identify the type of function shown in the graph.
Answers
The type of Function shown in the graph
Step-by-step explanation:
1.The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value.
2.Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each has a unique graph that is easy to visually differentiate from the rest.
3.we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.
Answer:
y= 1/2 csc (x)
Step-by-step explanation:
probably
Related Questions
plz help dont skip
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-2, 2) and point (4, 4) rounded to the nearest tenth?
4 units
5.7 units
1 unit
6.3 units
Answers
Answer:
The answer to your question is 6.3 units
Step-by-step explanation:
Data
A (-2, 2)
B (4, 4)
Distance = ?
Formula
dAB = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
Substitution
x1 = -2 x2 = 4 y1 = 2 y2 = 4
dAB = [tex]\sqrt{(4 + 2)^{2} + (4 - 2)^{2}}[/tex]
Simplification
dAB = [tex]\sqrt{6^{2} + 2^{2}}[/tex]
dAB = [tex]\sqrt{36 + 4}[/tex]
dAB = [tex]\sqrt{40}[/tex]
Result
dAB = 6.3 units
You are renting a limousine that charges certain rates to visit each of the following cities. You need to visit each city once and you need to start in Athens and end in Athens. Use the "Brute Force" Algorithm to find the cheapest route to visit each city and return home again to Athens.
Answers
Answer:
The cheapest route to visit each city and return home again to Athens is:
A→B→C→D→A or A→D→C→B→A.
Step-by-step explanation:
The Algorithm of Brute Force
List of all possible routesCalculate the charge of each route found in Step 1Pick the route which has the cheapest route.Let Athens ⇒A , Buford ⇒B , Cuming ⇒ C , Dacula ⇒ D
There are 6 routes to visit each city and return home again to Athens.
Route 1: A→B→C→D→A = 70 + 25 + 30 + 60 = $185
Route 2: A→B→D→C→A = 70 + 70 + 30 + 50 = $220
Route 3: A→C→B→D→A = 50 + 25 + 70 + 60 = $205
Route 4: A→C→D→B→A = 50 + 30 + 70 + 70 = $220
Route 5: A→D→B→C→A = 60 + 70 + 25 + 50 = $205
Route 6: A→D→C→B→A = 60 + 30 + 25 + 70 = $185
By checking the previous routes:
The cheapest charge will be $185 and it will be for the route
A→B→C→D→A or A→D→C→B→A.
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. The probability density function has what value in the interval between 20 and 28?a. 1.000 b. 0c. 0.125 d. 0.050
Answers
Answer:
The probability density function is f(x)=0.125.
Step-by-step explanation:
We have he continuous random variable x, which has a uniform distribution over the interval from 20 to 28. We calculate the probability density function has what value in the interval between 20 and 28.
We use the formula:
[tex]\boxed{f(x)=\frac{1}{b-a}}[/tex]
We have a=20 and b=28, we get
[tex]f(x)=\frac{1}{28-20}\\\\f(x)=\frac{1}{8}\\\\f(x)=0.125\\[/tex]
The probability density function is f(x)=0.125.
The value of the probability density function (pdf) in the interval between 20 and 28 is 0.125.
Explanation:The probability density function (pdf) of a continuous uniform distribution is represented by a horizontal line. Since the random variable x has a uniform distribution over the interval from 20 to 28, the pdf will also have a constant value over this interval.
To find the value of the pdf in the interval between 20 and 28, we need to calculate the area under the pdf curve in this interval. Since the pdf is a horizontal line, the area is simply equal to the height multiplied by the width of the interval.
Since the width of the interval is 8 (28 - 20) and the pdf is a uniform distribution, the height is 1/8. Therefore, the value of the pdf in the interval between 20 and 28 is 1/8 or 0.125.
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The side length of a square is (6x-1) inches Write a linear expression in simplest form to represent the perimeter of the square.Find the perimeter of x equals 3
Answers
Final answer:
The perimeter of a square with side length (6x-1) is expressed as P = 24x - 4. Substituting x with 3, the perimeter is calculated to be 68 inches.
Explanation:
The expression for the perimeter of a square is given by the formula P=4s, where 's' is the side length of the square. For a square with side length (6x-1) inches, the perimeter would be:
P = 4(6x-1)
This expression can be simplified to:
P = 24x - 4
When x equals 3, we substitute 3 in place of x:
P = 24(3) - 4
P = 72 - 4
P = 68 inches
Therefore, the perimeter of the square when x is 3 is 68 inches.
