The answer is approximately 2.2198, which is option (b).
How did we get the value?To evaluate log13(297) using the change-of-base formula, we can express it in terms of a logarithm with a base that we can easily calculate, such as the common logarithm (base 10) or the natural logarithm (base e).
Let's use the common logarithm:
log13(297) = log10(297) / log10(13)
We can use a calculator to find the decimal approximations of log10(297) and log10(13), and then divide them to get the final answer:
log13(297) ≈ 2.2198 (rounded to 4 decimal places)
Therefore, the answer is approximately 2.2198, which is option (b).
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what is the answer???
helppppppo
Answer:
18
Step-by-step explanation:
18
The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 16 mph and the Mystic travels at 20 mph. How far apart will they be in 2 hours?The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 16 mph and the Mystic travels at 20 mph. How far apart will they be in 2 hours?
They will be 72 km far apart after 2 hours. The solution has been obtained by using the concept of relative speed.
What is the relative speed?The speed of a moving body relative to another might be referred to as relative speed. The differential between two moving bodies is used to calculate their relative speed. Yet, the relative speed of two bodies travelling in opposition to one another is determined by summing their respective speeds.
We are given that the Serenity and the Mystic travels in the opposite direction at 16 mph and at 20 mph respectively.
So,
The relative speed = 16 + 20 = 36 mph
Now,
After 2 hours the distance between them will be as follows
36 × 2 = 72 mph
Hence, they will be 72 km far apart after 2 hours.
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Micah has 6565 feet of fencing to make a dog run in his yard. He wants the length to be 4.54.5 feet more than the width. Find the length, L�, by solving the equation 2L+2(L−4.5)=652�+2(�-4.5)=65.
The length of the dog run is 18.5 feet and the width is 14 feet. Micah can use his 65 feet of fencing to make a dog run with these dimensions.
To find the length of the dog run, we need to solve the equation for L. Here are the steps:
1. Start with the given equation: 2L + 2(L - 4.5) = 65
2. Distribute the 2 on the right side of the equation: 2L + 2L - 9 = 65
3. Combine like terms: 4L - 9 = 65
4. Add 9 to both sides of the equation: 4L = 74
5. Divide both sides of the equation by 4: L = 18.5
So, the length of the dog run is 18.5 feet. Since the length is 4.5 feet more than the width, we can find the width by subtracting 4.5 from the length:
W = L - 4.5
W = 18.5 - 4.5
W = 14
Therefore, the width of the dog run is 14 feet.
In conclusion, the length of the dog run is 18.5 feet and the width is 14 feet. Micah can use his 65 feet of fencing to make a dog run with these dimensions.
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The given expression is a polynomial with two variables. Factor the polynomial completely and check using multiplication. 60a^(3)b^(2)+10a^(2)-50a^(4)b^(2)
The factored form of the given polynomial is [tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}[/tex]
To factor the given polynomial completely, we need to find the greatest common factor (GCF) of all the terms. The GCF of 60a^(3)b^(2), 10a^(2), and -50a^(4)b^(2) is 10a^(2).
So, we can factor out 10a^(2) from each term to get:
[tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}[/tex]
Now, we can check our answer by multiplying the factors back together:
[tex]10a^{(2)}(6ab^{(2)}+1-5a^{(2)}b^{(2))}=60a^{(3)}b^{(2)}+10a^{(2)}-50a^{(4)}b^{(2)}[/tex]
Therefore, the factored form of the given polynomial is [tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}.[/tex]
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Slope intercept form of 8x+y= -4
Answer: y=mx+b
Step-by-step explanation:
How much water can a swimming pool hold? In volume yd
L x W x D cubic yards is the maximum amount of water the pool can contain.
Volume = Length x Width x Depth
what are volumes?Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Many forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to calculate the volume for each of these shapes.
from the question:
We need to know the pool's dimensions in order to calculate how much water it can store. Assume the pool has the following dimensions: L yards in length, W yards in breadth, and D yards in depth.
The following formula can be used to determine the pool's volume:
Volume = length, width, and depth
Volume = L, W, and D cubic yards.
The pool may therefore hold a maximum volume of water that is L x W x D cubic yards.
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The maximum amount of water that the pool can contain is the volume of the pool = L x W x D cubic yards.
What do you mean by volume?The volume of a closed surface or object is a three-dimensional mathematical measurement. Cubic volume metrics include m3, cm3, in3, etc.
Any three-dimensional solid's volume is the area it takes up.
Forms come in a wide range of volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylinders, cones, and more. In this lesson, we'll learn how to determine the volume of each of these forms.
