Lim as x approaches 0: (sin3x)/(2x-Sinx)
Taking the derivative of the numerator and denominator separately:
Numerator: d/dx(sin3x) = 3cos3x
Denominator: d/dx(2x - sinx) = 2 - cosx
Now, evaluate the limit using L'Hôpital's Rule:
Lim as x approaches 0: (3cos3x)/(2 - cosx)
Plugging in x = 0:
Lim as x approaches 0: (3cos(0))/(2 - cos(0))
= 3/2
Therefore, the limit as x approaches 0 of (sin3x)/(2x-Sinx) is 3/2.
Lim as x approaches infinity: x^-1 lnx
Taking the derivative of the numerator and denominator separately:
Numerator: d/dx(x^-1 lnx) = (1/x)lnx
Denominator: d/dx(1) = 0
Since the denominator is 0, we cannot apply L'Hôpital's Rule. However, we can still evaluate the limit:
Lim as x approaches infinity: x^-1 lnx
As x approaches infinity, the natural logarithm (lnx) grows without bound, so the overall limit is 0.
Therefore, the limit as x approaches infinity of x^-1 lnx is 0.
Lim x approaches infinity: x/ e^x
Taking the derivative of the numerator and denominator separately:
Numerator: d/dx(x) = 1
Denominator: d/dx(e^x) = e^x
Now, evaluate the limit using L'Hôpital's Rule:
Lim as x approaches infinity: 1/ e^x
As x approaches infinity, the exponential function e^x grows without bound, so the overall limit is 0.
Therefore, the limit as x approaches infinity of x/ e^x is 0.
please answer i am stuck
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
[tex]A(x)=324e^{0.066x}[/tex]
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
[tex]A(11)=324e^{0.066 \times 11}[/tex]
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
[tex]A(16)=324e^{0.066 \times 16}[/tex]
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
[tex]A(19)=324e^{0.066 \times 19}[/tex]
A(19) = $1135.4 billions.
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Point B is on line segment AC. Given AC = 2x + 7, BC = x, and
AB= 5x9, determine the numerical length of AB.
Answer:
Step-by-step explanation:
To determine the length of AB, we need to find the value of x.
We are given that AC = 2x + 7, BC = x, and AB = 5x + 9.
Since B is on the line segment AC, the sum of lengths AB and BC should equal the length of AC. Therefore, we can set up the equation:
AB + BC = AC
Substituting the given values, we have:
(5x + 9) + x = 2x + 7
Simplifying the equation:
6x + 9 = 2x + 7
Bringing like terms to one side:
6x - 2x = 7 - 9
4x = -2
Dividing both sides by 4:
x = -2/4
Simplifying:
x = -1/2
Now that we have the value of x, we can substitute it back into the expression for AB to find its numerical length:
AB = 5x + 9 = 5(-1/2) + 9 = -5/2 + 9 = (18 - 5)/2 = 13/2 = 6.5
Therefore, the numerical length of AB is 6.5.
4. Brooke earns a salary of $38 000 per year as a cook and works part-time in a department
store.
Her part-time job pays $10.25 per hour and she usually works 12 hours per week.
a) Determine her monthly income.
b) She is looking at renting a new apartment. The rent is $975 per month and includes
utilities. If she takes this apartment, will it fall within the guidelines for housing?
a) Brooke's monthly income is $3,166.67 from her full-time job as a cook, and an additional $532.59 from her part-time job, resulting in a total monthly income of $3,699.26.
b) Yes, the rent of $975 per month for the new apartment falls within the housing guideline of spending 30% or less of her monthly income on housing.
a) To determine Brooke's monthly income, we need to calculate her earnings from both her full-time and part-time jobs.
Full-time job income: Brooke earns $38,000 per year as a cook.
To find her monthly income from this job, we divide her annual salary by 12:
Monthly income from full-time job = $38,000 / 12 = $3,166.67
Part-time job income: Brooke earns $10.25 per hour and works 12 hours per week.
