Answer: Let's call the number of large boxes purchased "L" and the number of small boxes purchased "S".
From the problem, we know that:
Each small box has 100 nails, so the total number of nails from the small boxes is 100S.
Each large box has 450 nails, so the total number of nails from the large boxes is 450L.
The contractor bought 3 more small boxes than large boxes, so S = L + 3.
The total number of nails purchased is 2500, so 100S + 450L = 2500.
We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for L:
100S + 450L = 2500
Substituting S = L + 3:
100(L + 3) + 450L = 2500
Expanding the parentheses:
100L + 300 + 450L = 2500
Combining like terms:
550L + 300 = 2500
Subtracting 300 from both sides:
550L = 2200
Dividing both sides by 550:
L = 4
So the contractor purchased 4 large boxes of nails.
We can use the equation S = L + 3 to find the number of small boxes purchased:
S = L + 3 = 4 + 3 = 7
So the contractor purchased 7 small boxes of nails.
Therefore, the contractor purchased 4 large boxes and 7 small boxes of nails.
Step-by-step explanation:
What will be the coordinates of point G after
a 90° counterclockwise rotation about the
origin?
So, if we have the original coordinates of point G, we can swap the x and y values and negate the new y-value to find the coordinates of point G after a 90° counterclockwise rotation about the origin.
To perform a 90° counterclockwise rotation about the origin, we can use the following transformation:
x' = -y
y' = x
This means that the new x-coordinate (x') will be the negative of the original y-coordinate (y), and the new y-coordinate (y') will be the original x-coordinate (x).
If we have the coordinates of point G, we can apply this transformation to find the new coordinates after the rotation.
Let's say that the coordinates of point G are (x, y). Then, the new coordinates (x', y') after the rotation will be:
x' = -y
y' = x
So, the new coordinates will be (-y, x). Therefore, if we want to find the new coordinates after a 90° counterclockwise rotation, we just need to swap the x and y values and negate the new y-value. This gives us the following coordinates for point G after the rotation:
G' = (-y, x)
To know more about coordinates
https://brainly.com/question/17206319
#SPJ9
The mean of 50 observations was 250. Later it was found that the number 152 was wrongly copied as 102 for the computation of mean. Find the correct mean.
Answer:
[tex](250*50-102)+152[\tex]
The correct mean of the 50 observations is 249.96.
To find the correct mean, we need to adjust the value that was wrongly copied. The difference between 152 and 102 is 50, so the corrected total of the 50 observations would be:
Corrected total = (original total - 102) + 152
= [tex](250*50-102)+152[/tex]
= [tex]12498[/tex]
Therefore, the correct mean of the 50 observations is:
Correct mean = Corrected total / Number of observations
= [tex]12498 / 50[/tex]
= 249.96
Hence, the correct mean of the 50 observations is 249.96.
To learn more about Mean,
https://brainly.com/question/26547285?referrer=searchResults
You spend a $5 per turn on a fair game to win $15 for each winYou lose the first round but win the next two rounds. What was the net payoff ?
If you spend a $5 per turn on a fair game to win $15 for each win and you lose the first round but win the next two rounds, then the net payoff is $15
Since you spend $5 per turn and play three rounds, your total cost is $5 x 3 = $15.
If you win a game, you receive $15, so winning two games will give you $15 x 2 = $30.
However, since you lost the first round, you only won two out of three rounds. Therefore, your net payoff is:
= $30 - $15
Subtract the numbers
= $15
Therefore, your net payoff is $15
Learn more about net payoff here
brainly.com/question/24406282
#SPJ4
it is known that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75 % of the colege students will take more than how many minutes when trying to find a parking spot in the library parking lot? O A. 32 minutes B. 42 minutes C. 28 minutes O D. 3.4 minutes
75 % of the college students will take more than 4.25 minutes when trying to find a parking spot in the library parking lot.
What is experimental probability?Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A number of real experiments are carried out in order to ascertain the likelihood of any event. Random experiments are studies that don't have a predetermined outcome. The results of such tests are unpredictable. The chance of random experiments is calculated repeatedly. A trial is a repeating of an experiment that is performed a certain number of times.