Here we need to know the pool's dimensions in order to calculate how much water it can store.
Let the pool's length be L yards.
Let the pool's breadth be W yards.
Let the pool's depth be D yards.
The following formula can be used to determine the pool's volume:
Volume = length × width × depth
⇒ Volume = L × W × D cubic yards.
The pool may therefore hold a maximum volume of water that is:
L x W x D cubic yards.
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Overproduction of uric acid in the body can be an indication of
cell breakdown. This may be an advance indication of illness such
as gout, leukemia, or lymphoma.† Over a period of months, an adult
m
Overproduction of uric acid in the body is a condition known as hyperuricemia. It occurs when the body produces more uric acid than it can excrete. Uric acid is a waste product that is formed when the body breaks down purines, which are found in certain foods and drinks. If the body is unable to get rid of the excess uric acid, it can build up and form crystals in the joints, causing a painful form of arthritis known as gout.
Hyperuricemia can also be an indication of other health conditions, such as leukemia and lymphoma. These are types of cancer that affect the blood cells and the immune system, respectively. When cells in the body break down, they release uric acid into the bloodstream. If there is an overproduction of cells, as in the case of leukemia and lymphoma, this can lead to an excess of uric acid in the body.
It is important to monitor the levels of uric acid in the body, as it can be an early indication of these serious health conditions. A healthcare professional can conduct tests to measure the levels of uric acid in the body and determine the cause of the overproduction.
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Correct question is" Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advanced indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eleven blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.75 mg/dl. (a) Find a 95 % confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) (b) Find the sample size necessary for a 95 % confidence level with a maximal margin of error E = 1.02 for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)"
How do you find the x and y intercept given (1,1), (-5,7)
The x and y-intercept of the given point (1,1), (-5,7) is 2 and 2.
How to find the x and y-intercept of a line?The equation of a line can be represented in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope.
(1,1), (-5,7)
m = 7 - 1 / -5 - 1
m = 6 / -6
m = - 1
Let's find the x and y-intercept using (1, 1)
y = -x + b
1 = -1 + b
b = 1 + 1
b = 2
Therefore,
y = - x + 2
Let's find x and y-intercept
y = -(0) + 2
y = 2
- x = y + 2
-x = 0 + 2
x = 2
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is 90 rational please help
Answer:
Step-by-step explanation:
I'm assuming you mean is the number 90 a rational number. The answer is that yes, it is a rational number.
Let me explain:
Under all the possible numbers, there is a taxonomy to organize these types of numbers. It goes down a list from:
- all numbers, which is divided into two groups; complex and real
Under real numbers, there's rational and irrational:
Under rational, there's integers and fractions
Under integers, there's whole numbers and negative
Under whole numbers, there's natural numbers and 0 (yes, zero).
90 falls under natural numbers, which means it is also a rational number. Hope this helps!
as fast as you can answer what is 880,372-751,684 ?
Answer:
128688
Step-by-step explanation:
How many ways are there to choose 4 books from a collection of 11 books? Hint... does order matter? Type your answer...
There are 330 ways to choose 4 books from a collection of 11 books.
To solve this problem, we need to use the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of items, r is the number of items to choose, and ! means factorial (the product of all positive integers up to that number).
In this case, we have n = 11 (the total number of books) and r = 4 (the number of books to choose). Plugging these values into the formula, we get:
C(11, 4) = 11! / (4! * (11-4)!)
= 11! / (4! * 7!)
= (11 * 10 * 9 * 8 * 7!)/ (4! * 7!)
= (11 * 10 * 9 * 8)/ (4 * 3 * 2 * 1)
= 330
So there are 330 ways to choose 4 books from a collection of 11 books.
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the expression a[(9b-c)+z] is equivalent to
Answer:
The expression a[(9b-c)+z] can be simplified using the distributive property of multiplication. The distributive property states that:
a(b + c) = ab + ac
Using this property, we can distribute the a to the terms inside the brackets:
a[(9b-c)+z] = a(9b-c) + az
Now, we can distribute the a again to get:
a(9b-c) + az = 9ab - ac + az
Therefore, the expression a[(9b-c)+z] is equivalent to 9ab - ac + az.
Answer:
Step-by-step explanation: Equivalent to 9ab - ac + az.
16. Arden surveyed the 6th grade to see what there favorite colors were.
If 48
students chose yellow, how many students
were surveyed in all?"
How
students chose blue?
many
red?
How many chose purple, green& other?
