Mathematics High School

FACTORIZE PLEASE, A LOT OF POINTS

64x^(3)-48x^(2)+12xy^(2)-y^(3)

Answers

Answer 1
=> 64x³ - 48x²y + 12xy² - y³

=> (4x)³ - 3(4x)²(y) + 3(4x)(y)² - y³

We know the formula: (a - b)³ = a³ - 3a²b + 3ab² - b³

By applying this formula above, we will get

=> (4x - y)³. (Ans)

Hope this helps!
Answer 2

or you can just put it in a smaller form by saying (4x - y)³

Related Questions

This question is about finding the slope of the tangent line to an inverse function. I would love to know if my answer of 1/5 is correct.

g(1) = 2
g^-1(2) = 1

(g^-1(x))' = 1/(g'(g-1(x))
(g^-1(2))' = 1/g'(g-1(2))
(g^-1(2))' = 1/g'(1)

g(x) = x^3 + 2x - 1
g'(x) = 3x^2 + 2
g'(1) = 3+2=5
(g^-1(2))' = 1/5

Answers

Yes choice B) 1/5 is correct. You are using the correct formula and steps. Nice work.

Here's another way to look at it:

When you visually plot the inverse, you reflect everything over the line y = x. What happens is that every (x,y) point swaps coordinates. So if (1,2) is on g(x), then (2,1) is on the inverse, and vice versa. Swapping the x and y values will swap the nature of the tangent slope.

For any tangent on g(x), its slope is m = (dy)/(dx)

The corresponding slope on the inverse will be n = (dx)/(dy). All that's happened here is that the numerator and denominator flipped. Again because x and y have swapped places. If you wanted, you can picture the xy axis where the vertical axis is the x axis and the horizontal axis is the y axis. That's effectively what is going on here. 

So before you found that g'(1) = 5 meaning that m = 5/1 on g(x) at the point (1,2)
So n = 1/m = 1/5 for the point (2,1) on the inverse g function.

Suppose the diameter of a circle is \color{green}{10}10 start color green, 10, end color green. what is its radius

Answers

The diameter of the circle is given to be 10 units. We are to find the radius.

The diameter is always the twice of radius. If d represents the diameter and r represents the radius, we can write:

d = 2r

or

r = d/2

For d=10,

r = 10/2 = 5 units

So, the radius of the circle will be 5 units

What is the total surface area of the rectangular pyramid below?

(please see attached picture)

404 square feet
596 square feet
788 square feet
1,000 square feet

Answers

Answer:

596 square feet

Answer:

b I did the

Step-by-step explanation:

I really need help with these questions:

Use basic identities to find the simplified expression-

1. (cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)

2. cosine θ^2 / sine θ^2 + csc θ sin θ

Explanations would be greatly appreciated


Answers

If we take the Pythagorean identity identity sin^2 x + cos^2 x = 1 then
                          (cos^2 x + sin^2 x) / (cot^2 x - csc^2 x)
The numerator becomes 1 since addition order matters not.
                                                 1 / (cot^2 x - csc^2 x)
If we factor the denominator out a negative
                                                1 / -(csc^2 x - cot^2 x)
Consider sin^2 x + cos^2 x = 1. Divide both sides by sin^2 x to get
                                         1 + cot^2 x = csc^2 x
Subtract both sides by cot^2 x to get 1 = csc^2 x - cot^2 x.
Replace the denominator
                                                 1 / -(1) = -1
For cos^2 θ / sin^2 θ + csc θ sin θ, we use cscθ = 1/sinθ and cosθ/sinθ = cotθ so
                                = cos^2 θ / sin^2 θ + 1
                                = cot^2 θ + 1
We use 1 + cot^2 θ = csc^2 θ to simplify this to
                              = csc^2 θ

Answers:         -1
                          csc^2 θ
1)