Tony collected 16.2 pounds of pecans from the trees on his farm.He will give the same weight of pecans to each of 12 friends.How many pounds of pecans will each friend get.
Answers
Each friend will get 1.35 pounds of pecans.
To find this, simply divide 16.2 by 12 to find the weight of pecans everyone gets. Thus making 1.35 pounds of pecans the answer.
I hope this helps!
Factor the expression. d2 – 4d + 4
(d + 2)2
(d – 4)(d – 1)
(d – 2)2
(d – 2)(d + 2)
Answers
Because d2 is just 2*d so it’s 2d-4d+4 subtract 2d from 4d and you get (2d+4) and you can factor out a 2 from that 2(d+2)
The expression d^2 - 4d + 4 factors to (d - 2)^2.
To factor the expression d^2 + 4d + 4, we are looking for two binomials that will multiply together to give us the original quadratic expression. These binomials will be of the form (d - a)^2 because the last term is a perfect square (4 = 22) and the middle term is twice the product of the square roots of the first and last terms.
Here's the step-by-step factoring:
1. Identify the square root of the first term, which is d.
2. Identify the square root of the last term, which is 2.
3. Since our middle term is negative, we use negative signs in our binomials.
4. The factored form is (d - 2)^2, as this will expand to d^2 - 2*d*2 + 22, which simplifies to d^2 - 4d + 4.
Which of the following is not true? Choose the correct answer below. A. The area in any normal distribution bounded by some score x is the same as the area bounded by the equivalent z-score in the standard normal distribution. B. A z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution. C. A z-score is an area under the normal curve. D. If values are converted to standard z-scores, then procedures for working with all normal distributions are the same as those for the standard normal distribution.
Answers
Using concepts of the normal distribution, it is found that the statement which is not true is:
C. A z-score is an area under the normal curve.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The standard normal distribution has [tex]\mu = 0, \sigma = 1[/tex]. The z-score converts any distribution a standard normal. It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the area under the normal curve.Thus, statement C is false, as the p-value is the area under the normal curve, not the z-score.
A similar problem is given at https://brainly.com/question/14243195
Joyce knits baby sweaters and baby socks. The baby sweaters take 10 feet of yarn and the baby socks take 5 feet of yarn. She has 100 feet of yarn and wants to make 5 sweaters. What is the maximum number of socks she will be able to make from the leftover yarn?
Let x represent sweaters and y represent socks.
Select one:
A. 8
B. 9
C. 11
D. 10
Answers
Answer: the maximum number of socks she will be able to make from the leftover yarn is 10
Step-by-step explanation:
Let x represent the number of sweaters.
Let y represent the number of socks.
The baby sweaters take 10 feet of yarn and the baby socks take 5 feet of yarn. This means that the total number of feet of yarn needed to make x sweaters and y socks is expressed as
10x + 5y
She has 100 feet of yarn and wants to make 5 sweaters. This means that
10 × 5 + 5y = 100
50 + 5y = 100
5y = 100 - 50 = 50
y = 50/5
y = 10
dont skip help me plzzz will mark brainliest
Answers
Answer:
(6,-6)
Step-by-step explanation:
well if you count over to the right 6 and down 6 that points would be
(6,-6)
Answer:
(6,-6)
Step-by-step explanation:
The answer is that because the x-axis for A is positive and it is 6 points away from the origin. The y-axis for A should negative this is because the quadrants are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −). The point is also 6 units away from the origin.
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 10, 0 and negative 8, 2.
6
−3
−6
3
Answers
Answer:
6
Step-by-step explanation:
f(-4) = g(-10) = f(-10+k)
f(-2) = g(-8) = f(-8+k)
-4 = -10+k
k = -4+10
k = 6
If the line f passes through (-4,0) and (-2,2) it means:
f(-4)=0 and f(-2)=2
If the line g passes through (-10,0) and (-8,2) it means:
g(-10)=0 and g(-8)=2
We can see that
g(-10)=0=f(-4)
g(-10)=0=f(-10+6)
Also,
g(-8)=2=f(-2)
g(-8)=2=f(-8+6)
Therefore, k=6
You have an SRS of 23 observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a 95% confidence interval for the mean of the population?
Answers
Answer:
Therefore the critical value= 2.073
Step-by-step explanation:
The number of observation = 23.