Answer:
in all 240
60 chose blue
72 chose red
36 chose orange
7 chose purple
10 chose green
7 chose other
Step-by-step explanation:
48 x 5 = 240
48 = 20%
20% x 5 = 100%
The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor. This is an example of
a. Nominal data
b. Ordinal data
c. Interval data
d. Quantitative data
The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor is an example of Ordinal data.
Ordinal data is a type of data that is used to rank or order objects or individuals. It is a type of categorical data that can be ranked or ordered, but cannot be measured numerically. In this case, the machines are ranked based on their design quality, which is an example of ordinal data. Other examples of ordinal data include movie ratings, letter grades, and customer satisfaction ratings.
Therefore, the correct answer is option b. Ordinal data.
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Set up the equation and solve. The product of 2 consecutive odd integers is 195. Find the integers. Show all steps.
To set up the equation and solve for the 2 consecutive odd integers whose product is 195, we can follow these steps:
1. Let x be the first odd integer. 2.The next consecutive odd integer will be x+2. 3.The product of these two integers is 195, so we can set up the equation: x(x+2) = 195 4.Expand the equation: x^2 + 2x = 195
5.Rearrange the equation to get a quadratic equation: x^2 + 2x - 195 = 0 6. Use the quadratic formula to solve for x: x = (-2 ± √(2^2 - 4(1)(-195)))/(2(1)) 7. Simplify the equation: x = (-2 ± √784)/2 8. Solve for the two possible values of x: x = (-2 + 28)/2 or x = (-2 - 28)/2 9. Simplify the equations: x = 13 or x = -15 10. Since x is an odd integer, we can reject the solution x = -15. 11. The first odd integer is x = 13, and the next consecutive odd integer is x+2 = 15.
12. Therefore, the two consecutive odd integers whose product is 195 are 13 and 15.
The final answer is 13 and 15.
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Please solve this for me
Answer:
55%
Step-by-step explanation:
When you have a question that asks you about a percentage and it gives you a fraction, most of the time you just have to divide the numbers. In this case you will do 11/20=0.55 and you will change the decimal to a percentage. Which will be 55%.
Company C had 60 defective batteries out of 10,800. If Company C also manufactures 15,000 new batteries next month, how does this company compare to the others? Explain.
The expected number of defective batteries out of 15,000 batteries is of:
83.3.
Then this expected amount is compared to the number of different batteries of the other companies.
How to obtain the number of defective batteries?The number of defective batteries is obtained applying the proportions in the context of the problem.
Company C had 60 defective batteries out of 10,800, hence the proportion of defective batteries is of:
60/10,800.
Out of 15,000 batteries, the expected number of defective batteries is of:
60/10,800 x 15,000 = 83.3.
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Find all values of c that will make the polynomial a perfect square trinomial. 225r^(2)-120r+c
The value of c that will make the polynomial a perfect square trinomial is 16.
To find the values of c that will make the polynomial a perfect square trinomial, we need to use the formula for a perfect square trinomial, which is:
[tex](a+b)^(2) = a^(2)+2ab+b^(2)[/tex]
In this case, we have:
[tex]225r^(2)-120r+c = (15r+b)^(2)[/tex]
Expanding the right side of the equation, we get:
[tex]225r^(2)-120r+c = 225r^(2)+30rb+b^(2)[/tex]
Comparing the coefficients of the terms, we can see that:
-120r = 30rb
b = -4
Now, substituting b back into the equation, we get:
[tex]c = b^(2) = (-4)^(2) = 16[/tex]
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You afe choosing between two health clubs. Club A offers membership for a fee of$18plus a monthly fee of$15. Club B offers membership for a fee of$11plus a monthly lee of$16. After how many months will the totat cost of each health club be the same? What will be the fotal cost for each club? In months the total cost of each health dub will be the same.
Tthe total cost for each club after 7 months will be $123.
To find out when the total cost of each health club will be the same, we can use the equation:
Club A total cost = Club B total cost
18 + 15x = 11 + 16x
Where x is the number of months. We can rearrange the equation to solve for x:
15x - 16x = 11 - 18
-x = -7
x = 7
So the total cost of each health club will be the same after 7 months. To find the total cost for each club, we can plug x = 7 back into the equation:
Club A total cost = 18 + 15(7) = $123
Club B total cost = 11 + 16(7) = $123
So, the total cost for each club after 7 months will be $123.