[tex]\bf sin^2(\theta)+cos^2(\theta)=1 \qquad \qquad cot(\theta)=\cfrac{cos(\theta )}{sin(\theta)} \qquad csc(\theta)=\cfrac{1}{sin(\theta)}\\\\ -------------------------------\\\\ \cfrac{cos^2(x)+sin^2(x)}{cot^2(x)-csc^2(x)}\implies \cfrac{1}{\frac{cos^2(x)}{sin^2(x)}-\frac{1}{sin^2(x)}}\implies \cfrac{1}{\frac{cos^2(x)-1}{sin^2(x)}} \\\\\\ \cfrac{1}{\frac{-[1-cos^2(x)]}{sin^2(x)}}\implies \cfrac{1}{\frac{-[\underline{sin^2(x)}]}{\underline{sin^2(x)}}}\implies \cfrac{1}{-1}\implies -1[/tex]



2)

[tex]\bf \cfrac{cos^2(\theta )}{sin^2(\theta )}+csc(\theta )sin(\theta )\implies \cfrac{cos^2(\theta )}{sin^2(\theta )}+\cfrac{1}{sin(\theta )}\cdot sin(\theta ) \\\\\\ \cfrac{cos^2(\theta )}{sin^2(\theta )}+1\implies \cfrac{cos^2(\theta )+sin^2(\theta )}{sin^2(\theta )}\implies \cfrac{1}{sin^2(\theta )}\implies csc^2(\theta )[/tex]

Write an equation of te circle with the center (0,0) and radius square root of 15

Answers

Answer:
x² + y² = 15

Explanation:

The formula for the equation of a circle is (x - h)² + (y - k)² = r², where the center of the circle is ordered pair (h, k) and r represents the radius (in units).

Now, we plug the given information into the circle equation and simplify.
radius = √15
center (0, 0), h = 0, k = 0

(x - 0)² + (y - 0)² = (√15)²
(x)² + (y)² = (√15)²
x² + y² = 15

The equation of the circle is x² + y² = 15

The equation of the circle with a center at (0,0) and a radius of the square root of 15 is x² + y² = 15. The standard form of the circle equation, (x - h)² + (y - k)² = r², is used with h and k set to 0 to represent the origin.

To write an equation of a circle with the center at the origin (0,0) and a radius of the square root of 15, we use the standard form of the circle equation:

(x - h)² + (y - k)² = r²

Here, (h, k) represents the center of the circle and r is the radius. Since the center of the circle in question is at the origin, h = 0 and k = 0. The given radius is the square root of 15, so we have r = √15. Substituting these values into the standard form gives us the equation:

x² + y² = ( √15 )²

Which simplifies to:

x² + y² = 15

This is the equation for the desired circle centered at the origin with radius √15.

what is the value of x, if the volume of the cone is 12piem^3

Answers

V = π x² h/3

12π=πx²h/3

12=x²h/3

36=x²h

36/h=x²

x=6/√h=(6√h)/h

A cruise ship can cover 17 nautical miles in 374 minutes. How many nautical miles will it travel in 330 minutes?

Answers

374/17= 22 minutes per nautical mile. 
330/22= 15 nautical miles in 10 minutes

To check your work:
17/374=.04545 nautical miles per minute
.04545*330= 14.999 or 15.

So your answer is that the cruise ship covered 15 nautical miles in 330 minutes. I hope that helped!

The ship's speed in deep water is 0.045 nautical miles per minute. In shallow water, the ship's maximum speed typically decreases due to increased drag and turbulence.

To find the speed of the ship in very deep water:

Calculate speed = Distance / Time = 17 nmi / 374 min = 0.045 nautical miles per minute.For the ship's speed in shallow water:It depends on the water resistance; usually, in shallow water, the ship's maximum speed decreases due to increased drag and turbulence.

!! WILL GIVE BRAINEST TO WHOEVER ANSWERS FIRST !!

Simplify (2√5 + 3√7)² Show ALL your work.

