Trigonometry (Law of Sines)

Answer:

b.

Step-by-step explanation:

the result is created :

first result row first result element =

= first A row × first B column

first result row second result element =

= first A row × second B column

...

third result row second result element =

= third A row × second B column

third result row third result element =

= third A row × third B column

the multiplication of a row and a column is done by :

left row element × top column element +

middle row element × middle column element +

right row element × bottom column element

AB =

-4×3 + -3×-5 + 5×-1 -4×-4 + -3×-5 + 5×-3 -4×-1 + -3×1 + 5×2

-5×3 + -4×-5 + -2×-1 -5×-4 + -4×-5 + -2×-3 -5×-1 + -4×1 + -2×2

-1×3 + -2×-5 + -4×-1 -1×-4 + -2×-5 + -4×-3 -1×-1 + -2×1 + -4×2

=

-2 16 11

7 46 -3

11 26 -9

so, b is correct.

Answer:

t = I/(Pr)

Step-by-step explanation:

We divide P*r on both sides to isolate t and we get t=I/(P*r)

The equation of the line in slope intercept form is  y = - 1 / 2 x - 8.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Let's find the slope of the line before we can find the equation of the line.

The slope is the change in the dependent variable with respect to the change in the independent variable.

Hence,

m = y₂ - y₁ / x₂ - x₁

Therefore,

(0, -8)(-2, -7)

Hence,

slope = m = -7  + 8 / -2 - 0

m = 1  / -2

m = - 1 / 2

The y-intercept is -8.

Therefore, the equation of the line is y = - 1 / 2 x - 8.

learn more on slope intercept form here:https://brainly.com/question/14074784

#SPJ1

Answer:

Yeah, [tex] \sf b = 12 [/tex]

Step-by-step explanation:

Given equation,

→ b - 7 = 5

Now the value of b will be,

→ b - 7 = 5

→ b = 7 + 5

→ [ b = 12 ]

Hence, the value of b is 12.

Answer: Yes

Step-by-step explanation: If you plug 12 into b, you will get the equation 12 - 7 = 5.

Try solving 12-7. It is 5.

Make me brainliest! Have a nice day :)

The area of the Triangle is 24.11 inch².

The area of any triangle can be calculated using the lengths of two of its sides and the sine of their included angle.

The trigonometric formula for the area of triangles is

area sin C= 1/2  , where and are the lengths of two sides and is the measure of the included angle.

Given:

a= 14 inch

b= 6.5 inch

and, angle = 32 degree

Now, The area of Triangle

= ab sin [tex]\theta[/tex] /2

= 14 x 6.5 x sin 32 /2

= 7x 6.5 x sin 32

= 7 x 6.5 x 0.5299

= 24.11 inch²

hence, the area is 24.11 inch²

Learn more about area of Triangle here:

https://brainly.com/question/19305981

#SPJ1

The following equations which are equivalent are:

2 + x = 5

collect like terms

x = 5 - 2

x = 3

x + 1 = 4

Subtract 1 from both sides

x = 4 - 1

x = 3

9 + x = 6

Subtract 9 from both sides

x = 6 - 9

x = -3

x + (negative 4) = 7

x +(-4) = 7

Open parenthesis

x - 4 = 7

x = 7 + 4

x = 11

Negative 5 + x = negative 2

-5 + x = - 2

x = -2 + 5

x = 3

Therefore, 2 + x = 5; x + 1 = 4; Negative 5 + x = negative 2 are equivalent to each other.

Read more on equivalent equation:

https://brainly.com/question/2972832

#SPJ1

The volume of the solid generated by revolving the regions bounded by the curves and lines about the​ y-axis is  8.90 unit³.

Since the region is the one for  then the intersection we are interested on is x=1 as it can also be seen in the graph.

Where h(x) is the height of the shell which here is the distance between the parabola and the line, so  (since the line is on the top we subtract from it the parabola

Notice the limits of the integral are the x-axis (x=0) and the intersection of the parabola and the line that we found before (x=1)

We want the volume generated when the area bounded by the curves :

v = x2 v = 8 —7x , and

x = 0 for x > 0 is revolved about the y axis using the cylindrical shell method .

The intersection of y = x2 and y = 8 —7x is :

y= x2 = 8 — 7x x2 + 7x —8 = 0

(x + 8)(x — 1) = 0 x = —8 or

x = 1 .

We thus have for x > 0 the two curves intersect at x = 1 and y = 12 = 1 .

The limits for integration are --- 0 <x < 1 .

The upper curve is --- y2 = 8 —7x ,

and the lower curve is --- yi = x2 .