For the mean of the population the confidence interval = 95%.
Here mean and stander deviation of the distribution is not given. So we use t distribution.
T distribution is called as student's t distribution.
Sample number =n =23.
Confidence level = c= 95% =0.95
The degree of freedom is sample size decreased by 1
df=n-1 = 23-1 =22.
The critical value [tex]t^*[/tex] can be found in the row df = 22 and column with 0.95 of the T distribution table .
[tex]t^*[/tex] = 2.073
Therefore the critical value= 2.073
To calculate the critical value for a 95% confidence interval when the sample size is small (less than 30), we need to use the t-distribution. The critical value from the t-distribution will depend on the sample size (specifically, the degrees of freedom) and the desired level of confidence.
Here's how you could calculate this step by step without using the Python function mentioned:
**Step 1: Identify the desired confidence level.**
For a 95% confidence interval, we are interested in capturing the central 95% of the t-distribution.
**Step 2: Determine the degrees of freedom.**
The degrees of freedom (df) for a t-distribution is equal to the sample size minus 1. So with 23 observations, df = 23 - 1 = 22.
**Step 3: Find the critical t-value.**
We want to find the critical t-value for the t-distribution with 22 degrees of freedom that corresponds to the 95% confidence interval. This means we want to find the t-value such that 95% of the distribution lies between -t and +t. Because the t-distribution is symmetric, we can look up the critical value for 97.5% (to split the remaining 5% evenly on both tails of the distribution).
Using a t-distribution table (often found in the appendices of statistics textbooks) or a statistical computing resource, you would find the t-value that corresponds to a cumulative probability of 0.975 with 22 degrees of freedom.
**Step 4: Interpret the table or resource correctly.**
If you were looking at a table, you would look down the degrees of freedom column until you find 22, then right to the column that represents the 97.5% cumulative probability (remember, this is for the two-tailed test). That entry is the critical t-value that corresponds to a 95% confidence interval.
**Step 5: Use the critical t-value for constructing the interval.**
Once you have the critical t-value, you would use it to construct the confidence interval for the population mean by multiplying this t-value by the standard error of the sample mean and then add and subtract this value from the sample mean.
**Important Note:**
Please be aware that the exact t-value varies depending on the source of the statistical tables or the statistical software being used. The value also depends on the precision (number of decimals) presented in the table.
If you perform these steps with a standard statistical table or software, you should find that the critical t-value for a 95% confidence interval with 22 degrees of freedom is approximately 2.074.
Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn's estimate?2.13%2.18%12%46.83%
Answers
Answer:
is d
Step-by-step explanation:
Answer:
2.13%
Step-by-step explanation:
Inaccurate measurement = 5.5cm
Actual measurement = 5.62cm
Difference= actual - inaccurate
=> 5.62 - 5.5
Therefore, the measurement Jocelyn obtained is off by 0.12cm (difference)
Note: error = difference
% diff = error÷ actual measurement × 100
= 0.12/5.62 × 100
% diff. = 2.13 (to the nearest decimal place)
A line segment that passes through the center and has endpoints on the circumference is called
Answers
Answer:
Diameter
Step-by-step explanation:
Knowing that a diameter is the largest chord as it passes through the center point of a circle, if the definition of the chord is a line segment with it's two endpoints on the circle (here by circle we mean circumference) then a diameter is a line segment that passes through the center and has endpoints on the circumference.
A theater ticket costs $20. The function h(x) = 20x represents the cost of purchasing x theater tickets. a. How much does it cost to buy 7 theater tickets? b. How many theater tickets can you buy with 460?
Answers
Answer:
A.) it costs 140$ for 7 tickets B.) 460$ = 23 tickets
Step-by-step explanation:
If it is 20 dolors for 1 ticket if you buy 7 you do 7 x 20 = 140.
But if you have 460$ then you do the opisit you do 460/20=23
Find [g•h](x) and [h•g] (x) g(x)=2x h(x)=-10x-10
Answers
Answer:
-40x(x+1)
Step-by-step explanation:
Find [g•h](x) and [h•g] (x)
g(x)=2x
h(x)=-10x-10
[g•h](x) = 2x(-10x-10)= -20x^2-20x = -20x(x+1)
[h•g](x) = (-10x-10)2x= -10x(2x)-10(2x) = -20x^2-20x
[g•h](x) and [h•g] (x)
and means addition
-20x^2-20x + (-20x^2-20x)
-20x^2-20x-20x^2-20x
choose like terms
-20x^2-20x^2-20x-20x
-40x^2-40x
-40x(x+1)
At December 31, bonds payable of $109,993,000 are outstanding. The bonds pay 12% interest every September 30 and mature in installments of $27,498,250 every September 30, beginning September 30, 2018.