Answers

a = 2√5 , b = 3√7

(a+b)² = a² + 2ab + b² = (2√5)² + 2(2√5)(3√7) + (3√7)²
= 4*5 + 12√35 + 9*7
= 83 + 12√35

FIRST CORRECT ANSWER GETS BRAINLIEST!!!
PLS HELP ME!!!!! ONEHUNDRED POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

ruth was hauling a wide load out of portland. at 7:00 am she headed north from exit 102 at an average speed of 35 pmh. michael headed north from the same exit at 9:00 am in his pontiac. by 3:00 pm the same day michael was 20 miles ahead of ruth. what was michael's average speed

Answers

ruth was out of portland at 35mph at 7:00am
so at 9 am, she was 70 mile ahead of michael
but michael was 20 miles ahead by 3 pm.
so in 6 hours, he went past ruth by 90 miles which is 90/6 = 15mph
michael speed = ruth speed + 15
= 35 + 15
= 50mph

Answer:

Ruth was out of Portland at 35mph at 7:00 am

so at 9 am, she was 70 miles ahead of Michael

but Michael was 20 miles ahead by 3 pm.

so in 6 hours, he went past Ruth by 90 miles which is 90/6 = 15mph

Michael speed = ruth speed + 15. = 35 + 15 = 50mph

Solve by graphing y= -5/3x + 4 y= -5/3x + 3

Answers

For this case we have the following system of equations:
 y = -5 / 3x + 4
 y = -5 / 3x + 3
 We note that the lines have the same slope:
 m = -5 / 3
 Therefore, the lines are parallel.
 Thus, the system has no solution.
 Answer:
 It has no solution (parallel lines).
 See attached image.

A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum hieght

Answers

For this case we have the following equation:
 h = -16t ^ 2 + 184t + 20
 Deriving we have:
 h '= -32t + 184
 We equal zero and clear t:
 -32t + 184 = 0
 32t = 184
 t = 184/32
 t = 5.75 s
 Then, the maximum height is given by:
 h (5.75) = -16 * (5.75) ^ 2 + 184 * (5.75) + 20
 h (5.75) = 549 feet
 Answer:
 It takes the boulder to reach its maximum height about:
 t = 5.75 s
 the boulder's maximum hieght is:
 h (5.75) = 549 feet

Answer:

The answer should be C.

A number x, rounded to 1 decimal place is 12.3 write down the error interval for x

Answers

Final answer:

The error interval for a number x rounded to 12.3 is 12.25 ≤ x < 12.35, indicating the range that x could be before rounding to one decimal place.

Explanation:

If a number x, rounded to 1 decimal place, is 12.3, the error interval for x defines the range of values that x could be in order to round to 12.3. Since the value is rounded to one decimal place, we consider half of a tenth (0.05) on either side of 12.3 to find the error interval. Hence, the lower bound of the error interval would be just below 12.3 (12.25), and the upper bound would be just before it would round up to the next tenth (12.35).

The error interval for x can be written as: 12.25 ≤ x < 12.35.

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Error interval for [tex]\( x \)[/tex] rounded to 1 decimal place as 12.3 is from 12.25 to 12.35.

To find the error interval for the number [tex]\( x[/tex], rounded to 1 decimal place as 12.3, we need to consider the possible range of values that [tex]\( x \)[/tex] could have been before rounding.

1. Lower Bound: To find the lower bound, we need to consider the smallest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The smallest value that would round up to 12.3 is 12.25.

2. Upper Bound: Similarly, to find the upper bound, we need to consider the largest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The largest value that would round down to 12.3 is 12.35.

So, the error interval for [tex]\( x \)[/tex] is from 12.25 to 12.35.

How do science and math relate to each other?

Answers

Many if not all sciences require math at some point whether it be measurements of chemicals, balancing chemical reactions, plotting data for how often a certain animal does a certain thing, how much of a medicine to give a patient to cure their ailment but not cause any side effects, etc. etc. 

Final answer:

Mathematics and science are foundational to engineering, providing the tools and understanding necessary for the engineering design process. They enable engineers to create models, solve design problems, and innovate, thus influencing education and daily life through engineered products.

Explanation:

Science and mathematics are intimately related, especially in fields such as engineering. Mathematics provides the language and tools for abstract reasoning and quantitative analysis, which are fundamental in engineering. Math is used to create mathematical models that describe physical phenomena and to evaluate the merit of different possible solutions. Science, on the other hand, offers understanding of natural phenomena and constraints that inform engineering solutions. Together, math and science are essential throughout the engineering design process, from conceptualization to detailed design implementation, and in team decision-making.

