term of the series is 588, 451.

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The volume of the coffee can rounded to the nearest 10th of a decimal place is 226. 08 cubic inches

It is important to note that the coffee can takes the shape of a cylinder.

The formula for calculating the volume of a cylinder is expressed with the equation;

V = πr²h

This is so as the parameters are enumerated thus;

Also, r = diameter/2 = 6/2 = 3 inches

From the information given, we have that;

Volume = 3.14 × (3)² × 8

Multiply the values

Volume = 226. 08 cubic inches

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Answer:

I guess the value be 26x

hope it helps u

mark me brainlist

Answer:

The first five natural number are 1, 2, 3, 4 and 5. Hence, the mean of the five natural numbers is 3.

Answer:

3

Step-by-step explanation:

[tex]\frac{1+2+3+4+5}{5}[/tex] =  [tex]\frac{15}{5}[/tex] = 3

The natural numbers are also called the counting numbers.  They are the set of numbers: 1, 2, 3, ....

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

[tex]a)\quad AB[/tex]

[tex]b)\quad AB[/tex]

[tex]c)\quad AC[/tex]

[tex]d)\quad BC[/tex]

[tex]e)\quad BC[/tex]

[tex]f)\quad AC[/tex]

Answer:   8x + 6y = $56.50

Step-by-step explanation:

I think this is right!

Answer:

B. [tex]\sqrt[3]{-x-9}[/tex]

Step-by-step explanation:

Switch x and y, and then solve for y.

[tex]y = -x^3-9\\x=-y^3-9\\x+9=-y^3\\-x-9=y^3\\\sqrt[3]{-x-9} =y[/tex]

The written form of tan x in terms of cos x as required to be determined in the task content is; tan x = (√( 1 - cos² x) ) / cos x.

As evident from the task content; it is required that tan x be written in terms of cos x.

Hence, recall from trigonometric identities that;

tan x = sin x / cos x

However, since sin² x = 1 - cos² x from ( sin²x + cos²x = 1)

It follows that; sin x = √( 1 - cos² x)

Hence, it can be written that;

tan x = (√( 1 - cos² x ) ) / cos x.

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Liam saved $192.05 from his summer jobs.

It is based on the probability that something will happen. The fundamental underpinning of theoretical probability is the justification for probability. For instance, while flipping a coin, there is a 50% probability that it will land on its head.

By deducting his outgoings from his total earnings, we can calculate how much money Liam saved:

m = 328.65 - 136.60

Condensing the phrase:

m = 192.05

Liam was able to save $192.05 as a result of his summer jobs.

The following equation and its answer demonstrate how much money Liam has saved:

m = 328.65 - 136.60

m = 192.05

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