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a) Determine whether the following set of vectors inR4is linearly independent or linearly dependent.S={(1,0,−1,0),(1,1,0,2),(0,3,1,−2),(0,1,−1,2)}b) Write the vectoru=(10,1,4)as a linear combination of the vectorsv1=(2,3,5),v2=(1,2,4) and v3=(−2,2,3)
The given set of vectors in R4 is linearly independent and the vector u as a linear combination of the vectors v1, v2, and v3 can be written as u = (7,12,22)
a) To determine if the set of vectors in R4 is linearly independent or linearly dependent, we can use the rank of the matrix formed by these vectors. If the rank of the matrix is equal to the number of vectors, then the set is linearly independent. Otherwise, it is linearly dependent.
First, let's form the matrix using the vectors:
| 1 0 -1 0 |
| 1 1 0 2 |
| 0 3 1 -2 |
| 0 1 -1 2 |
Next, let's find the rank of the matrix. We can do this by using Gaussian elimination to reduce the matrix to row echelon form:
| 1 0 -1 0 |
| 0 1 1 -2 |
| 0 0 4 -6 |
| 0 0 0 4 |
The rank of the matrix is 4, which is equal to the number of vectors. Therefore, the set of vectors is linearly independent.
b) To write the vector u as a linear combination of the vectors v1, v2, and v3, we need to find the scalars a, b, and c such that:
u = av1 + bv2 + cv3
This gives us the following system of equations:
10 = 2a + b - 2c
1 = 3a + 2b + 2c
4 = 5a + 4b + 3c
We can use Gaussian elimination to solve this system of equations:
| 2 1 -2 | | a | = | 10 |
| 3 2 2 | | b | = | 1 |
| 5 4 3 | | c | = | 4 |
After reducing the matrix to row echelon form, we get:
| 1 0 1 | | a | = | 2 |
| 0 1 -2 | | b | = | 3 |
| 0 0 0 | | c | = | 0 |
From the third equation, we can see that c can be any value. Let's choose c = 0. Then, from the first two equations, we get:
a = 2
b = 3
Therefore, the vector u can be written as a linear combination of the vectors v1, v2, and v3 as follows:
u = 2v1 + 3v2 + 0v3
u = (2)(2,3,5) + (3)(1,2,4) + (0)(-2,2,3)
u = (4,6,10) + (3,6,12) + (0,0,0)
u = (7,12,22)
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En el año 2013 HUBO 1400 ALmnos que seleciona la asgnatura optativa de religion. En 2014 esta cifra bajo un 4% ¿cuantos alumnos la seleccionaran en 2014
Number of students that selected the elective subject of religion in 2014 is 1344
The problem tells us that in 2013, there were 1400 students who selected the elective subject of religion.
Then, in 2014, this figure decreased by 4%. This means that the new figure in 2014 will be 4 percentage less than the figure in 2013.
To calculate what 4% of 1400 is, we need to multiply 1400 by 4/100, which gives us 56. So, 56 students did not select the elective subject of religion in 2014 compared to 2013.
So, the number of students who selected the elective subject of religion in 2014 is
= 1400 - 56
= 1344
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Multiply 0. 035 times a power of ten so that the product is greater than 1, but less than 100. Write the expression. It's an Essay
Answer:
3.5 * 10²
Step-by-step explanation:
In standard form, the number before the point has to be less than ten so
0.035 = 3.5 *10²
Solving x^(2)+14x+3=0 by completing the square method produces an equation of the form (x+h)^(2)=k. Find h and k.
The values of h and k are h=7 and k=46. The equation in the form (x+h)^(2)=k is (x+7)^(2)=46.
To solve the equation x^(2)+14x+3=0 by completing the square method, we need to follow these steps:
1. Rearrange the equation so that the constant term is on the right side: x^(2)+14x=-3
2. Find the value of h by taking half of the coefficient of the x term: h=14/2=7
3. Add the square of h to both sides of the equation: x^(2)+14x+7^(2)=-3+7^(2)
4. Simplify the right side of the equation: x^(2)+14x+49=46
5. Write the left side of the equation in the form (x+h)^(2): (x+7)^(2)=46
Therefore, the values of h and k are h=7 and k=46. The equation in the form (x+h)^(2)=k is (x+7)^(2)=46.
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PLS HELP!! "What is the area of the shaded region"
Answer: 64.24 cm square
Step-by-step explanation:
length x width
11 x 7 = 77cm square
The radius of the circle is 2cm
The area of the circle =
r^2 = 2^2 12.57
Hence the area of the shaded region=
Area of rectangle – area of circle= 77 – 12.57= 64.43 cm2
What is the slope of the line graphed below?
Answer:
B
Step-by-step explanation:
I think so because the rise is going downward, which means it’s a negative number. Therefore m= -1/4
2. Given the matrix
\( A=\left(\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 11-6 \\ 0 & 1 & 10-6\end{array}\right) \)
(a) Show that A is invertible and determine by caculate A^−1
Yes, matrix A is invertible.