The height of the shell is --- h = y2 -yi = 8 —7x — x2 •

The radius of the shell is --- R = x •

[tex]$$The surface area of the shell is :$$A=2 \pi \mathrm{Rh}=2 \pi x\left(8-7 x-x^2\right)=2 \pi\left(8 x-7 x^2-x^3\right) .$$The differential of volume which is the cylindrical shell is :$$\mathrm{dv}=\mathrm{Adx}=2 \pi\left(8 x-7 x^2-x^3\right) \mathrm{dx}$$[/tex]

[tex]$$We then have the volume of revolution is :$$\begin{aligned}v & =2 \pi \int_0^1\left(8 x-7 x^2-x^3\right) \mathrm{d} x \\& =2 \pi\left(4 x^2-\frac{7}{3} x^3-\frac{1}{4} x^4\right)_0^1 \\& =2 \pi\left[4\left(1^2-0^2\right)-\frac{7}{3}\left(1^3-0^3\right)-\frac{1}{4}\left(1^4-0^4\right)\right] \\& =2 \pi\left(4-\frac{7}{3}-\frac{1}{4}\right) \\& =2 \pi\left(\frac{48-28-3}{12}\right) \\& =2 \pi\left(\frac{17}{12}\right) ; \text { or, we have : } \\v & =\frac{17 \pi}{6} .\end{aligned}$$[/tex]

17π/6 = 8.90 unit³

Thus, The volume of the solid generated by revolving the regions bounded by the curves and lines about the​ y-axis is  8.90 unit³.

To learn more about volume of solid refers to:

brainly.com/question/13170128

#SPJ1

Answer:30

Step-by-step explanation:2*5 + 2*4 + 2*2 + 2*4

=10+8+8+4

=30

The second function 100(.1593)^t decays faster than the first function 100(.2661)^t.

To find which function decays the fastest, we need to compare the decay rates of the two functions.

The decay rate of a function is determined by the exponent in the function. In this case, the exponent is t.

The smaller the exponent, the faster the decay rate.

So, in the first function 100(.2661)^t, the exponent is t.

In the second function 100(.1593)^t, the exponent is also t.

We can compare the decay rates of the two functions by comparing the values of the bases, .2661 and .1593.

The base of a function represents the rate of decay, the smaller the base the faster the decay rate.

Read more about exponential function at

https://brainly.com/question/2456547

#SPJ1

Answer:

in 3 days Tom made $149.25

Step-by-step explanation:

If Tom made 298.50 in 6 days, you can find the amount made in 3 days by dividing that number in half.

298.5 / 2 = 149.25

Answer:

9 students

Step-by-step explanation:

34 -25

Part (a)

Line p can be named as "line RV" or "line AV" since these points are on line p. The order of the lettering doesn't matter.

==============================================

Part (b)

Pick any three non-collinear points in plane W. In other words, we pick three points in the plane that do not fall on the same line.  

The following points are located in this plane: S, R, Q, T, Z

Here are some possible names:

Something like "Plane SRQ" isn't valid since those three points are on the same line. Infinitely many planes pass through these three points.

The ordering of the letters doesn't matter. For instance, "plane STR" is the same as "plane RTS".

==============================================

Part (c)

As mentioned in part (b) earlier, these points fall on the same straight line. Hence they are considered collinear.

==============================================

Part (d)

Pick any four points that reside in plane W.

You have this list to choose from: S, R, Q, T, Z

Let's say we pick the first four to write S, R, Q, T as the answer

These points are coplanar because they reside in the same plane. The non-coplanar points are A and V since they are outside the plane W.

==============================================

Part (e)

Technically there aren't any line segments shown. Instead the diagram shows lines. But we can focus on a subset of a particular line to form a segment.

For instance, line p has points A and V on it. Therefore we can form segment AV

The symbolic notation for this would be to write [tex]\overline{\text{AV}}[/tex]

==============================================

Part (f)

Reason:

A line is composed of opposite rays. For instance, a vertical line consists of a ray pointing north and a ray pointing south. The two rays are glued together at the endpoints.

For line p, we can glue together ray RA and ray RV to form this line. Unlike the other naming conventions, the order does matter. Something like "ray RV" is not the same as "ray VR". The first letter tells us the endpoint that doesn't go on forever.

So, The line is a horizontal one, and the equation is y = -2 of a line in slope-intercept form if the slope is 0 and the point is (-3, -2).

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

Positive slope lines lean to the right, and they become steeper as the slope increases. A line with a negative slope slopes left, and the slope's magnitude determines how steep the line is. Since there is no slope on a horizontal line, it has a slope of zero.

The slope of the line is 0, which means the line is horizontal.