To find her weekly income from this job, we multiply her hourly rate by the number of hours she works:
Weekly income from part-time job = $10.25/hour x 12 hours/week = $123
To find her monthly income, we multiply her weekly income by the average number of weeks in a month (approximately 4.33):
Monthly income from part-time job = $123/week x 4.33 weeks/month = $532.59 (rounded to the nearest cent)
To calculate Brooke's total monthly income, we add her full-time and part-time job incomes:
Total monthly income = $3,166.67 + $532.59 = $3,699.26 (rounded to the nearest cent)
b) The rent for the new apartment is $975 per month, including utilities. To determine if it falls within the housing guidelines, we need to compare it to a percentage of Brooke's monthly income.
Typically, a common guideline is to spend no more than 30% of your monthly income on housing.
Percentage of monthly income for housing = 30% of total monthly income
= 30/100 x $3,699.26
= $1,109.78 (rounded to the nearest cent)
Since the rent of $975 is lower than the guideline of $1,109.78, if Brooke takes this apartment, it will fall within the housing guidelines.
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Please help what is the slope of the line?
Answer:
-5/4
Step-by-step explanation:
Let [tex](x_1,y_1)=(-4,4)[/tex] and [tex](x_2,y_2)=(0,-1)[/tex]. The slope of the line would be:
[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}[/tex]
Answer: -5/4
Step-by-step explanation:
To find the slope between two points, you can use the formula:
Slope = (y2 - y1)/(x2 - x1)
Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:
slope = (4 - (-1))/(-4 - 0)
slope = (4 + 1)/(-4)
slope = 5/-4
Therefore, the slope between the two points is -5/4.
PLEASE HELPP: 2.11.2 Project: Performance Task: The Parallax Problem (For San Francisco)
The Scenario: You’re looking for a sponsor to pay for you to participate in a sailboat race. Now that you’ve solved the parallax problem, use the same skills you used there to write a proposal that shows that you can win the race.
The Project: Use the information provided in the performance task to estimate your travel costs and to calculate your average speed and the speed of last year’s winner. Use the questions below to help you gather information to write your proposal
3. What is the distance between buoy A and B? (5 points)
4. What are the lengths of the other two triangle legs? (4 points: 2 points each)
Remember what you know about the shape of the Race Course.
5. What is the total length of the race course? (4 points: 3 for calculation, 1 for answer)
Part VIII: Calculate the winner’s speed. (10 points)
1. What was the winner’s speed during last year’s race? (5 points: 3 points for speed. 2 points for conversion to knots).
2. How does the winner’s speed compare with your average speed? How much faster or slower are you? (5 points)
Part IX: Write your proposal. (8 points)
Now it’s time to make your proposal to the sponsor. Your sponsor will have their logo on your boat, so they want to be sure it’s likely to do well. The sponsor also needs to know what the expenses and risks are, so they know how much their investment in you will cost.
1. Complete the table to summarize the results of your study. (4 points)
Category:
Race:
Risk Analysis:
Itemized Travel Cost
Safety hazards
Competitive Analysis:
My time and speed
Last year's winning time and speed
Reward Analysis:
My chances of winning
2. Write a summary paragraph explaining why the sponsor should accept your proposal. (4 points)
The proposal is as follows
Part III - The distance between buoys A and B is 12.8 kilometers.
Part IV - The length of the other two triangle legs are 10.2 kilometers and 8.4 kilometers.
Part V - The total length of the race course is 31.4 kilometers.
Part VIII - The winner's speed during last year's race was 10.8 knots.
See the proposal attached.
Why the sponsor should accept your proposalDear Sponsor,
I'm seeking sponsorship for the San Francisco sailboat race.
With a proven track record and the determination to win, your investment of $5,500 covers travel costs and potential hazards.
By associating your brand with a winning sailor, you'll gain significant exposure to thousands of spectators. Join me in this thrilling race for success.
Sincerely,
[Your Name]
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IfmZC = 142° and m LI = 48°, find mU B.
The measure of angle of arc UB is 46°
What is arc angle relationships?An arc is a part of the circumference.
If two arcs in circles with equal radii have the same length, then their central angles (and measures) will be equal.
To find the measure of angle of arc UB, we use the theorem that says;
angle I = 1/2( angle ZC - angle UB)
angle I = 48°
angle ZC = 142°
Therefore ;
represent angle UB by x
48 = 1/2( 142-x)
142 - x = 96
x = 142 -96
x = 46°
Therefore the measure of angle of arc UB is 46°
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Which complex number is equivalent to this expression? 1/3(6+3¡)-2/3(6-12¡)
So, the complex number equivalent to the given expression is 0 + 9i, which can also be written as 9i.