Given that, mean of 3.5 minutes and a standard deviation of 1 minute.
Now, for 75% we have:
P(X > x) = 0.75
The z-score is given by:
0.75 = (X - μ) / σ
Substituting the formula we have:
0.75 = (X - 3.5) / 1
0.75 = X - 3.5
X = 0.75 + 3.5 = 4.25.
Hence, 75 % of the college students will take more than 4.25 minutes when trying to find a parking spot in the library parking lot.
Learn more about z-score here:
https://brainly.com/question/30557336
#SPJ1
Points C and D are plotted on a graph.
C has coordinates (1, -5) and D has coordinates (6, 4)
Calculate the length of the line segment CD.
Leave your answer to 2 decimal places.
Answer:
The length of line segment CD is 10.3 units (rounded to 2 decimal places).
Step-by-step explanation:
To find the length of line segment CD, we need to use the distance formula, which is:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Here, (x1, y1) = (1, -5) and (x2, y2) = (6, 4).
So, substituting these values in the distance formula, we get:
Distance = √[(6 - 1)^2 + (4 - (-5))^2]
= √[5^2 + 9^2]
= √(25 + 81)
= √106
≈ 10.3 (rounded to 2 decimal places)
Therefore, the length of line segment CD is 10.3 units (rounded to 2 decimal places).
Hope this helps!
A = 1/2bh or A = bh/2
Area: 256.5 cm2
base: 27cm
What is the height?
I need to know the answer asap
256 is the lateral surface area.
What's the lateral surface area?
Side indicates the side of commodity. thus, lateral surface area is set up by chancing the face area of the sides of the object.
This is done by chancing the border of the base and multiplying it by the height of any three- dimensional figure.
For the given situation,
The sides of the triangle are 5 cm, 6 cm, 5 cm.
The length of the prism = 16 cm
The formula for lateral surface area of triangular prism is
LSA = (perimeter)(length)
On substituting the above values,
LSA = (5 + 6 + 5)(16)
= (16)(16)
= 256
Learn more about lateral surface area
brainly.com/question/14001755
#SPJ1
'If vector a =k times vector b, what is the angle between a and b where k is a scalar quantity?,
Angle between vector a and vector b is 0 degrees or 180 degrees.
What is vector?
A vector is a quantity that not only indicates magnitude but also indicates how an object is moving or where it is in relation to another point or item. Euclidean vector, geometric vector, and spatial vector are other names for it.
In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.
What is scalar quantity?
Physical quantities with merely magnitude and no direction are referred to as scalar quantities. These physical quantities can be explained just by their numerical value without any further guidance. These physical values can be added according to the basic algebraic rules, and in this case, only their magnitudes are added.
GIVEN:
If vector a is equal to k (scalar quantity)times vector b.
then vector a and vector b are parallel to each other.
The angle between two parallel vectors is 0 degrees or 180 degrees.
So, the angle between vector a and vector b is
0 degrees or 180 degrees.
To know more about scalar and vector quantity visit:
brainly.com/question/774036
#SPJ1
There are 2 boys and 2 girls working on an art project. They are sharing 10 ounces of paint equally. How much paint should each child get?
Answer:
2 ounces per person
Step-by-step explanation:
find arc length of the partial circle
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =90 \end{cases}\implies s=\cfrac{(90)\pi (8)}{180}\implies s=4\pi[/tex]
Challenge A store is giving out cards labeled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 30% discount. Otherwise, you get a 25% discount. The table shows the results of 200 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants approximately half of the customers to receive the 25% discount, does this seem like an appropriate method? explain
Answer: To find the relative frequency for each discount, we need to divide the number of customers who received each discount by the total number of customers.
Discount Number of customers Relative Frequency
10% 70 0.35
25% 99 0.495
30% 31 0.155
To determine if it is appropriate for the manager to want approximately half of the customers to receive the 25% discount, we can calculate the relative frequency for the 25% discount and compare it to 0.5 (or 50%).