The point-slope form of the equation of a line is: y - y1 = m(x - x1)

With the point (-3, -2) and the slope of 0, we have:

y - (-2) = 0(x - (-3))

y = -2

The slope-intercept form of the equation of a line is: y = mx + b

The y-intercept of the line is -2, so the equation of the line in slope-intercept form is: y = 0x + (-2)

The line is a horizontal one and it's equation is y = -2

To know more about Equation visit: https://brainly.com/question/29657983

#SPJ1

A particular sort of bar chart known as an OHLC chart displays the open, high, low, and final prices with each period.

It is obvious from the information provided that the chart being discussed is the Continuously compounded chart.It should be mentioned that an expansive chart (OHLC) is just a term used to describe a sort of chart that is used to depict price changes in a financial instrument over a specific time period.

Here,

The chart's vertical line depicts the price range as a function of time. Since it displays the entire price range for the time period, it is helpful in gauging volatility.

The four main data points throughout a period are displayed on OHLC charts, which are helpful since many traders believe the closing price to be the most significant of the four.

In addition to displaying the opening and closing values of the market for the same time period, open-high-low-close charts also display the high and low price that a stock achieved during that time.

To learn more about OHLC refers to;

brainly.com/question/25878632

#SPJ1

Answer:

a. To determine how many seats should be reserved for premium ticket holders, Frank can use revenue management techniques. One common method is to use the expected revenue per seat, which is calculated by multiplying the number of seats by the expected price per seat and then multiplying that by the probability of that number of seats being sold. Frank can then compare the expected revenues for different numbers of premium seats and choose the number of seats that maximizes the expected revenue.

b. If the number of premium seats is 1,000, then the expected revenue is:

(1,000 x $200 x 0.10) + (75,000 - 1,000) x $40 x 1 = $200,000 + $3,000,000 = $3,200,000

If the number of premium seats is 5,000, then the expected revenue is:

(5,000 x $200 x 0.30) + (75,000 - 5,000) x $40 x 0.7 = $3,000,000 + $2,330,000 = $5,330,000

If the number of premium seats is 10,000, then the expected revenue is:

(10,000 x $200 x 0.24) + (75,000 - 10,000) x $40 x 0.76 = $4,800,000 + $3,768,000 = $8,568,000

and so on for the rest of the numbers.

From the above calculations, we see that the expected revenue is maximized at 10,000 premium seats, which is expected to generate $8,568,000.

c. Using the expected value of the number of premium seats would be calculated by multiplying the number of seats by its probability. The expected value of the number of premium seats is:

1,000 x 0.10 + 5,000 x 0.30 + 10,000 x 0.24 + 15,000 x 0.15 + 20,000 x 0.10 + 25,000 x 0.06 + 30,000 x 0.05 = 10,000.

Comparing this with the number of seats obtained by maximizing the expected revenue (10,000), we see that both approaches yield the same number of premium seats. This means that both approaches would yield the same potential revenue.

Total amount in the account after 25 years is, $5,500.

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

We have to given that;

Kimi Skuban deposits $2,000 at the beginning of each year.

The account pays 7% compounded annually.

Now, We know that;

⇒ Interest = PRT / 100

Where, P is principal amount, R is interest rate and T is time in years.

Substitute all the values, we get;

⇒ Interest = PRT / 100

⇒ Interest = 2000 × 7 × 25/ 100

⇒ Interest = $3,500

Hence, Total amount in the account after 25 years is,

⇒ $2,000 + $3,500

⇒ $5,500

Learn more about the simple interest visit;

brainly.com/question/2294792

#SPJ1

Answer: -2

Step-by-step explanation:

So, the arithmetic sequence formula for the nth term is as follows.

Tₙ = a + (n-1)d

So,

2nd term or (x + 1) = a + d

x + 1 = a + 5   (d = 5).   -   1

6th term or (-x + 17) = a + 5d

- x + 17 = a + 25.   -    2

Subtract 2 from 1, we get,

2x - 16 = -20

2x = -4

x = -2

You can check it if you want,

Second term = - 1

Sixth term will be  - 1 + 5 + 5 + 5 + 5 = 19

There you go.

The correct statement regarding the graph of the function f(x) = (x - 2)(x - 1)(x - 4) is given as follows:

The graph starts at the bottom left, continues up through the x axis at 1 to a maximum around y equals one half, goes back down through the x axis at 2 to a minimum at y equals negative 2, and goes back up through the x axis at 4.

The function is defined as follows:

f(x) = (x - 2)(x - 1)(x - 4).