To simplify the expression 1/3(6 + 3i) - 2/3(6 - 12i), we can perform the necessary calculations.
First, let's simplify each term separately:
1/3(6 + 3i) = 2 + i (divide each term by 3)
2/3(6 - 12i) = 4 - 8i (divide each term by 3)
Now, let's substitute these simplified terms back into the original expression:
2 + i - (4 - 8i)
When subtracting complex numbers, we distribute the negative sign:
2 + i - 4 + 8i
Combine like terms:
(-2 + 2) + (i + 8i) = 0 + 9i
The expression 1/3(6 + 3i) - 2/3(6 - 12i) simplifies to 9i.
We can make the necessary computations to simplify the statement 1/3(6 + 3i) - 2/3(6 - 12i).
Let's first simplify each phrase individually:
Divide each term by 3 to get 1/3(6 + 3i) = 2 + i.
Divide each term by 3 to get 2/3(6 - 12i) = 4 - 8i.
Let's now add these abbreviated terms back into the original phrase:
2 + i - (4 - 8i)
Distributing the negative sign while subtracting complex numbers is as follows:
2 + i - 4 + 8i
combining similar terms
(-2 + 2) + (i + 8i) = 0 + 9i
A simplified version of the phrase 1/3(6 + 3i) - 2/3(6 - 12i) is 9i.
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The sum of the measures of the angles is 180. The sum of the measures of the second and third angles is two times the measure of the first angle. The third angle is 20 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
QUESTION 3: Given: f(x)=1/x-1 -2 3.1 Write down the equation(s) of the asymptote(s) of f. 3.2 Determine the x-intercept of f.
Given the function `f(x)=1/x-1 -2` the task is to write the equation of the asymptote(s) of f and determine the x-intercept of f. Asymptotes are lines that the curve of a function approaches but never touches. There are two types of asymptotes: vertical and horizontal.
Vertical Asymptote Vertical asymptotes occur when a function approaches infinity or negative infinity at a specific value of x. This can occur in a rational function where there is a division by zero.
A vertical asymptote is found when the denominator of the rational function becomes zero. Since division by zero is undefined, it means that the rational function approaches infinity or negative infinity.
The equation of the vertical asymptote is x = a where a is the value that makes the denominator zero.
Horizontal AsymptoteA horizontal asymptote occurs when a function approaches a constant value (y) as x approaches infinity or negative infinity. A horizontal asymptote occurs when the degree of the numerator and denominator is the same.
The horizontal asymptote is found by comparing the degrees of the numerator and denominator and dividing the leading coefficient of the numerator by the leading coefficient of the denominator.3.1 Equation of the asymptotes of the equation of the vertical asymptote is x=1.
The degree of the numerator is less than the degree of the denominator. Therefore, the horizontal asymptote is y=0The equation of the horizontal asymptote is y=0.3.2 X-intercept of fTo find the x-intercept of f, set y=0.f(x) = 0= 1/(x-1) -2Add 2 to both sides2 = 1/(x-1)Take the reciprocal of both sides of the equation.1/2 = (x-1)x-1 = 2x = 3Hence, the x-intercept of the function is (3,0)
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Find the missing side. 30° 23 x = [?] Round to the nearest tenth. Remember: SOHCAHTOA
Answer:
x = 11.5
Step-by-step explanation:
using the sine ratio in the right triangle
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{23}[/tex] ( multiply both sides by 23 )
23 × sin30° = x , then
x = 11.5
Let f(x) = 4x² - 7.
Using the definition of derivative
Answer:
56
Step-by-step explanation:
f(x)=4x^2-7
f'(x)=8x
f'(7)=56
Generate a continuous and differentiable function f(x) with the following properties:
f(x) is decreasing at x=−5
f(x) has a local minimum at x=−3
f(x) has a local maximum at x=3
The function f(x) = -0.5(x + 5)³(x + 3)(x - 3) satisfies the specified conditions of decreasing at x = -5, having a local minimum at x = -3, and a local maximum at x = 3.