Relative frequency for 25% discount = 99/200 = 0.495
Since the relative frequency for the 25% discount is already very close to 0.5, it seems like an appropriate method to achieve the manager's goal. However, it's worth noting that this method may not be the most effective in terms of maximizing profits or customer satisfaction. It's always important for businesses to carefully consider their pricing strategies and discount policies.
Step-by-step explanation:
At the shelter 0.6 of the animals are dogs, If there are 260 totally animals how many are not dogs?
Answer: 104
Step-by-step explanation:
If .6 or 60% of the animals in the shelter are dogs, then we can multiply .6 by 260 to get how many are dogs.
.6 times 260 is 156.
260-156=104.
The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function f(x)equalsnegative 3. 439 x Superscript 4 Baseline plus 35. 952 x cubed minus 99. 139 x squared plus 41. 541 x plus 178. 192 where x is the number of years since 1996. Find the number of bald eagles in the state in the winter of 1999
The number of bald eagles in the state in the winter of 1999 is 273.909, where The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function.
by the given information the equation is
[tex]f(x) = -3.439(x)^4 + 35.952(x)^3 - 99.139(x)^2 + 41.541(x) + 178.192[/tex]
where x = number of years since 1996
The given quartic function must be changed to x = 3 in order to determine the number of bald eagles in the state during the winter of 1999:
[tex]f(3) = -3.439(3)^4 + 35.952(3)^3 - 99.139(3)^2 + 41.541(3) + 178.192[/tex]
When we condense this expression, we get:
f(3) = -3.439(81) + 35.952(27) - 99.139(9) + 41.541(3) + 178.192
f(3) = -1107.759 + 970.104 - 892.251 + 124.623 + 178.192
f(3) = 273.909
Hence, in the winter of 1999, there were roughly 273.909 bald eagles in the state.
learn more about the quartic function
brainly.com/question/30180400
#SPJ4
Find the values of the variables and the measures of the indicated angles.
Answer:
115°
Step-by-step explanation:
You want the measure of angle S opposite angle (4x+5)° in an inscribed quadrilateral in which the other two angles are (5x-2)° and (7x+2)°.
Inscribed quadrilateralThe measure of an inscribed angle is half the measure of the arc it intercepts.
Two opposite angles in an inscribed quadrilateral intercept arcs that total the full circle. Since the sum of double those angles is 360°, the sum of opposite angles of an inscribed quadrilateral is 180°—they are supplementary.
We can use this to find the value of x:
(5x -2)° +(7x +2)° = 180°
12x = 180 . . . . . . simplify
x = 15 . . . . . . . divide by 12
Now, the angle opposite S can be found to be ...
(4x +5)° = (4·15 +5)° = 65°
Angle S is the supplement of this:
S = 180° -65°
S = 115°
What is the remainder when \( f(x)=-6 x^{23}+x^{11}-x^{6}+2 x \) is divided by \( x+1 \) ? The remainder is
The remainder when f(x)=-6x^23+x^11-x^6+2x is divided by x+1 is -7.
Explanation: In this question, we can solve the problem by using the Remainder Theorem. The remainder theorem states that when we divide a polynomial f(x) by x−a then we get a remainder equal to f(a). So, here we can take a=−1 and find the remainder of f(x).
Here is the given polynomial,
()=−6^23+^11−^6+2
We are asked to find the remainder when f(x) is divided by x+1. Using the remainder theorem, we can find the remainder of f(x) by evaluating f(−1).
(−1)=−6(−1)^23+(−1)^11−(−1)^6+2(−1)=6+1+1−2=6
Now, we have the remainder as 6. However, we need the remainder when f(x) is divided by x+1. The relationship between the remainder and the divisor of a polynomial is that when we divide a polynomial f(x) by x−a, we get a remainder of r(x) such that:
()=(−)()+()
where q(x) is the quotient of the division.
So, the question asks us to divide the polynomial f(x) by x+1 and get the remainder. Here is the long division of f(x) by x+1:
The remainder is −7. Therefore, the remainder when f(x) is divided by x+1 is -7.
