The first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
What are the first 5 terms of the sequence?From the question, we have the following parameters that can be used in our computation:
The sequence is generated by using gn = 2(gn-1)
Such that g1 = 1/3 and n is a whole number greater than 1.
Using the above as a guide, we have the following:
The sequence means that we multiply the current term by 2 to get the next term
So, we have the following representations
a(2) = 2 * 1/3 = 2/3
a(3) = 2 * 2/3 = 4/3
a(4) = 2 * 4/3 = 8/3
a(5) = 2 * 8/3 = 16/3
Hence, the first 5 terms of the sequence are 1/3, 2/3, 4/3, 8/3 ans 16/3
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For the function f(x)=|x-3 | select all the true statements. A. The function is increasing on the interval [3, 5) B. The function is increasing of the Interval (0, 3) C. The vertex is (0, 3) D. The vertex is (3, 0). E. The y-intercept is (0, 3). F. The y-intercept is (3, 0).
Answer:
D and E----------------------
See attached graph to help with answer choices.
Given function:
f(x) = | x - 3 |Answer choices:
A. The function is increasing on the interval [3, 5) - False, correct interval is [3, + ∞)B. The function is increasing on the Interval (0, 3) - False, as shown aboveC. The vertex is (0, 3) - False, the vertex is (3, 0)D. The vertex is (3, 0) - TRUEE. The y-intercept is (0, 3) - TRUEF. The y-intercept is (3, 0) - False, the correct one is given aboveHow many games did the team play last season?
The number of games that the team did play in the last season is 23.
What is the frequency?The frequency is the number of times an event happens. Therefore, frequency is the number of repetitions of a digit or an event.
The given frequency table represents the frequency of different runs scored by the team in the entire season.
The frequency is written in tally form, which means that each of the vertical lines represents the count of 1, while a group of fours lines such that the four lines are vertical while the fifth line cuts the other four represents a count of 5 as shown in the second column of the second row.
Therefore, the frequency table can be made as:
Number of runs Frequency
0 8
1 5
2 3
3 6
4 1
Total: 23
Hence, the team played 23 games.
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For the right triangle below, find the measure of the angle.
Figure is not to scale.
For the given right-angled triangle the measure of the angle is 11.30°.
Given adjacent base of the triangle = 10
given opposite side of the triangle = 2
To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.
So, we can use the above tan ∠ relation to find the angle.
Tan ∠ = opposite side / adjacent side
Tan ∠ = 2/10
Tan ∠ = 1/5
∠ = Tan⁻¹(1/5)
∠ = 11.30°.
From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.
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Sarah uses a square and two semicircular7 inches regions to design a heart shaped poster find the area of the heart then find the approximate area by using 3.14radius
The poster has an area equal to 192.423 square inches.
How to determine the area of a heart shaped poster
In this problem we must determine the area of a heart shaped poster, that is, the combination of the areas of a square and two semicircles, whose resulting formula is introduced below:
A = D² + (π / 4) · D²
Where:
A - Area of the heart shaped poster, in square inches.D - Side length of the square, in inches.If we know that π = 3.14 and D = 7 in, then the area of the poster is:
A = 7² + (π / 4) · 7²
A = (5π / 4) · 7²
A = 192.423 in²
The area of the poster is equal to 192.423 square inches.
Remark
The image is missing and the statement is not well explained. A correct statement is shown below:
Sarah uses a square with side length of 7 inches and two semicircles with diameter of 7 inches to design a heart shaped poster. Find the area of the heart. Then, find the approximate area by using 3.14.
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1a. Model the periodic motion of the horses using an
equation and a graph.
Horse Equation: Use function notation in degrees. Your
function will graph below
The amount of time it takes the horse to complete a full cycle of motion is known as the period of the motion and can be calculated as follows:
T = 2π/ω.
What is the explanation for the above response?Let's assume that a straightforward harmonic motion can be used to simulate the horse's movements. The simple harmonic motion equation is:
y = A sin(ωt + φ)
where:
The deviation from equilibrium is represented by the number y.
The maximum displacement's amplitude is A.
The angular frequency is equal to two times the frequency ω.
It's time t
The phase angle is φ
The equation can be written as follows, assuming that the horse is moving vertically and that its highest point corresponds to y = 0.
y = A sin(ωt)
where is the angular frequency and A is the motion's amplitude.