Considering the linear factors of the function, the values of x through which the function intercepts the x-axis are given as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

As the function has three zeros with multiplicity one, it is a cube function, hence:

More can be learned about the end behavior of a function at brainly.com/question/1365136

#SPJ1

Answer:

(i) (x+4)(x-4)

Step-by-step explanation:

(ii)64m² - 800mn +2500n²

Answer: B. Exponential decay

Step-by-step explanation:

An exponential function is a function of the form f(x) = ab^x where a and b are constants, x is the independent variable, and b is a positive number not equal to 1. In this case, f(x) = -3(4^x). The base of the exponential function is 4, and it is a common base of exponential decay, because the base is less than 1, and the exponent is positive, this means that the output of the function will decrease as the input increases. Therefore, the function represented by f(x) = -3(4^x) is an exponential decay function.

Answer:

Exponential Decay

Step-by-step explanation:

In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula y=a(1-b)x wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed

Substitute the given value into the function and evaluate.

f(x)= -3⋅4^x/8

Answer:

Step-by-step explanation:

Interest per annum - 4.5

Interest per 1/3 of an annum - 4.5 x 1/3 = 1.5%

Use the S.I formula,

2400 x (100 + interest)/100

= 2400 x (100 + 1.5)/100

= 24 x 101.5

= 12 x 203

= 2436.

Pls mark as brainliest for no real reason. Cheers

The value of x for the given figure is 4√2.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

ΔMNO is a right triangle.

Applying the Pythagorean theorem.

MO² = ON² + MN²

8² = x² + x²

64 = 2x²

2x² = 64

x² = 32

x = √32

x = √(16 x 2)

x = √(4² x 2)

x = 4√2

Thus,

The value of x is 4√2.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ1

Answer: 8.8 hours

Step-by-step explanation:

To start off, we’ll make an equation that “connects” both companies:

10 + 4.75h = 21 + 3.5h (we put h to represent the number of hours)

Move all similar terms to one side:

4.75h - 3.5h = 21 - 10

Simplify:

1.25h = 11

h = 8.8

I hope this helps!

The plotted graph is shown below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

s (h) = √64h

now, when h=0

s(0) = √64h = 0

and, when h= 5

s(5) = √64h

        = √64 x 5

       = 8 x 2.25

       = 17.88

and, when h= 10

s(25) = √64h

        = √64 x 10

       = 8 x 3.162

       = 25.29

and, when h= 15

s(25) = √64h

        = √64 x 15

       = 30.98

and, when h= 20

s(25) = √64h

        = √64 x 20

       = 35.77

and, when h= 25

s(25) = √64h

        = √64 x 25

       = 8 x 5

       = 40

The plotted graph is shown below.

Learn more about Function here:

https://brainly.com/question/12431044

#SPJ1

Answer:

Line B slope = 9

Step-by-step explanation:

When dealing with perpendicular lines, we can let the slope we know represent m1, while the slope we don't know represents m2.

Thus, to find m2, we use the formula:

[tex]m_{2}=\frac{-1}{m_{1} }[/tex]

If we plug in -1/9 for m1, we have:

[tex]m_{2}=-\frac{1}{(-1/9)} \\m_{2}=9[/tex]

Answer:

5 hours and 40 minutes late

Step-by-step explanation:

I am assuming by 1435 hours you meant 14:35 -- 2:35 pm.

Hence you subtract 8:15 by 2:35 as the two times you're subtracting should always be the same time format (12 or 24-hour) which is 12 hours in this case.

 08:15

- 02:35

Since the minutes of the time above (:15) is higher than 35, we need to add 60 to 15 minutes and at the same time, reduce 8 hours by 1 hour to 7 hours since we are adding 60 minutes (1 hour) to :15:

 07:75 (15+60)

- 02:35

and answer will be 5 hours and 40 minutes

Volume of earth in shape of a sphere is 1 Trillion km^3 i.e. D.

What is a sphere?

A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.

The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere. Examples of spheres are a ball, a globe, the planets, etc.

Volume of sphere=4/3πr^3. where r=radius.

Surface area=4πr^2.

Now,

Given radius for earth=6371 km

so, Volume of earth=4/3*3.14*6371^3≈1Trillion km^3.

To know more about sphere visit the link

https://brainly.com/question/9994313?referrer=searchResults

#SPJ1

The expression in the mathematical form will be (1/4)( 2 - 3x ) / ( 2x ).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The word form of the expression is given as adding one-fourth of two subtracted from thrice a number to twice the same number.​

The expression can be written as,

E = (1/4)( 2 - 3x ) / ( 2x ).

Hence, the expression will be (1/4)( 2 - 3x ) / ( 2x ).

To know more about an expression follow

https://brainly.com/question/14268778

#SPJ1