How to Generate a Continuous and Differentiable Function?One possible function that satisfies the given properties is:
f(x) = -0.5(x + 5)³(x + 3)(x - 3)
Check as follows:
Decreasing at x = -5:
Taking the derivative of f(x) and evaluating it at x = -5, we have:
f'(x) = -1.5(x + 5)²(x + 3)(x - 3) - 0.5(x + 5)³
f'(-5) = -1.5(0)²(-2)(-8) - 0.5(0)³ = 0 - 0 = 0
The derivative is zero at x = -5, therefore the function has a critical point at that location. To check if it is a maximum or minimum, we can examine the second derivative.
Taking the second derivative:
f''(x) = -3(x + 5)(x + 3)(x - 3) - 3(x + 5)²(x - 3)
f''(-5) = -3(0)(-2)(-8) - 3(0)²(-8) = 0 - 0 = 0
The second derivative is also zero at x = -5. However, since the first derivative is negative for x < -5 and positive for x > -5, this means that f(x) is decreasing at x = -5.
Local minimum at x = -3:
To check if f(x) has a local minimum at x = -3, we can examine the first and second derivatives at that point.
Taking the first derivative:
f'(-3) = -1.5(2)²(0)(-6) - 0.5(2)³ = 0
The first derivative is zero at x = -3, indicating a critical point.
Taking the second derivative:
f''(-3) = -3(2)(0)(-6) - 3(2)²(-6) = 0 - 72 = -72
Since the second derivative is negative at x = -3, this confirms the presence of a local minimum.
Local maximum at x = 3:
To check if f(x) has a local maximum at x = 3, we can again examine the first and second derivatives at that point.
Taking the first derivative:
f'(3) = -1.5(8)²(6)(0) - 0.5(8)³ = 0
The first derivative is zero at x = 3, indicating a critical point.
Taking the second derivative:
f''(3) = -3(8)(6)(0) - 3(8)²(0) = 0 - 0 = 0
The second derivative is zero at x = 3, indicating that the test is inconclusive. However, since the first derivative is positive for x < 3 and negative for x > 3, this means that f(x) is decreasing at x = 3.
Therefore, the function f(x) = -0.5(x + 5)³(x + 3)(x - 3) satisfies all the given conditions.
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A graph has time driven (hours) on the x-axis, and Distance Driven (miles) on the y-axis. Points are grouped closely together an increase slightly. Points (2, 225) and (8, 75) are outside of the cluster.
The scatterplot shows the time driven on a trip compared to the distance driven. Inspect the scatterplot to determine if it has outliers.
How many outliers does the data set have?
The point
is an outlier in the data se
The data set has two outliers, namely the points (2, 225) and (8, 75).
Based on the given information about the scatterplot, we can observe that most of the points are grouped closely together and show a slight increase.
There are two points that lie outside of this cluster, specifically (2, 225) and (8, 75).
To determine if these points are outliers, we need to consider their deviation from the general pattern exhibited by the majority of the data points.
If these points deviate significantly from the overall trend, they can be considered outliers.
In this case, since (2, 225) and (8, 75) lie outside of the cluster of closely grouped points and do not follow the general pattern, they can be considered outliers.
These points are noticeably different from the majority of the data points and may have influenced the overall trend of the scatterplot.
The data set has two outliers, namely the points (2, 225) and (8, 75).
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Five years older than Mukhari. Find the value of the expression if Mukhari is 43 years old.
Es el conjunto de deshielo determinante de la matriz x 2
5 7
Es igual a 4 cual es el valor de x
con un conjunto de deshielo determinante igual a 4, es x = 2.
Para determinar el valor de x en la matriz x 2
5 7
dado que el conjunto de deshielo determinante es igual a 4, necesitamos utilizar la propiedad de que el determinante de una matriz 2x2 se puede calcular utilizando la siguiente formula:
determinante = (a × d) - (b × c)
Donde a, b, c, y d son los elementos de la matriz.
En este caso, tenemos la matriz:
x 2
5 7
Aplicando la formula del determinante, podemos establecer la siguiente ecuacion:
( x × 7 ) - ( 2 × 5 ) = 4
Simplificando la ecuacion, obtenemos:
7x - 10 = 4
A continuacion, vamos a resolver la ecuacion para encontrar el valor de x:
7x = 4 + 10
7x = 14
Dividiendo ambos lados de la ecuacion por 7, obtenemos:
x = 2
Por lo tanto, el valor de x en la matriz x 2
5 7
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please help ?