For further information on Polynomials, refer below:
https://brainly.com/question/11536910
#SPJ11
The graph plots four equations, A, B, C, and D:
Line A joins ordered pair negative 6, 16 and 9, negative 4. Line B joins ordered pair negative 2, 20 and 8, 0. Line C joins ordered pair negative 7, negative 6 and 6, 20. Line D joins ordered pair 7, 20 and 0, negative 7.
Which pair of equations has (4, 8) as its solution?
Equation A and Equation C
Equation B and Equation C
Equation C and Equation D
Equation B and Equation D
(It is not option D or A)
Answer: To find the equation that passes through (4, 8), we need to check which equation contains that point.
Line A has an equation of y = (2/5)x + (194/5). Plugging in x = 4, we get y = (2/5)(4) + (194/5) = 198/5, which is not equal to 8.
Line B has an equation of y = (-5/5)x + 30. Plugging in x = 4, we get y = (-5/5)(4) + 30 = 26, which is not equal to 8.
Line C has an equation of y = (13/13)x - 7. Plugging in x = 4, we get y = (13/13)(4) - 7 = -3, which is not equal to 8.
Line D has an equation of y = (-27/7)x + (491/7). Plugging in x = 4, we get y = (-27/7)(4) + (491/7) = 377/7, which is not equal to 8.
Therefore, none of the given equations has (4, 8) as its solution.
Step-by-step explanation:
A mixture of 50 liters of paint is 25% red tint, 30% yellow tint and 45% water.
5 liters of yellow tint are added to the original mixture.
The percent of yellow tint in the new mixture is ____?
Answer must be correct to 1 decimal place
From the given information provided, the percent of yellow tint in the new mixture is 36.4%.
The total amount of yellow tint in the original mixture is:
0.30 × 50 liters = 15 liters
When 5 liters of yellow tint are added to the mixture, the total amount of yellow tint becomes:
15 + 5 = 20 liters
The total amount of new mixture is:
50 + 5 = 55 liters
To find the percentage of yellow tint in the new mixture, we divide the amount of yellow tint by the total amount of the mixture and multiply by 100:
(20/55) × 100 = 36.4%
Learn more about percentage here: brainly.com/question/843074
#SPJ4
The first equation in the system models the height, h, of a falling volleyball as a function of time, t. The second equation models the height, h, of the hands of a player jumping up to spike the ball as a function of time, t. Which statement describes the situation modeled by this system?
StartLayout Enlarged Left-Brace 1st Row h = 14 minus 16 t squared 2nd Row h = 7 + 24 t minus 16 t squared EndLayout
The volleyball is 7 feet above the ground at the instant the player begins her jump.
The volleyball is 14 feet above the ground at the instant the player begins her jump.
The volleyball is 16 feet above the ground at the instant the player begins her jump.
The volleyball is 24 feet above the ground at the instant the player begins her jump.
Answer:
The volleyball is 14 feet above the ground at the instant the pl;ayer begins her jump.
B is correct.
Step-by-step explanation:
Here we have two situation of system of models.
[tex]\text{The height (h) of a falling volleyball as function of time (t):h}(t)=14-16t^2[/tex]
[tex]\text{The height (h) of the hands of a player as function of time (t):h}(t)=7-24t-16t^2[/tex]
We need to find the height of ball above the ground at the instant the player begins jump.
At t=0, player begins jump.
We put t=0 into [tex]h(t)=7+24t-16t^2[/tex]
Height of player hand at t=0 , h=7 feet.
Now we will set t=0 for first model.
[tex]h(0)=14-16\times0^2 \ = > 14[/tex]
Thus, The volleyball is 14 feet above the ground at the instant the pl;ayer begins her jump.
B is correct.
Answer: B
Step-by-step explanation:
EDGE 2023
One pump can fill a swimming pool in 4 hours. A second pump can fill the pool in 6 hours. If the pool starts empty, what part of the pool will be filled in each situation? The first pump works for 2 hours and the second pump works for 3 hours.
Answer:
1/2 of the pool is filled, and in the second situation, the entire pool is filled.
Step-by-step explanation:
Let's start by finding the hourly filling rate of each pump. The first pump can fill the pool in 4 hours, so its hourly rate is 1/4 of the pool. The second pump can fill the pool in 6 hours, so its hourly rate is 1/6 of the pool.