On a graph, where the horizontal axis denotes time and the vertical axis denotes displacement, we can draw this function as a sine wave. The
amount of time it takes the horse to complete a full cycle of motion is known as the period of the motion and can be calculated as follows:
T = 2π/ω
We need to know the duration of the horse's motion in order to predict when Ivan will have another chance to make a flawless shot. It's challenging to determine the period precisely in the absence of more details.
You can name the graph of the carousel equation θ = A cos(ωt) as follows:
The time, t, is displayed on the x-axis as seconds.
The angular position from the midline, θ, expressed in degrees, is shown on the y-axis.
The horizontal axis at θ = 0 degrees is the midline.
The largest angle of departure from the midline, or the distance between the wave's crest (highest point) or trough (lowest point), is known as the amplitude, or A.
The interval between two consecutive wave crests or troughs is known as the period, or T, which is the length of time it takes for one full cycle of motion.
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cot0 equals 6, lies in quadrant 3 sin20
The exact value of sin 2θ is 12/37
How to find the exact value of sin 2θ?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
We have:
cot θ = 6
Thus, tan θ = 1/6
Using the given information, we can sketch the location of the angle θ in the quadrant (See the attached image).
Thus, we can calculate the value of the hypotenuse using the Pythagoras theorem. That is:
hypotenuse = √((-6)² + (-1)²) = √37
sin θ = -1/√37
cos θ = -6/√37
Using trig. identity:
sin 2θ = 2sinθ·cosθ
sin 2θ = 2 * (-1/√37) * (-6/√37)
sin 2θ = 12/37
Therefore, the exact value of sin 2θ is 12/37
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Complete Question
If cot θ = 6,and θ lies in quadrant 3, find the exact value of sin 2θ
Non mutually exclusive events !
The missing probability is P(A or B) = 131/200
How to calculate the probabilityIt should be noted that in order to find the probability of the union of two events A and B, i.e., P(A or B), we can use the following formula:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - P(A and B) = (9/20) + (1/4) - (9/200)
Simplifying the expression, we get:
P(A or B) = 45/100 + 25/100 - 9/200 = (90+50-9)/200 = 131/200
The probability is 131 / 200.
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Choose yes or no to tell whether the equation has the given solution 1/4×+3=3=4×+ 1,x=8
Answer:
[tex]\large\boxed{\tt No.}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to determine if the equation has a solution given a value.}[/tex]
[tex]\textsf{Since x is given to us, we can use the \underline{Substitution Property of Equality} to evaluate}[/tex]
[tex]\textsf{the equation.}[/tex]
[tex]\large\underline{\textsf{What is the Substitution Property of Equality?}}[/tex]
[tex]\textsf{The Substitution Property of Equality is a Property that allows us to substitute}[/tex]
[tex]\textsf{a known term, or expression for an unknown variable, or some kind of placeholder.}[/tex]
[tex]\textsf{After Substitution, we can prove that the expressions are still equal with this}[/tex]
[tex]\textsf{property.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\tt \frac{1}{4} x + 3 = " 3 = " 4x+1[/tex]
[tex]\textsf{There's likely a typo in your equation given, hence I will fix it.}[/tex]
[tex]\tt \frac{1}{4} x + 3 = 4x+1[/tex]
[tex]\textsf{Substitute 8 for x in both sides of the equation using our property.}[/tex]
[tex]\underline{\textsf{Use the Substitution Property of Equality;}}[/tex]
[tex]\tt \frac{1}{4} (8) + 3 = 4(8)+1[/tex]
[tex]\underline{\textsf{Follow PEMDAS, multiply first;}}[/tex]
[tex]\tt 2 + 3 = 32+1[/tex]
[tex]\underline{\textsf{Evaluate;}}[/tex]
[tex]\tt 5 \neq 33[/tex]
[tex]\textsf{If the "typo" was the actual equation;}[/tex]
[tex]\tt 5 \neq 3 \neq 33[/tex]
[tex]\large\boxed{\tt No.}[/tex]
If a, b, c are in H.P.; prove that b+ca+ca+b ac' ab bc are also in A.P.
If a, b, c are in Harmonic Progression, b+ca+ca+b ac' ab bc are in Arithmetic Progression.
How to prove Harmonic Progression and Arithmetic Progression?Given a, b, c are in H.P.:
1/a + 1/b = 2/c
Multiplying both sides by abc:
bc + ac = 2ab
Adding c to both sides:
bc + ac + c = 2ab + c
Rearranging the terms:
c + ab = ac + bc
Adding the terms b + ca and ca + b to both sides:
b + ca + ca + b + ac' + ab + bc = ac + bc + b + ca + ca + b
Simplifying:
b + ca + ca + b + ac' + ab + bc = 2ac + 2b
Dividing both sides by 2:
(b + ca + ca + b + ac' + ab + bc)/2 = ac + b
Hence, b+ca+ca+b ac' ab bc are in A.P.