In high school and college, a strong foundation in math and science courses is crucial for success in engineering education. For instance, courses like thermodynamics, circuits, and fluids—commonly referred to as engineering science courses—are grounded in these basic disciplines. The role of science and mathematics in engineering extends beyond educational prerequisites; they are operational tools that engineers use in their work every day to innovate and create products that improve our lives, such as the pocket radio, cell phones, and computers.

The connections between math, science, and engineering are dynamic and multidimensional. They enable engineers to navigate through the iterative steps of the engineering design process, which include analyzing problems, developing solutions, and optimizing products, often moving nonlinearly as real-world complexities dictate adjustments and refinements.

On two​ examinations, you have grades of 83 and 89. there is an optional final​ examination, which counts as one grade. you decide to take the final in order to get a course grade of​ a, meaning a final average of at least 90

Answers

Let's say you get x on the third examination.
The average of all three examinations must be at least 90 to get an A.

[tex] \dfrac{x + 83 + 89}{3} \ge 90 [/tex]

[tex] x + 172 \ge 270 [/tex]

[tex] x \ge 98 [/tex]

In order to get an A, you must get at least a 98 on the third examination.

When Mr. Peters drives from Boston to Worcester it takes him 30 minutes travelling at a speed of 60 miles per hour. Mrs. Peters drives from Boston to Worcester and leaves 5 minutes after Mr. Peters but travels at a speed of 90 miles per hour. Who will arrive first? By how many minutes?

Answers

Since the problem is requesting the answer in minutes, we are going to convert the speed of Mr. Peter to miles per minutes; to do that, we are going to multiply his speed by the multiplier [tex] \frac{60min}{1h} [/tex]:
[tex]60 \frac{miles}{h} * \frac{1h}{60min} =1 \frac{mile}{min} [/tex]

Now, to find the distance from Boston to Worcester, we are going to use the distance formula: [tex]d=vt[/tex]
where
[tex]d[/tex] is the distance
[tex]v[/tex] is the speed
[tex]t[/tex] is the time 

We know that the speed of Mr. Peter is [tex]1 \frac{mile}{min}[/tex] and his time is 30 minutes. Lets replace those values in our formula:
[tex]d=1 \frac{mile}{min} *30min[/tex]
[tex]d=30miles[/tex]

Now, lets concentrate on Mr. Peter clone, Mr. P:
Lets convert the speed of Mr. P to miles per minute:
[tex] \frac{90miles}{h} * \frac{1h}{60min} =1.5 \frac{miles}{min} [/tex]
We also know that they will cover the same distance, 30 miles. Lets replace the values in our formula one more time to find t:
[tex]d=vt[/tex]
[tex]30miles= 1.5\frac{miles}{min} *t[/tex]
[tex]t= \frac{30miles}{1.5\frac{miles}{min}} [/tex]
[tex]t=20min[/tex]
But since Mr. P leaves 5 minutes after Mr. Peters, we need to add those 5 minutes to M. P's time:
[tex]t=20min+5min[/tex]
[tex]t=25min[/tex]

We can conclude that Mr. P will arrive first, 5 minutes before Mr. Peter.

Mrs. Peter arrives 5 minutes before Mr. Peter

To find who arrives first we first need to find the speed and time they require to arrive.

Given : From Boston to Worcester

            Mr. Peter takes [tex]\rm time=30 \; minutes \; and \;speed= 60 miles /hr[/tex]

            Mrs. Peter takes [tex]\rm speed=90 miles/hr[/tex]

We will now calculate Mr. Peters speed,

[tex]\rm 60 \dfrac{miles}{h} \times \dfrac{h}{60minutes}=\dfrac{mile}{min}[/tex]

How to find distance from Boston to Worecester?

To find the distance, we will use distance formula

[tex]\rm Distance=speed\times time[/tex]

Here,given that the Mr Peters speed is [tex]\rm 60 miles /hr[/tex] and time is [tex]\rm 30 minutes[/tex]so by distance formula we will find distance of Mr. Peter

[tex]\rm Distance=\dfrac{mile}{min} \times 30 minutes[/tex]

[tex]\rm Distance= 30 miles[/tex]

Similarly, we will now calculate Mrs. Peters speed,

[tex]\rm \dfrac{90miles}{h} \times \dfrac{h}{60minutes}=1.5\times \dfrac{miles}{min}[/tex]

by the given informations we know both covers the same distance

[tex]\rm ie. \;30 miles[/tex]

we will now find distance of Mrs. Peter

[tex]\rm Distance=speed\times time\\ 30miles=1.5\dfrac{miles}{min} \times time\\ time=\dfrac{30miles}{1.5\dfrac{miles}{min}}\\\\ time=20 minutes[/tex]

Here, we know that Mrs.Peter leaves from Boston to Worcester 5 minutes after Mr.Peter so we will add 5 minutes to Mrs. Peters time.