For the first situation, the first pump works for 2 hours, so it fills 2/4 or 1/2 of the pool. The second pump does not work in this situation, so it fills 0 of the pool. Therefore, the total amount of the pool filled is 1/2.
For the second situation, the first pump works for 2 hours and fills 1/2 of the pool. The second pump works for 3 hours and fills 3/6 or 1/2 of the pool. Therefore, the total amount of the pool filled is 1/2 + 1/2 = 1.
So, in the first situation, 1/2 of the pool is filled, and in the second situation, the entire pool is filled.
what is 46x squared times 24x squard
Answer:
the answer to ur question is: 1218816
Hello!
Please help me for this geometry problem
I appreciate it!
Answer:
x = 48
Step-by-step explanation:
given a line parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally, that is
[tex]\frac{x}{18}[/tex] = [tex]\frac{56}{21}[/tex] ( cross- multiply )
21x = 18 × 56 = 1008 ( divide both sides by 21 )
x = 48
fsUse the conversion 8 km/h = 5 mph to convert 32 m/s into mph. If your answer is a decimal, give it to 1 d.p.
Answer:
72mph
Step-by-step explanation:
To convert km/hr into m/s, simply multiply the speed value by 5/18
To convert 8Km/hr to m/s, multiply 8 by 5/18 or divide by 3.6
8 x 5/18 = 2.22m/s
You can say that 2.22m/s = 5mph since 8km/hr = 5mph
If 2.2m/s =5mph, 1m/s = 5mph/ 2.2 (Divide both sides by 2.2)
Then 32m/s = 5mph/2.2 x 32
2.25 x 32 = 72 mph
Using the conversion, 32 m/s is equivalent to 72 mph.
We have,
To convert 32 m/s to mph using the conversion factor 8 km/h = 5 mph,
We can follow these steps:
- Convert 32 m/s to km/h by multiplying by the conversion factor:
32 m/s x (3.6 km/h / 1 m/s) = 115.2 km/h
- Convert 115.2 km/h to mph using the conversion factor 8 km/h = 5 mph:
115.2 km/h x (5 mph / 8 km/h) = 72 mph
Therefore,
Using the conversion, 32 m/s is equivalent to 72 mph.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ6
Which of the following rectangles has an area that can be represented by the algebraic expression 9x+9
?
Responses
Image with alt text:
Image with alt text:
Image with alt text:
Image with alt text:
Answer: we can't see the images
Step-by-step explanation:
Answer:
Step-by-step explanation:
be can not see the pictures sir do better ni***
Do the three lines 5x - y = 7, x + 3y = 11, and 2x + 3y = 13 have a common point of intersection? If so, find it. if not, explain why not .
Answer:
429
Step-by-step explanation:
There are 2 boys and 2 girls working on an art project. They are sharing 10 ounces of paint equally. How much paint should each child get? show work
Answer:
2.5 oz each
Step-by-step explanation:
2 boys and 2 girls
10 divided by 2 is 5, 5 is not an even number.
there would be 2 left after our calculation.
meaning that 2 in half's (hence .5) is 4 so each child would get 2.5 oz of paint.
Hope this helps, thanks :)
Answer: 2 1/2
Step-by-step explanation:
Mike's Bakery recently spent a total of $392 on new equipment, and their average hourly operating costs are $9. Their average hourly receipts are $10. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?
For Mike's Bakery the total expenses will be $3528 and the total receipts will be $3920 and it will take 392 hours.
Let number of hours the bakery needs to operate in order to make back the amount it invested in equipment be = "h".
To find "h", we need to find the profit per hour,
The profit per hour is = difference between hourly receipts and hourly operating costs;
Profit per hour = Hourly receipts - Hourly operating costs
Profit per hour = $10 - $9
Profit per hour = $1
The total profit required to make back the $392 investment is = $392,
We know that,
⇒ Total profit = (Profit per hour) × (Number of hours)
⇒ $392 = $1 × h
⇒ h = $392/$1
⇒ h = 392
So, bakery needs to operate for 392 hours to make back the amount it invested in equipment.