I'm not good at this type of stuff(worth 10 points)
1. the linear equation 5(x + 7) - 3(x - 4) = 7x + 2, x = 9
2. In linear equation 4(3x + 5) - 3 = 9x - 7, x = -8
3. the linear equation 1/3(5x - 9) = 2(1/3x + 6), x = 15
What is a linear equation?A linear equation is an equation in only on variable.
1. To solve the linear equation 5(x + 7) - 3(x - 4) = 7x + 2, we proceed as follows
5(x + 7) - 3(x - 4) = 7x + 2
Expanding the brackets, we have
5x + 35 - 3x + 12 = 7x + 2
Collecting like terms in the expression, we have
5x + 35 - 3x + 12 = 7x + 2
5x - 3x - 7x = 2 - 35 - 12
-5x = -45
x = -45/-5
x = 9
2. To solve linear equation 4(3x + 5) - 3 = 9x - 7, we proceed as follows
4(3x + 5) - 3 = 9x - 7
Expanding the brackets, we have
12x + 20 - 3 = 9x - 7
Collecting like terms in the expression, we have
12x - 9x = - 7 + 3 - 20
3x = -24
x = -24/3
x = -8
3. To solve the linear equation 1/3(5x - 9) = 2(1/3x + 6), we proceed as follows
1/3(5x - 9) = 2(1/3x + 6)
Expanding the brackets, we have
5x/3 - 3 = 2/3x + 12
Collecting like terms, we have
5x/3 - 2x/3 = 12 + 3
3x/3 = 15
x = 15
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please answer i am stuck
9.
Find the volume of the cylinder. All measurements are in
centimeters. Keep your answer exact.
5
Answer:
The volume of the cylinder is 628.318530718
Step-by-step explanation:
The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.
The radius is 5, and the height is 8. Plug these values into the equation and solve:
[tex]v =\pi *5^2*8[/tex]
[tex]v = 628.318530718[/tex]
So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32
Answer:
200π or 628
Step-by-step explanation:
Note: your picture is not clear so I am assuming the height to be 8.
r = 5
h = 8
Volume = πr²h
= π * 5² * 8
= (25*8) π
= 200π
= 200*3.14
= 628
Help excel college student
EOP511
The total petty cash expenditures would be =$130.84
How to calculate the petty cash expenditures?To calculate the petty cash expenditures, the following is added up as follows;
The cost for stamp = $12.50
The cost for coffee supplies = $25.19
The cost for pizza delivery = $15.50
The cost for white board markers = $20.00
The cost for sympathy greeting card= $5.78
The cost of flowers for Jean's retirement farewell = $39.87
The cost of courier = $12.00
Therefore the total petty cash expenditures would be= 12.50+25.19+15.50+20+5.78+39.87+12= $130.84
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A man goes 10m North and turns left and covers 6m. He again turns left and walks 5m. Which direction is he in from starting point?
The man is in the south direction from the starting point.
Let's visualize the movements of the man step by step:
The man starts by going 10 meters north.
He then turns left (which means he is now facing west) and covers 6 meters in that direction.
Next, he turns left again (which means he is now facing south) and walks 5 meters.
To determine the final direction of the man from the starting point, we can consider the net effect of his movements.
Starting from the north, he moved 10 meters in that direction. Then, he turned left twice, which corresponds to a 180-degree turn, effectively changing his direction by 180 degrees.
Since he initially faced north and then made a 180-degree turn, he is now facing south. Therefore, the direction he is in from the starting point is "south."
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Find the sum of the first 33 terms of the following series, to the nearest
integer.
2, 11, 20,...
Step-by-step explanation:
Common difference , d, is 9
Sn = n/2 ( a1 + a33) a33 = a1 + 32d = 2 + 32(9) = 290
S33 = 33/2 ( 2+290) = 4818
In circle M below, diameter AC, chords AB and BC, and radius MB
are drawn.
Which statement is not true?
(1) AABC is a right triangle. (3) mBC = m/BMC
(2) AABM is isosceles.
(4) mAB = mLACB
The statement which is not true include the following: (2) AABM is isosceles.