[tex]\rm time=20 minutes+ 5 minutes\\ time=25 minutes[/tex]

Therefore, it is clear that Mrs.Peter arrive before Mr Peter by 5minutes.

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If the pattern below follows the rule "Starting with four, every consecutive line has a number one more than the previous line," how many marbles must be in the seventh line?

Answers

7 - 4 (becaause there already is 4 rows) = 3. 

3 x 1 = 3. 

Basically you have to add 3 to the number that is in the 4th row. This should be 10, because 7 + 3 = 10

The number of balls in 7th line would be 10.

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is a pattern as shown in the image.

An arithmetic sequence is of the form -

       a, a + d, a + 2d, a + 3d, ......,

{d} is common difference and {a} is first term.

We can write the pattern as -

4, 5, 6, 7, .....

This is a arithmetic progression. We can write the nth term as -

a{n} = a + (n - 1)d

a{7} = 4 + (7 - 1) x 1

a{7} = 4 + 6

a{7} = 10

Therefore, the number of balls in 7th line would be 10.

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If a person uses $700 in credit with an interest of 14%,what is that person going to owe after three billing cycles with simple interest

Answers

Simple interest:  i = p*r*t, where r is the annual interest rate and t is the number of years.
                                14%
This boils down to ----------- interest per month:  a monthly rate of 0.0117.
                                12 mo

Thus, after 3 months, the amount owed, including the original $700, would be $700 + 3($700)(0.0117) = $724.57.

Which is least expensive per oz rounded to the nearest cent: 20 oz for $1.79 or 2 lb 2 oz for $2.59?

A.) 20 oz
B.) 2 lb 2 oz
C.) Neither

Answers

20 / 1.79 = 11.17 
11.17 = 11.2

2 lb 2 oz / 2.59 = 0.82
0.82 = 0.8

So the answer is B) 2 lb 2 oz.

Hope this Helps!

Answer:

B.) 2 lb 2 oz

Step-by-step explanation:

$1.79 for 20 ounces gives us

1.79/20 = $0.0895 ≈ $0.09 per ounce.

1 lb = 16 oz.; this means that 2 lb = 2(16) = 32 oz.

$2.59 for 2 lb 2 oz then gives us

2.59/34 = $0.07617647059 ≈ $0.08 per ounce.

The second choice is cheaper by 1 cent.


Simplify the expression -2x^2(4x − 3).
-8x3 − 6x2
-8x3 + 6x2
8x3 − 6x2
8x3 + 6x2

Answers

To simplify the expression we are going to use the distributive property of multiplication: [tex]a(b+c)=ab+ac[/tex].
We can infer from our problem that [tex]a=-2x^2[/tex], [tex]b=4x[/tex], and [tex]c=-3[/tex]. So lets apply the property to simplify our expression:
[tex]-2x^2(4x-3)=(-2x^2)(4x)+(-2x^2)(-3)[/tex]
[tex](-2x^2)(4x)+(-2x^2)(-3)=-8x^3+6x^2[/tex]

We can conclude that the correct answer is -8x3 + 6x2

Find the surface area of a rectangular prism with a height of 6 inches, a width of 7 inches, and a length of 13 inches. A) 338 in2 B) 422 in2 C) 520 in2 D) 1364 in2
If you can, please explain. Thank you vv much! :D

Answers

Answer:

422 in.2

Step-by-step explanation:

Substitute the measurements of the rectangular prism into the formula SA = 2(lw) + 2 (lw) + 2(lh): 2(13)(7) + 2(6)(7) + 2(13)(6) = 422 in2.