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Ted made $56 in interest by placing $700 in a savings account with simple interest for 1 year. What was the interest rate?
The interest rate if Ted made $56 in interest for 1 year on a principle of $700 will be 8%.
Given, the interest amount is $56.
The principal amount is $700.
The time period of investment is 1 year.
Now, we have to find the interest rate.
The formula to find the simple interest is,
S.I = PTR/100.
Now, we need to substitute the values in the above formula.
S.I = PTR/100
56 = 700×1×R / 100
56 = 700R/100
5600 = 700R
R = 5600/700
R = 8
Therefore, the interest rate is 8%.
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Someone help i really need help with this
The equation which can be used to find the amount the admission tickets cost would be 4x + 25 = 175. The cost of the admission tickets would therefore be $ 37.50.
How to find the equation ?The total spent by Ms. Boi was $ 175.00 so this is what the entire equation would be equal to. The cost of admission tickets will be denoted as x because they are the unknown figure.
There are 4 tickets purchased so the equation would be:
4 x Cost of tickets - Parking cost = Total spent
4 x - 25 = 175
The cost of each admission ticket is:
4 x - 25 = 175
x = 150 / 4
x = $ 37.50
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HELP ASAP!!!
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The IQR of 10 is the most accurate to use, since the data is skewed.
The range of 10 is the most accurate to use, since the data is skewed.
The IQR of 45 is the most accurate to use to show that they need more money.
The range of 45 is the most accurate to use to show that they have plenty of money.
A measure of variability which the charity should use to accurately represent the data include the following: D. The range of 45 is the most accurate to use to show that they have plenty of money.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 10.
First quartile (Q₁) = 13.75.
Median (Med) = 20.
Third quartile (Q₃) = 26.25.
Maximum (Max) = 55.
For the IQR, we have:
IQR = Third quartile (Q₃) - First quartile (Q₁)
IQR = 26.25 - 13.75
IQR = 12.50
For the range, we have;
Range = maximum - minimum
Range = 55 - 10
Range = 45.
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Hey folks help me out for some points :)
Answer:
C
Step-by-step explanation:
Positive numbers represent a positive situation. And negative numbers coincide with a negative situation.
Ex: An increase in temperature corresponds to a positive number, and a decrease in temperature with a negative number.
The hypotenuse of a certain right triangle is twice the length of the
shorter leg. The shorter leg is 4 cm.
Answer:
Step-by-step explanation:
If the hypotenuse of a right triangle is twice the length of the shorter leg and the shorter leg is 4 cm, then the hypotenuse is 2 * 4 cm = 8 cm.
Using the Pythagorean theorem, we can find the length of the longer leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Letting c represent the length of the hypotenuse and a and b represent the lengths of the other two sides, we can write this as c^2 = a^2 + b^2.
Substituting in the known values for c and one of the other sides (let’s say a), we have:
8^2 = 4^2 + b^2 64 = 16 + b^2 b^2 = 48 b = sqrt(48)
So, the length of the longer leg is sqrt(48) cm, or approximately 6.93 cm.
$800000 into a 25:17 ratio. How much do each get
Answer: Therefore, the first person gets $476,190.48 and the second person gets $323,809.52.
Step-by-step explanation: To divide $800,000 into a 25:17 ratio, we first need to add the ratio terms (25 + 17 = 42) to determine the total number of parts. Then, we divide the total amount by the total number of parts to determine the value of each part. Finally, we multiply the value of each part by the respective ratio term to determine the amount that each person gets.
The calculation steps are as follows:
Determine the total number of parts: 25 + 17 = 42
Determine the value of each part:
Value of each part = Total amount / Total number of parts
= $800,000 / 42
= $19,047.62 (rounded to two decimal places)
Determine the amount that each person gets by multiplying the value of each part by the respective ratio term:
First person gets: 25 parts * $19,047.62 per part = $476,190.48
Second person gets: 17 parts * $19,047.62 per part = $323,809.52
M7|L5
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
Enter ✔
Answer:
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
If mZRST = 70, mZQST = 2x, and mZQSR = 3x - 10, what is the mZQSR
16
48
32
38
Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.