What is an isosceles triangle?In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length and two (2) equal angles.
By critically observing circle M shown above, we can reasonably infer and logically deduce the following true statements:
ΔABC is a right triangle.
BM = MC (radius of circle M).
mBC = m∠BMC
mAB = 1/2m∠ACB (intersecting secant theorem).
In this context, we can logically conclude that triangle ABM does not represent an isosceles triangle because it does not have two (2) sides that are equal in length.
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Determine the equation of the hyperbola with foci... 100pts
Answer:
[tex]\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1[/tex]
Step-by-step explanation:
To write the equation of the hyperbola with foci (7, -8) and (-19, -8), and vertices (-1, -8) and (-11, -8), we first need to determine the orientation of the hyperbola.
As the y-values of the foci are the same, the foci are located horizontally from the center of the hyperbola, and therefore the hyperbola is horizontal (opening left and right).
The standard equation for a horizontal hyperbola is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]
where:
center = (h, k)vertices = (h±a, k)foci = (h±c, k) where c² = a² + b²The center of a hyperbola is the midpoint of the vertices.
Given that the vertices are (-1, -8) and (-11, -8), we can use the midpoint formula to find the coordinates of the center:
[tex](h,k)=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)[/tex]
[tex](h, k)=\left(\dfrac{-1-11}{2},\dfrac{-8-8}{2}\right)[/tex]
[tex](h, k)=\left(-6,-8\right)[/tex]
The value of "a" is the distance between the center of the hyperbola and each vertex. To find the value of a, calculate the distance between the x-coordinates:
[tex]a=-1-(-6)=5[/tex]
[tex]a=-6-(-11)=5[/tex]
The value of "c" is the distance between the center of the hyperbola and each focus. Given that the foci are (7, -8) and (-19, -8), and the center is (-6, -8), to find the value of c, calculate the distance between the x-coordinates:
[tex]c = 7-(-6)=13[/tex]
[tex]c = -6-(-19)=13[/tex]
Now we have determined the values of a and c, we can use c² = a² + b² to find the value of b:
[tex]c^2 = a^2 + b^2[/tex]
[tex]13^2 = 5^2 + b^2[/tex]
[tex]169 = 25 + b^2[/tex]
[tex]b^2=144[/tex]
[tex]b=12[/tex]
Finally, substitute the found values of a, b, h and k into the standard equation of a hyperbola:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]
[tex]\dfrac{(x-(-6))^2}{5^2}-\dfrac{(y-(-8))^2}{12^2}=1[/tex]
[tex]\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1[/tex]
Therefore, the equation of the hyperbola with foci (7, -8) and (-19, -8), and vertices (-1, -8) and (-11, -8) is:
[tex]\boxed{\dfrac{(x+6)^2}{25}-\dfrac{(y+8)^2}{144}=1}[/tex]
seven more than a certain number is nin nine less than twice the number. find the number.
Answer:
number is 16
Step-by-step explanation:
let n be the number , then 7 more than the number is n + 7 and 9 less than twice the number is 2n - 9
equating the 2 expressions
2n - 9 = n + 7 ( subtract n from both sides )
n - 9 = 7 ( add 9 to both sides )
n = 16
the required number is 16
The answer is:
n = 16Work/explanation:
Let's call the number n.
Seven more than n = n + 7
Nine less than twice n = 2n - 9
Put the expressions together : n + 7 = 2n - 9
Now, we have an equation that we can solve for n.
First, flop the equation
2n - 9 = n + 7
Subtract n from each side
n - 9 = 7
Add 9 to each side
n = 16
Therefore, n = 16.On January 1, 2022, ABC Company was established (trading firm engaged in buying and selling of laptop computers ), with an initial owner’s equity of P1,000,000. The company has an inventory 10 laptops each costing P50,000. In addition, it purchased a delivery equipment amounting to P250,000 (five years depreciation, straight line). The rest of the assets were in the form of cash.
At the end of 2022, operations showed that 5 laptops were sold at P50,000 each, 50% cash, 50% to be received in March of P2022. Aside from depreciation, a total of P50,000 (paid in cash) was incurred as operating expenses. Taxes are 50% of operating income to be paid in the same year of operations, if there are any. (Tax will not be deducted if there is an operating loss).