Therefore, the inverse of matrix A is A-1 =
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
To calculate A-1, we can use the following formula:
A-1 = (1/detA) x adj(A)
Where detA is the determinant of A, and adj(A) is the adjugate of A.
To calculate the determinant of A, we can use the following formula:
detA = (1 x (-1) x 10-6) + (-1 x (11-6) x 1) + (1 x (-1) x (2))
= 1 x (-1) x 4 - (-1) x 5 x 1 + 1 x (-1) x 2
= 4 - 5 + 2
= 1
Now we can calculate the adjugate of A. To do this, we need to calculate the cofactors of each element in A, and then take the transpose of the matrix.
The cofactors of A can be calculated as follows:
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
Now, taking the transpose of this matrix, we get the following:
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
Now, multiplying the determinant of A and the adjugate of A, we can calculate A-1:
A-1 = (1/1) x
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
=
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
Therefore, the inverse of matrix A is:
A-1 =
[tex]\begin{array}{ccc} -1 & -3 & 1 \\ 10-6 & 8 & 5 \\ -2 & -2 & -2\end{array}[/tex]
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what expression is equivalent to 8x+4
The expression that is equivalent to the given expression, 8x + 4, is 4(2x +1)
Determining the expression that is equivalent to the given expressionFrom the question, we are to determine the expression that is equivalent to the given expression.
The given expression is:
8x + 4
To determine the expression that is equivalent to the given expression, we will factorize the given expression.
First, we will determine the Greatest common factor (GCF) of the terms in the expression.
The terms in the expression are 8x and 4
The GCF of 8x and 4 is 4
Thus,
We can factor the expression as shown below:
8x + 4
4(2x + 1)
Hence, the expression is 4(2x + 1)
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At the sewing store, Janet bought a bag of mixed buttons. The bag included 270 buttons, of which 80% were large. How many large buttons did Janet get?
Answer: 216
Step-by-step explanation:
Equation:
270 x 80% = large buttons
To multiply by a percent, move the decimal to the left two places:
270 x 0.80 = large buttons
Solve:
270 x 0.80 = 216
Janet got 216 large buttons
Hope this helps!
On a bicycle, Kiara rides for 6 hours and is 26 miles from her house. After riding for 9 hours, she is 38 miles away. What is Kiara's rate?
Kiara's rate is 4 miles per hour. Take note that this simply asks for her current rate, not an average rate.
To find Kiara's rate at the 9-hour mark, we can subtract the distance she has traveled so far (26 miles) from the total distance (38 miles) to get the distance she traveled in the last 3 hours, which is 12 miles.
Then, we can divide the distance she traveled in the last 3 hours by the time taken (9 - 6) to get her rate:
Kiara's rate: 12/3Kiara's rate: 4 miles per hour.Therefore, Kiara's current rate is 4 miles per hour.
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Find Key Features of an Ellipse from Conic Form Feb 21, 10:24:52 AM Find the foci of the ellipse defined by the equation ((x+4)^(2))/(4)+((y+3)^(2))/(9)=1. If necessary round to the nearest tenth.
The required foci of the ellipse are also at (-4, -3).
To find the foci of the ellipse defined by the equation:
[tex]\dfrac{(x+4)^2}{4}+\dfrac{(y+3)^2}{9}=1[/tex]
We need to identify the values of 'a' and 'b' from the equation, where 'a' is the semi-major axis, and 'b' is the semi-minor axis of the ellipse.
The general equation of an ellipse centered at (h, k) is given by:
[tex]\dfrac{(x - h)^2}{ a^2} + \dfrac{(y - k)^2}{ b^2} = 1[/tex]
Comparing this with the given equation, we can see that the center of the ellipse is at (-4, -3), so (h, k) = (-4, -3).
Next, we find 'a' and 'b':
For the x-term: a² = 4
a = √4
a = 2
For the y-term: b² = 9
b = √9
b = 3
So, the semi-major axis 'a' is 2 units, and the semi-minor axis 'b' is 3 units.
Now, the distance from the center of the ellipse to the foci is given by:
[tex]c = \sqrt{(a^2 - b^2)[/tex]
[tex]c = \sqrt{(2^2 - 3^2)[/tex]
[tex]c=\sqrt{-5[/tex]
The distance is imaginary, which means the foci are not real, and the ellipse is degenerate. A degenerate ellipse is essentially a circle. Since we have a degenerate ellipse, the foci coincide with the center of the ellipse.
Therefore, the foci of the ellipse are also at (-4, -3).
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