Explain about the adjacent angles:If two angles share a side and a vertex, they are said to be neighbouring in geometry. In other words, neighbouring angles do not overlap and are placed next to one another immediately.
We may infer from our criteria and the aforementioned instances that any pair of neighbouring angles has a shared vertex and a common side. They really aren't adjacent if one of these elements is absent. By searching for these two characteristics, we can categorise pairs of angles as neighbouring or not adjacent.There are numerous unique connections between angles in pairs. You can recognise other angle connections, such as supplementary and complementary angles, by recognising nearby angles.Given data:
m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10From the figure:
m∠RST = m∠QST + m∠QSR
Put the values
70 = 2x + 3x - 10
5x = 80
x = 16
Thus,
m∠QSR = 3x - 10 = 3(16) - 10
m∠QSR = 38
Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.
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Complete question:
If m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10, what is the m∠QSR?.
The figure is attached:
16
48
32
38
Is 93 + 7 positive or negative?
Answer:
93 + 7 = 100
Step-by-step explanation:
I would assume positive because 100 is above the x-axis not below it.
PLEASE HELP I have 30 minutes! What is the end behavior of this equation and how did you get it?
The limit of the function will be:
lim f(x) = ∞ as x → ∞
lim f(x) = 0 as x → -∞
How to explain the functionThe limit of f(x) as x goes towards infinity is infinite while the limit of f(x) approaches 0 when x tends to a negative value. Mathematically speaking,
lim f(x) = ∞ as x → ∞
lim f(x) = 0 as x → -∞
We can comprehend such behavior because the function's base is greater than 1 which explains how its growth accelerates as x increases and diminishes quickly as x declines towards zero.
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Bree is replacing the wire on her farm paddock fences. She has measured a couple of the sides and drawn a sketch of the paddock shape. (pic below)
a. Find the two missing sides and calculate the perimeter of the paddocks
Perimeter?
b. The cost of fencing wire is $5 per meter. How much will the wire cost
Cost?
a. The perimeter of the paddock is 120 meters
b. The cost of the wire will be $600
a. To find the missing sides and calculate the perimeter of the paddock, let's analyze the given sketch.
The length of the missing side on the left can be determined by subtracting the known length of 10m from the total height of 20m. Therefore, the left side has a length:
20m - 10m = 10m.
The missing side on the right is equal in length to the known side of 40m.
Now we can calculate the perimeter by adding up all the side lengths:
Perimeter = 10m + 40m + 20m + 10m + 40m
= 120m.
b. To calculate the cost of the wire, we need to multiply the perimeter of the paddock by the cost per meter of fencing wire, which is $5/m.
Wire Cost = Perimeter × Cost per meter
= 120m × $5/m
= $600.
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PLS HELP ASAP PLSSSSSS
Answer:
a) |x -8| = 6
b) |x -15| = 0
Step-by-step explanation:
You want the values of 'b' and 'c' for the cases where the solutions to the equation |x -b| = c are ...
2 and 1415SolutionsThe solutions to |x -b| = c are the solutions to ...
x -b = c ⇒ x = b +c
x -b = -c ⇒ x = b -c
ParametersGiven the two solutions P and Q, the values of 'b' and 'c' can be found from ...
P = b +c
Q = b -c
Adding these two equations gives ...
P +Q = 2b ⇒ b = (P +Q)/2
Subtracting the second equation from the first gives ...
P -Q = 2c ⇒ c = (P -Q)/2
a) Solutions 2 and 14b = (2 +14)/2 = 8
c = (14 -2)/2 = 6
The equation is ...
|x -8| = 6
b) Solutions 15 and 15b = (15 +15)/2 = 15
c = (15 -15)/2 = 0
The equation is ...
|x -15| = 0
What is the value of "x", when 1/3x = 9 1/3?
Answer:
x=28
Step-by-step explanation:
solve for x by simplifying both sides of the equation, then isolating the variable.
have a good day :)
Answer
x=3 1/9
Step-by-step explanation:
A number rounded to the nearest thousand is 47,000 which number could be the number that was rounded
Answer:
Anything greater than or equal to 46,500, and less than or equal to 47,499 could be the answer.
For example, a number, let's say 46,589 falls within that range and may have been the number that was rounded.
Husk takes out a 3200 student loan at 6.7% to help him
Part (a) find the total amount interest that will accrue for loan 1(community college )
Part (b) find the total amount of intrest that will a cure for loan 2 state university
Part (c) find the total amount intrest that accrues until payment begin
(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.