Answers
Answer:
Explanation:
If 112% interest of bond amount = $27,498,250
∴ 100% principal amount = 27,498,250 X 100/112 = $24,552,008.93
10% bond interest = $24,552,008.93 X 0.10 = $2,455,200.89
Between October 2018 and August 2019, it amounts = $2,455,200.09 X 11 = $27,007,209.82
The amount accrued up to September 2019 = $(27,007,209.82 + 27,498,250) = $54,505,459.82
From October 2019 to August 2020, it will amount = $(27,007,209.82 + 54,505,459.82) = $81,512669.64
The amount accrued up to September 2020 = $(81,512,669.64 + 27,498,250) = $109,010,919.64
a swimming pool is shaped like a cylinder with a radius of 15 feet and a height of 6 feet. if one cubic foot holds 7.48 gallons of the water how much gallons of water can the swimming pool hold.
Answers
Answer: the swimming pool can hold 31707.72 gallons of water.
Step-by-step explanation:
The swimming pool is shaped like a cylinder. The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Where
r represents the radius of the cylindrical swimming pool.
h represents the height of the pool.
π is a constant whose value is 3.14
Therefore, volume of the swimming pool is
Volume = 3.14 × 15² × 6 = 4239 cubic feet
if one cubic foot holds 7.48 gallons of the water, then the number of gallons of water that the swimming pool can hold is
4239 × 7.48 = 31707.72 gallons of water
Answer:
the swimming pool can hold 31707.72 gallons of water.
Step-by-step explanation:
Write the quadratic function in standard form.
y = -(x + 2)^2
Answers
Answer:
Step-by-step explanation:
-(x+2)^2 --> -(x+2)(x+2) --> -(x^2+4x+4) = -x^2-4x-4
Answer:
[tex]x^{2} -4x+4[/tex]
Step-by-step explanation:
[tex]y =-(x+2)^{2}[/tex]
The negative sign multiplies the positive in the bracket
[tex]y=(x-2)^{2}[/tex]
[tex](x-2) X (x-2)[/tex]
[tex]x^{2} -2x-2x+4[/tex]
That gives us
[tex]x^{2} -4x+4[/tex]
An arc on a circle measures 295°. The measure of the central angle
Answers
Answer:
59/36π
Step-by-step explanation:
We know that an angle is measured in either degrees or radians and The arc's angle measurement, taken at the center of the circle the arc is part of, is measured in degrees (or radians)
Let's convert 90 degrees into radians
295° = 295 * π/180 = 59/36π
The height of a volleyball, h, in feet, is given by h = −16t2 + 11t + 5.5, where t is the number of seconds after it has been hit by a player. The top of the net is 7.3 feet above the floor. Does the volleyball travel high enough to clear the top of the net?
Answers
Answer:
It will travel high enough
Step-by-step explanation:
Find the vertex of the parabola:
x=-b/2a
x=-11/2(-16)
x=-11/-32
x=11/32
Plug x=11/32 into quadratic to get the y-coordinate:
h=-16(11/32)^2+11(11/32)+5.5
h=7.391
Since 7.391>7.3, the volleyball will travel high enough (aka. yes)
To determine if the volleyball clears the net, we calculate the maximum height using the vertex of the parabola from the quadratic equation representing the ball's trajectory. By finding the time at the vertex and substituting it back into the equation, we get the maximum height, which needs to be compared with the net's height.
Explanation:To determine whether the volleyball travels high enough to clear the net, we need to calculate the maximum height reached by the ball using the given quadratic equation h = −16t2 + 11t + 5.5. The maximum height will be at the vertex of the parabola represented by the quadratic function. The t-coordinate of the vertex can be found using the formula t = -b/2a, where a and b are the coefficients from the quadratic term and the linear term respectively.