To calculate the total expenses and receipts, we can use the following formulas:
⇒ Total expenses = (Operating costs) × (Number of hours)
⇒ Total expenses = $9 × 392
⇒ Total expenses = $3528
⇒ Total receipts = (Hourly receipts) × (Number of hours)
⇒ Total receipts = $10 × 392
⇒ Total receipts = $3920
Therefore, the total expenses is $3528 and total receipts is $3920.
Learn more about Expense here
https://brainly.com/question/20931468
#SPJ4
What is the advantage
of a two-way relative frequency table for
showing relationships between sets of
paired data?
A two-way relative frequency table, in general, is an effective instrument for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and conduct methodical hypothesis testing.
A tool used to display the connection between two sets of paired data is a two-way relative frequency table, which arranges the data in rows and columns. The frequency of each combination is indicated in the chart, which can also be used to determine its relative frequency, which is calculated as the frequency of the combination divided by the total number of observations.
The benefit of using a two-way relative frequency table to illustrate relationships between pairs of paired data is that it gives a more comprehensive image of the data and the interrelationships between the variables. More specifically, it enables us to:
Finding patterns and trends is simple thanks to the table's presentation of the data. We can see which combinations are more or less prevalent than others by examining the relative frequencies of each set of values, and we can spot patterns in the data that might not be obvious otherwise.
Calculate conditional probabilities: Conditional probabilities are the likelihoods of one event given the occurrence of another event, and they can be determined using the chart. We can determine the likelihood that a smoker is male or female and the likelihood that a non-smoker is male or female, for instance, if we have a two-way table illustrating the connection between gender and smoking status.
Testing hypothesis: The table can be used to evaluate theories about how the variables are related to one another. A chi-square test, for instance, can be used to determine whether gender and smoking status are significantly associated.
In general, a two-way relative frequency table is an effective tool for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and test theories in a methodical manner.
Learn more about frequency here:
https://brainly.com/question/5102661
#SPJ4
Use substitution to solve the system of equations. Show your work.
Check your answer to show proof that the solution works in each equation.
[tex]4x+y=14\\y=8+2x[/tex]
Answer:
x = 1 , y = 10
Step-by-step explanation:
Given : y = 8 + 2x
by substitution,
4x + 8 + 2x = 14
6x + 8 = 14
6x = 14 - 8
6x = 6
x = 6/6 = 1
y = 8 + 2x
y = 8 + 2(1)
y= 10
Proof :
if x = 1,
4 (1) + 8 +2 (1) = 14
4 + 8 + 2 = 14
14 = 14
if y = 10 and x = 1
4 ( 1) + 10 = 14
4 + 10 = 14
14 = 14
For both equations, LHS = RHS
Therefore Proved.
hope it helps!
-8x253.96 pls help if you can because i'm stuck on this problem, so please help if you can.
Determine the eccentricity for r=5/2+1sin theta
0. 5
5
2
1
Determine the equation of the directrix of r=26. 4/4+4. 4 cos theta
X=-6
Y=6
X=6
The eccentricity for r=5/2+1sin theta and the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6
To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:
r = 5/2 + 1sin(θ)
r = 5/2 + 1y/r
r^2 = (5/2)r + y
x^2 + y^2 = (5/2)r + y
x^2 + y^2 = (5/2)√(x^2 + y^2) + y
x^2 - (5/2)√(x^2 + y^2) + y^2 = 0
We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:
x^2/a^2 + y^2/b^2 = 1
Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:
e = √(1 - b^2/a^2)
Plugging in our values, we get:
e = √(1 - 1/(5/2))
e = √(3/5)
e ≈ 0.5
Therefore, the answer is (A) 0.5.
To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:
r = 26.4/4 + 4.4cos(θ)
r = 6.6 + 4.4x/r
r^2 = 6.6r + 4.4x
x = (r^2 - 6.6r)/4.4
We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:
y = (1/4p)x^2
Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:
y = 1.65
However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:
x = 0
Therefore, the answer is (C) x = 6.
To learn more about directrix refer to:
brainly.com/question/17376399
#SPJ4