Miriam bought a bushel of apples from the apple orchard to bake apple pies for a bake sale. She started with 126 apples. After the first day of baking, she had 108 apples left. After the second day, she had 90 apples. After the third day, she had 72 apples left.If she continues this pattern, how many apples will she have left after 7 days of baking?

Answers

Miriam will have no apples left after the 7th day of baking.

Here is the number of apples she will have after each day starting with after the 1st day of baking.

126, 108(1st day), 90(2nd day), 72(3rd day), 54(4th day), 36(5th day), 18(6th day), 0(7th day).

Each day the number of apples decreases by 18.

Arithmetic, because the sequence has a common difference. answer on edgenui......

Write an expression for the total Surface Area (SA) of a rectangular prism whose base is a square with side of length x and height of y.

Answers

For this case we have the following expression:
 S.A = 2x ^ 2 + 2x *y + 2x * y
 Rewriting we have:
 S.A = 2x ^ 2 + 4x *y
 S.A = 2 (x ^ 2 + 2x * y)
 Where,
 x: side length of a square base
 y: height of the prism
 Answer:
 an expression for the total Surface Area (SA) of a rectangular prism is:
 S.A = 2 (x ^ 2 + 2x * y)

a construction company is replacing a window in a house. the window is currently 3 feet wide by 4 feet tall. The homeowner wants to add 4 1/2 inches to each side of the window. What is the new perimeter of the window in feet? Justify your reasoning.

Answers

For this case, the first thing you should do is take into account the following unit conversion:
 1 foot = 12 inches
 Therefore, the perimeter of the new window is given by:
 p = 2w + 2l
 Where,
 w: width
 l: long
 Substituting values:
 p = 2 * (3 + ((4 1/2) / 12)) + 2 * (4 + ((4 1/2) / 12))
 p = 15.5 feet
 Answer:
 The new perimeter of the window in feet is:
 p = 15.5 feet

True or false ???????????????please help

Answers

1  True   because 19^3  = 6859
2. False
3. True because 8000 ^1/3  can be written as 100^1/3 * 8^1/3
4 False 
5 True because they are both = 15

If you have a scientific calculator you can check these out yourself

The table below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often?

Options:
20%
31%
43% is wrong
57%

(I already did my other questions, this is the only one I needed help with)

Answers

The first thing we must do for this case is to observe the highest relative frequency of the table in the total column.
 For the white car we have:
 Male = 0.11
 Female = 0.20
 Total = 0.31
 The percentage is given by:
 (0.31) * (100) = 31%
 Answer:
 The percentage that represents the car bought most often is:
 31%

1.) How is the graph of y equals negative 2 x squared minus 5 different from the graph of y equals negative 2 x squared?

2.)

Answers

-2x^2 - 5  is same shape as -2x^2 except that the whole graph is translated verticall downwards 5 units

The transformation on the graph of y = -2x²- 5 is described as 5 units downward.

What is transformation on the graphs?

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

As per the given information:

The graphs are let f(x) = y = -2x²- 5 and g(x) = y = -2x².

As per the definition, the transformation on the graph can be described as,

-5 < 0.

The graph shifts downward.

Therefore, the graph of y = -2x²- 5 is 5 units down than y = -2x².

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Brand x copier has improved its copier so that it produces 10% more copies than its old model. if the old model ran 420 copies per hour, how many copies would the new model run? round your answer to the nearest whole number.
a. 221 copies per hour
c. 462 copies per hour
b. 435 copies per hour
d. 447 copies per hour

Answers

Hello!

to solve this, do the following equation:
x=brand x copier
y=old version

x=y+(y*.1)  or  x=y*1.1

using either of these equations, the math I will show will get you the correct answer

462=420+(420*.1)  or  462=420*1.1

your final answer is:  the new copier produces 462 copies per hour

I hope this helps, and have a nice day!

Answer:

462

Step-by-step explanation:

Two lighthouses are located 40 miles from each other. A boat is spotted at an angle of 37 degrees northeast of the western lighthouse. At this point, the boat is 28 miles from the eastern lighthouse. How far is the boat from the western lighthouse?

A. 46.27 miles
B. 17.43 miles
C. Either 46.27 miles or 17.43 miles
D. There is no possible solution.

Answers

The arrangement of the Eastern and Western lighthouses and the position of the boat are as shown in the attached diagram.