For the given equation h = -16t2 + 11t + 5.5, a is -16 and b is 11. Thus,
t = -b/2a = -11/(2 * -16) = 11/32
Substitute t back into the equation to find maximum height, h
h = -16(11/32)2 + 11(11/32) + 5.5
Doing the calculation will reveal the maximum height of the volleyball. If this height is greater than 7.3 feet, the height of the net, then the volleyball clears the net.
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Rachel gets her midterm grades and finds that she has a 2.4 in OB. She expected a better grade point average to date. Rachel is _________ her performance.
Answers
Answer:
Answer is; Evaluating
Step-by-step explanation:
Student self-assessment involves students evaluating their own work and learning progress.
Through self-assessment evaluation, students can:
* See where their knowledge is weak
* See where to focus their attention in learning.
* Set realistic goals
* Revise their work
* Track their own progress.
In Rachel's case, after writing her midterm exams, she already set her goal grade. So when she got her midterm grades, she needed to evaluate her work to find out her performance.
Therefore, according to the question, Rachel is EVALUATING her performance.
PLEASE HELP IM BEING TIMED
Answers
Answer:
The 3rd option Summation(4^i-4)
Step-by-step explanation:
Summation(4^i-4)
When i = 1
4^I-4 = 4^1-4 = 4^-3 = 1/64
When i = 2
4^i-4 = 4^2-4 = 4^-2 = 1/16
When i = 3
4^i-4 = 4^3-4 = 4^-1 = 1/4
When i = 4
4^i-4 = 4^4-4 = 4^0 = 1
When i = 5
4^i-4 = 4^5-4 = 4^1 = 4
Answer:
[tex]\sum _{i=1}^54^{i-4}[/tex]
Step-by-step explanation:
[tex]a_{1} \\[/tex] = First term
In this case, our first term is [tex]\frac{1}{64}[/tex]
The ratio of all of the adjacent terms is 4
[tex]a_{1} \\[/tex] = [tex]4^1^-^4[/tex]
[tex]a_{1}=\frac{1}{64}[/tex]
~Hope this helps!~
Tarun has 4 more than the twice the number of tshirts Deepak has.Mahesh has 2 more than thrice the number of T-shirts that Tarun has.If the ratio is 6:7 find the number of T-shirts each of them has.
Answers
Answer:
Deepak: 4 t-shirts,
Tarun: 12 t-shirts,
Mahesh: 14 t-shirts.
Step-by-step explanation:
Let x represent number of t-shirts that Deepak has.
Please consider the complete question.
Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has. Mahesh has 2 more than thrice the number of T-shirts Deepak has. If the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, find out the number of the t-shirt each of them has.
Since Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has, so the number of t-shirts that Tarun has would be [tex]2x+4[/tex].
We are also told that Mahesh has 2 more than thrice the number of T-shirts Deepak has. So the number of t-shirts that Mahesh has would be [tex]3x+2[/tex].
Since the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, so we can represent this information in an equation as:
[tex]\frac{2x+4}{3x+2}=\frac{6}{7}[/tex]
Cross multiply:
[tex]6(3x+2)=7(2x+4)[/tex]
[tex]18x+12=14x+28[/tex]
[tex]18x-14x+12-12=14x-14x+28-12[/tex]
[tex]4x=16[/tex]
[tex]x=\frac{16}{4}=4[/tex]
Therefore, Deepak has 4 t-shirts.
The number of t-shirts that Tarun has would be [tex]2x+4\Rightarrow 2(4)+4=4+4=12[/tex]
Therefore, Tarun has 12 t-shirts.
The number of t-shirts that Mahesh has would be [tex]3x+2\Rightarrow 3(4)+2=12+2=14[/tex]
Therefore, Mahesh has 14 t-shirts.
-2x^(2)+10x=-14 complete the square
Answers
Step-by-step explanation:
[tex]-2x^2+10x=-14\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x^2}{-2}+\dfrac{10x}{-2}=\dfrac{-14}{-2}\\\\x^2-5x=7\qquad(a-b)^2=a^2-2ab+b^2\qquad(*)\\\\x^2-2(x)(2.5)=7\qquad\text{add}\ 2.5^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(2.5)+2.5^2}_{(*)}=7+2.5^2\\\\(x-2.5)^2=7+6.25\\\\(x-2.5)^2=13.25[/tex]
[tex]\text{If you want the solution, then:}\\\\(x-2.5)^2=13.25\iff x-2.5=\pm\sqrt{13.25}\\\\x-\dfrac{25}{10}=\pm\sqrt{\dfrac{1325}{100}}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{1325}}{\sqrt{100}}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{25\cdot53}}{10}\\\\x-\dfrac{25}{10}=\pm\dfrac{\sqrt{25}\cdot\sqrt{53}}{10}\\\\x-\dfrac{25}{10}=\pm\dfrac{5\sqrt{53}}{10}\\\\x-\dfrac{5}{2}=\pm\dfrac{\sqrt{53}}{2}\qquad\text{add}\ \dfrac{5}{2}\ \text{to both sides}\\\\x=\dfrac{5}{2}\pm\dfrac{\sqrt{53}}{2}[/tex]
[tex]\huge\boxed{x=\dfrac{5\pm\sqrt{53}}{2}}[/tex]
A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?