Construct the following :
a.) Balance sheet as of January 1, 2022 and December 31, 2022.
b.) Income Statement for the year ended Dec. 31, 2022 .
c.) Statement of Cash Flows for the year ended Dec. 31, 2022.
a) Balance Sheet as of January 1, 2022: Total Assets: P1,750,000
b) Income Statement for the year ended December 31, 2022: Net Income: Operating Income - Tax Expense
c) Statement of Cash Flows for the year ended December 31, 2022: None (Assuming no financing activities are mentioned in the information)
a) Balance Sheet as of January 1, 2022:
Assets:
Cash: P1,000,000
Inventory (10 laptops * P50,000): P500,000
Delivery Equipment (less depreciation): P250,000
Total Assets: P1,750,000
Liabilities:
None (Assuming no liabilities are mentioned in the given information)
Owner's Equity: P1,750,000
Balance Sheet as of December 31, 2022:
Assets:
Cash: (Assuming no cash transactions are mentioned in the information)
Accounts Receivable (50% of P50,000): P25,000
Inventory (5 laptops * P50,000): P250,000
Delivery Equipment (less depreciation): P200,000
Total Assets: P475,000
Liabilities:
Accounts Payable (50% of P50,000): P25,000
Income Tax Payable: (50% of Operating Income)
Total Liabilities: P25,000 + Income Tax Payable
Owner's Equity: (Initial Owner's Equity + Net Income)
b) Income Statement for the year ended December 31, 2022:
Sales Revenue: 5 laptops * P50,000 = P250,000
Operating Expenses: P50,000
Operating Income: Sales Revenue - Operating Expenses
Tax Expense: (50% of Operating Income)
Net Income: Operating Income - Tax Expense
c) Statement of Cash Flows for the year ended December 31, 2022:
Cash Flows from Operating Activities:
Cash received from sales: (50% of P250,000)
Cash paid for operating expenses: P50,000
Tax payments: (50% of Tax Expense)
Cash Flows from Investing Activities:
Purchase of delivery equipment: P250,000
Cash Flows from Financing Activities:
None (Assuming no financing activities are mentioned in the information)
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if 3+5 equals 8 then what does 5+3 equal?
Answer:
8
Step-by-step explanation:
Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
The angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°
How to calculate for angle between the intersection of a secant and a tangent.To calculate for the angle between the intersection of a secant and a tangent we need to know the measure of the intercepted arc, and then divide it by 2 to get the angle.
If the measure of the arc HM is given to be equal to 108°, then the measure of angle MHU is calculated as:
angle MHU = 108°/2
m∠MHU = 54°
Therefore, the angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°
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HELP THIS QUESTION IS HARD
Answer:
a)
[tex] \frac{1}{( - 7)^{4} } [/tex]
Answer:
[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]
Step-by-step explanation:
The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.
According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.
Thus, the negative exponent rule is given as:
[tex]b^-^n=\frac{1}{b^n}[/tex]
Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]
Which of the following are necessary when proving that the opposite sides of
a parallelogram are congruent? Check all that apply.
A. Opposite sides are parallel.
B. Corresponding parts of congruent triangles are congruent.
C. Opposite sides are perpendicular.
D. Corresponding parts of similar triangles are similar.
SUBMIT
Answer:
It's A and B: Opposite sides are parallel and Corresponding parts of congruent triangles are congruent.
Step-by-step explanation:
I need help understanding how to format this:
f(x)-4
f(x)=2x+1
an example of another question for it (if you're not sure what im asking), another question was to answer this:
f(4)
f(x)=2x+1
f(4)=2(4)+1
this one is easy to get, but i'm not too sure how to put it on the first one...
Answer:
Step-by-step explanation:
To format and solve the equation "f(x) - 4" with the given function "f(x) = 2x + 1," we substitute the function into the equation and solve for x. Here's how it can be done:
f(x) - 4 = 2x + 1 - 4
Simplifying further:
f(x) - 4 = 2x - 3
To answer the question "f(4)" using the function f(x) = 2x + 1, we substitute x = 4 into the function:
f(4) = 2(4) + 1
Simplifying further:
f(4) = 8 + 1
f(4) = 9
Therefore, the value of f(4) is 9 when using the function f(x) = 2x + 1.