How to solve(a) For loan 1, $3200 at 6.7% for 4 years and 7 months (4 years in college + 3 months deferment), the simple interest = 3200 * 0.067 * (55/12) ≈ $1023.33.
(b) For loan 2, $12,000 at 7.3% for 2 years and 7 months (2 years in college + 3 months deferment), simple interest = 12000 * 0.073 * (31/12) ≈ $2362.33.
(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.
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Which expression is equivalent to 2^3 . 5^-2 ?
Solve 8 • w ≤ 72. Graph the solution.
Please help
Answer:
w≤9
Step-by-step explanation:
8w ≤ 72
Divide by 8 on both sides
w ≤ 9
For graph, draw a number line and label a point as 9. Draw a solid line facing to the left and having a closed point at 9. The line should not extend past 9.
You’re planning to buy a car and you want to have $25,000 to purchase a car in cash in 5 years. If you’re able to receive 10% interest rate for investing the money, how much money should you invest today in order to have $25,000 in 5 years?
You have to invest $15,506.08
How to solve for the investmentPV = FV / (1 + r)^n
where:
PV = present value (amount of money you need to invest today)
FV = future value (amount of money you want to have in 5 years, which is $25,000)
r = interest rate (10% or 0.1)
n = number of periods (5 years)
Plugging in the values into the formula:
PV = $25,000 / (1 + 0.1)^5
PV = $25,000 / 1.61051
PV = $15,506.08
Therefore, you need to invest approximately $15,506.08 today at a 10% interest rate in order to have $25,000 in 5 years to purchase a car in cash.
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Construct a truth table for the statement (~ pVq) →q.
Here is the truth table for the statement (~ p V q) → q:
```
p q ~p ~p V q (~p V q) → q
---------------------------------------
T T F T T
T F F F T
F T T T T
F F T F T
```
In the table, `p` and `q` represent the truth values of the propositions `p` and `q`, respectively. The symbol `~` represents negation (i.e., "not"). The symbol `V` represents the logical connective "or" (i.e., "inclusive or"). The symbol `→` represents the conditional connective "implies" (i.e., "if...then").
To fill in the truth table, we first evaluate `~p` and `~p V q` for each combination of truth values for `p` and `q`. Then, we evaluate `(~p V q) → q` for each combination of truth values.
We can see that the statement is always true, regardless of the truth values of `p` and `q`, except for the case where `p` is true and `q` is false.
1. Ashenge Private Limited Company is about to start production of new products. Before the start of the new production, it cost the company $200,000 to construct the factory building. Once the construction is over, the cost per unit of production is estimated to be Birr 20. Upon selling, the company will incur a 20% commission expense. Moreover, the price per unit of products is decided to be Birr 50.
Required:
a) Construct the total cost equation in terms of quantity.
b) Determine the break-even quantity and break-even revenue.
The total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
Given that a company is starting a new production, it cost the company $200,000 to construct the factory building.
The cost per unit of production is estimated to be Birr 20.
The company will incur a 20% commission expense.
The price per unit of products is decided to be Birr 50.
We need to find the total cost equation in terms of quantity and determine the break-even quantity.
a) The fixed cost of the company is $200,000, and 40 per unit sell,
Therefore for n units the total cost =
200,000 + 40n
b) BEQ = FC / P−VC
= 200,000 / 50-40
= 20,000
Hence the total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
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Identify an equation in standard form for ellipse with its center at the origin, a vertex at (3, 0), and a focus at (1, 0). HELP ASAP! This is due in 15 minutes!!
Answer:
Step-by-step explanation:
The standard form equation for an ellipse with center at the origin is:
x^2/a^2 + y^2/b^2 = 1
where 'a' is the distance from the center to the vertices along the x-axis and 'b' is the distance from the center to the vertices along the y-axis.
In this case, the center is at the origin, and a vertex is at (3, 0). So, we know that 'a' = 3.
We also know that the distance from the center to the focus is 'c', and that:
c^2 = a^2 - b^2
Since the center is at the origin, 'c' is the distance from the focus (1, 0) to the origin, which is 1. So, we can solve for 'b' as:
c^2 = a^2 - b^2
1^2 = 3^2 - b^2
b^2 = 3^2 - 1^2
b^2 = 8
b = sqrt(8) = 2sqrt(2)
Substituting these values into the standard form equation, we get:
x^2/3^2 + y^2/(2sqrt(2))^2 = 1
Simplifying:
x^2/9 + y^2/8 = 1
So, the equation in standard form for the given ellipse is:
9x^2 + 8y^2 = 72