Answers
Answer:
If length of the field is 30 ft, then width is 120 ft.
If the length of the field is 60 ft, then width is 60 ft.
Step-by-step explanation:
Let us assume the length of the rectangular park = L ft
Let us assume the breadth of the rectangular park = B ft
Now, AREA of the given park = L x B
⇒ L x B = 3,600 sq ft ... (1)
Also, the perimeter of three sides = 180 ft
⇒ 2 L + B = 180 ..... (2)
Now, from (1) and (2), we get:
L x B = 3,600
2 L + B = 180 ⇒ B = 180 - 2 L
Substitute this in(1) , we get:
L x B = 3,600 ⇒ L x (180 - 2 L) = 3600
[tex]\implies 180 L - 2L^2 = 3600\\\implies L^2 -90L + 1800 = 0\\\implies (L-30)(L-60)= 0[/tex]
⇒ L = 30 or L = 60
So, if L = 30 ft , then B = 180 - 2L = 180 - 60 = 120 ft
So, if L = 60 ft , then B = 180 - 2L = 180 - 120 = 60 ft
So, if length of the field is 30 ft, then width is 120 ft.
And if the length of the field is 60 ft, then width is 60 ft.
Jamie is riding a Ferris wheel that takes fifteen seconds for each complete revolution. The diameter of the wheel is 10 meters and its center is 6 meters above the ground. (a) When Jamie is 9 meters above the ground and rising, at what rate (in meters per second) is Jamie gaining altitude? (b) When is Jamie rising most rapidly? At what rate?
Answers
Answer:
The answers to the question is
(a) Jamie is gaining altitude at 1.676 m/s
(b) Jamie rising most rapidly at t = 15 s
At a rate of 2.094 m/s.
Step-by-step explanation:
(a) The time to make one complete revolution = period T = 15 seconds
Here will be required to develop the periodic motion equation thus
One complete revolution = 2π,
therefore the we have T = 2π/k = 15
Therefore k = 2π/15
The diameter = radius of the wheel = (diameter of wheel)/2 = 5
also we note that the center of the wheel is 6 m above ground
We write our equation in the form
y = [tex]5*sin(\frac{2*\pi*t}{15} )+6[/tex]
When Jamie is 9 meters above the ground and rising we have
9 = [tex]5*sin(\frac{2*\pi*t}{15} )+6[/tex] or 3/5 = [tex]sin(\frac{2*\pi*t}{15} )[/tex] = 0.6
which gives sin⁻¹(0.6) = 0.643 =[tex]\frac{2*\pi*t}{15}[/tex]
from where t = 1.536 s
Therefore Jamie is gaining altitude at
[tex]\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) =[/tex] 1.676 m/s.
(b) Jamie is rising most rapidly when the velocity curve is at the highest point, that is where the slope is zero
Therefore we differentiate the equation for the velocity again to get
[tex]\frac{d^2y}{dx^2} = -5*(\frac{\pi *2}{15} )^2*sin(\frac{2\pi t}{15})[/tex] =0, π, 2π
Therefore [tex]-sin(\frac{2\pi t}{15} )[/tex] = 0 whereby t = 0 or
[tex]\frac{2\pi t}{15}[/tex] = π and t = 7.5 s, at 2·π t = 15 s
Plugging the value of t into the velocity equation we have
[tex]\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) =[/tex] - 2/3π m/s which is decreasing
so we try at t = 15 s and we have [tex]\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi *15}{15}) = \frac{2}{3} \pi[/tex]m/s
Hence Jamie is rising most rapidly at t = 15 s
The maximum rate of Jamie's rise is 2/3π m/s or 2.094 m/s.