Using sine rule,
28/Sin 37 = 40/Sin B => Sin B = (40 Sin 37)/28 = 0.8597 => B = Sin ^-1(0.8597) = 59.287°
Therefore,
Angle E = 180 - (37+59.287) = 83.713°

Using the sine rule again;
BW/Sin E = 28/Sin 37 => BW = (28 Sin 83.713)/Sin 37 = 46.246 ≈ 46.27 miles.

The boat is 46.27 miles from the western lighthouse. The correct answer is A.

Answer:

C. Either 46.27 miles or 17.43 miles

Find one pair of real numbers, $(x,y),$ such that $x + y = 6$ and $x^3 + y^3 = 144.$

Answers

[tex]\[\{(3 + \sqrt{5}, 3 - \sqrt{5})}\][/tex] is the one pair of real numbers [tex]\((x, y)\)[/tex] that satisfies the given equations.

Given the system of equations:

[tex]\[x + y = 6\][/tex]

[tex]\[x^3 + y^3 = 144\][/tex]

We can use the identity for the sum of cubes:

[tex]\[x^3 + y^3 = (x + y)(x^2 - xy + y^2)\][/tex]

Substitute [tex]\(x + y = 6\):[/tex]

[tex]\[x^3 + y^3 = 6(x^2 - xy + y^2)\][/tex]

Given [tex]\(x^3 + y^3 = 144\)[/tex], we substitute this into the equation:

[tex]\[144 = 6(x^2 - xy + y^2)\][/tex]

Divide both sides by 6:

[tex]\[24 = x^2 - xy + y^2\][/tex]

Next, we use the square of the sum:

[tex]\[(x + y)^2 = x^2 + 2xy + y^2\][/tex]

Substitute [tex]\(x + y = 6\):[/tex]

[tex]\[6^2 = x^2 + 2xy + y^2\][/tex]

[tex]\[36 = x^2 + 2xy + y^2\][/tex]

We already have [tex]\(x^2 - xy + y^2 = 24\)[/tex]. Let’s denote the first and second equations:

1. [tex]\(x^2 - xy + y^2 = 24\)[/tex]

2. [tex]\(x^2 + 2xy + y^2 = 36\)[/tex]

Subtract the first equation from the second equation:

[tex]\[(x^2 + 2xy + y^2) - (x^2 - xy + y^2) = 36 - 24\][/tex]

[tex]\[3xy = 12\][/tex]

[tex]\[xy = 4\][/tex]

Now, we have two equations:

1. [tex]\(x + y = 6\)[/tex]

2. [tex]\(xy = 4\)[/tex]

We solve these equations using the quadratic formula. Consider the quadratic equation:

[tex]\[t^2 - (x+y)t + xy = 0\][/tex]

[tex]\[t^2 - 6t + 4 = 0\][/tex]

Solve for [tex]\(t\)[/tex] using the quadratic formula [tex]\(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):[/tex]

[tex]\[t = \frac{6 \pm \sqrt{36 - 16}}{2}\][/tex]

[tex]\[t = \frac{6 \pm \sqrt{20}}{2}\][/tex]

[tex]\[t = \frac{6 \pm 2\sqrt{5}}{2}\][/tex]

[tex]\[t = 3 \pm \sqrt{5}\][/tex]

Thus, the solutions for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] are:

[tex]\[x = 3 + \sqrt{5}, \quad y = 3 - \sqrt{5}\][/tex]

or

[tex]\[x = 3 - \sqrt{5}, \quad y = 3 + \sqrt{5}\][/tex]

PLS ANSWER! THE WORLD HATES ME!!

0.29999999999 As a fraction

Answers

Here is your answer:

All you need to do is keep the 29 and then add a hundred because of how many 9's there are.

Also, you could see that:

[tex] .29999999999 \neq \frac{29999999999}{100000000000} [/tex]

Which would also mean that:

[tex] \frac{29999999999}{100000000000} \neq \frac{29}{100} [/tex]

Therefore the answer is "29/100."

Hope this helps!

Answer:

13/46

Step-by-step explanation:


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