(a) When Jamie is 9 meters above the ground and rising, she is gaining altitude at approximately 1.68 meters per second. (b) Jamie is rising most rapidly when the cosine function is at its maximum, which happens at the lowest point of the Ferris wheel, and the rate is approximately 2.094 meters per second.
Part (a): Rate at Which Jamie is Gaining Altitude
1. Identify the position function of Jamie on the Ferris wheel:
The height h of Jamie above the ground as a function of time t can be modeled by the equation of a sinusoidal function:
[tex]\[ h(t) = 6 + 5\sin\left(\frac{2\pi}{15}t\right) \][/tex]
Here, 6 meters is the height of the center of the Ferris wheel above the ground, and 5 meters is the radius of the wheel.
2. Differentiate the height function to find the rate of change of height:
To find the rate at which Jamie is gaining altitude, we need to differentiate h(t) with respect to t:
[tex]\[ h'(t) = \frac{d}{dt} \left( 6 + 5\sin\left(\frac{2\pi}{15}t\right) \right) = 5 \cdot \frac{2\pi}{15} \cos\left(\frac{2\pi}{15}t\right) \][/tex]
Simplifying,
[tex]\[ h'(t) = \frac{2\pi}{3} \cos\left(\frac{2\pi}{15}t\right) \][/tex]
3. Determine t when Jamie is at 9 meters above the ground and rising:
[tex]\[ 9 = 6 + 5\sin\left(\frac{2\pi}{15}t\right) \] Solving for \( \sin \left(\frac{2\pi}{15}t\right) \): \[ 3 = 5\sin\left(\frac{2\pi}{15}t\right) \] \[ \sin\left(\frac{2\pi}{15}t\right) = \frac{3}{5} \][/tex]
Jamie is rising when [tex]\( \cos \left(\frac{2\pi}{15}t\right) > 0 \)[/tex].
4. Find the rate at which Jamie is gaining altitude at this instant:
Substitute [tex]\(\sin \left(\frac{2\pi}{15}t\right) = \frac{3}{5}\)[/tex] into the derivative [tex]\( h'(t) \)[/tex]:
[tex]\[ \cos \left(\frac{2\pi}{15}t\right) = \sqrt{1 - \sin^2 \left(\frac{2\pi}{15}t\right)} = \sqrt{1 - \left(\frac{3}{5}\right)^2} = \sqrt{\frac{16}{25}} = \frac{4}{5} \][/tex]
Thus, the rate of change of height:
[tex]\[ h'(t) = \frac{2\pi}{3} \cdot \frac{4}{5} = \frac{8\pi}{15} \approx 1.68 \text{ meters per second} \][/tex]
Part (b): When Jamie is Rising Most Rapidly
1. Identify when Jamie is rising most rapidly:
Jamie rises most rapidly when [tex]\( \cos \left(\frac{2\pi}{15}t\right) = 1 \)[/tex], which corresponds to the maximum value of the cosine function.
2. Rate of change of height at maximum rise:
[tex]\[ h'(t) = \frac{2\pi}{3} \cdot 1 = \frac{2\pi}{3} \approx 2.094 \text{ meters per second} \][/tex]
In a game, a player earns 100 points for each question answered correctly and earns −30 points for each question answered incorrectly. A player answered 14 questions correctly and 6 questions incorrectly. Write a numeric expression to represent the total number of points the player earned. What is the total number of points the player earned?
Answers
Answer:
1220
Step-by-step explanation:
Given that in a game, a player earns 100 points for each question answered correctly and earns −30 points for each question answered incorrectly.
Let x be the no of questions correctly answered . Then 20-x would be the question wrongly answered since total number of questions = 14+6 =20
Points gained for correct answer = 100(x) = 100x
Points lost for wrong answer = -30(20-x) = -600+30x
So total points gained when x questions are answered right
= [tex]100x-600+30x\\= 130x-600[/tex]
A player answered 14 questions correctly and 6 questions incorrectly.
Here x =14
Hence we substitute x =14 to get total points earned
Total points earned
[tex]= 130(14)-600\\= 1820-600\\=1220[/tex]
In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C and a so that P(x)equalsCa Superscript x minus 2000 models the population of a country in year x. (b) Estimate the country's population in 2010. (c) Use P to determine the year when the country's population might reach 1.4 billion. (a) Cequals nothing (Type an integer or decimal rounded to five decimal places as needed.)
Answers
Answer:
(a) The value of C is 1.
(b) In 2010, the population would be 1.07555 billions.
(c) In 2047, the population would be 1.4 billions.
Step-by-step explanation:
(a) Here, the given function that shows the population(in billions) of the country in year x,
[tex]P(x)=Ca^{x-2000}[/tex]
So, the population in 2000,
[tex]P(2000)=Ca^{2000-2000}[/tex]
[tex]=Ca^{0}[/tex]
[tex]=C[/tex]
According to the question,
[tex]P(2000)=1[/tex]
[tex]\implies C=1[/tex]
(b) Similarly,
The population in 2025,
[tex]P(2025)=Ca^{2025-2000}[/tex]
[tex]=Ca^{25}[/tex]
[tex]=a^{25}[/tex] (∵ C = 1)
Again according to the question,
[tex]P(2025)=1.2[/tex]
[tex]a^{25}=1.2[/tex]
Taking ln both sides,
[tex]\ln a^{25}=\ln 1.2[/tex]
[tex]25\ln a = \ln 1.2[/tex]
[tex]\ln a = \frac{\ln 1.2}{25}\approx 0.00729[/tex]
[tex]a=e^{0.00729}=1.00731[/tex]
Thus, the function that shows the population in year x,
[tex]P(x)=(1.00731)^{x-2000}[/tex] ...... (1)
The population in 2010,
[tex]P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555[/tex]
Hence, the population in 2010 would be 1.07555 billions.
(c) If population P(x) = 1.4 billion,
Then, from equation (1),
[tex]1.4=(1.00731)^{x-2000}[/tex]
[tex]\ln 1.4=(x-2000)\ln 1.00731[/tex]
[tex]0.33647 = (x-2000)0.00728[/tex]
[tex]0.33647 = 0.00728x-14.56682[/tex]
[tex]0.33647 + 14.56682 = 0.00728x[/tex]
[tex]14.90329 = 0.00728x[/tex]
[tex]\implies x=\frac{14.90329}{0.00728}\approx 2047[/tex]
Therefore, the country's population might reach 1.4 billion in 2047.
A satellite views the Earth at an angle of 20°. What is
the arc measure, x, that the satellite can see?
O 40°
O 80°
160°
0 320
Answers
Answer:
The answer is 160
Step-by-step explanation:
The value of x is (πr - 20).
What is the arc length of a circle?The arc length of a circle is the distance between two points on the curve of the circle.
We have,
The measure of an angle formed by two tangents outside the circle.
= Difference of the intercepted arc / 2 ______(1)
Now,
Larger arc = (2πr - x)
Small arc = x
Angle = 20
Substituting in (1).
20 = (2πr - x - x) / 2
40 = 2πr - 2x
20 = πr - x
x = πr - 20
Thus,
The value of x is (πr - 20).
Learn more about arc lengths here:
https://brainly.com/question/16403495
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The growth of a local raccoon population approximates a geometric sequence where an is the number of raccoons in a given year and n is the year. after 6 years there are 45 raccoons and after 8 years there are 71 raccoons.
Answers
Answer:
GENERAL EXPLICIT SEQUENCE IS GIVEN [tex]a_n = (14.74)(r)^{n-1)}[/tex]
Step-by-step explanation:
Let n be the number of year the data is recorded in.
a: The number of raccoons taken initially.
r: The multiplying factor
[tex]a_n[/tex] : The number of raccoon in the nth year.
As given: [tex]a_6 = 45, a_8 = 71[/tex]
Now, as the given situation can be expressed as GEOMETRIC SERIES:
[tex]a_n = a r^{(n-1)}[/tex]
Applying the same to given terms, we get:
[tex]a_6 = a r^{(6-1)} = ar^5 = 45\\\implies ar^5 = 45[/tex]
[tex]a_8 = a r^{(8-1)} = ar^7 =71\\\implies ar^7 = 71[/tex]
Dividing both equations, we get:
[tex]\frac{ar^7}{ar^5} = \frac{71}{45} \\\implies r^2 = 1.58\\\implies r = 1.25[/tex]
So, the first term [tex]a = \frac{45}{(1.25)^5} = 14 .74 \approx 15[/tex]
So, the GENERAL EXPLICIT SEQUENCE IS GIVEN as: [tex]a_n = (14.74)(r)^{n-1)}[/tex]