The differential equation that can represent all circles in the xy plane is given as follows:
[tex]\frac{dy}{dx} = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
How to obtain the differential equations for a circle?The equation of a circle of center (h,k) and radius r is given as follows:
(x - h)² + (y - k)² = r².
The equation can be arranged to isolate the variable y as follows:
(y - k)² = r² - (x - h)²
y - k = square root (r² - (x - h)²)
y = square root (r² - (x - h)²) + k
To obtain the differential equation, then this equation must be differentiated towards variable x as follows:
[tex]\frac{dy}{dx} = \frac{d}{dx}(\sqrt{r^2 - (x - h)^2} + k)[/tex]
Applying the chain rule, along with the derivative for the square root, we have that:
[tex]\frac{d}{dx}(\sqrt{r^2 - (x - h)^2} + k) = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
Meaning that the differential equation is given as follows:
[tex]\frac{dy}{dx} = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
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problem 9-6 determine the distance yc to the center of gravity of the homogeneous rod bent into the parabolic shape. given: a
Step 1
We are given a homogenous rod in a cubic curve shape having two free ends, upper end B
and lower end x
The distance of the upper end from x
axis is 1m
and from y axis is 2m.
The rod is bent in a cubic curve shape between two ends and the equation for the rod is given by
[tex]y=2 x^3[/tex]
Here, [tex]$\bar{x}_1$[/tex]and [tex]$\bar{y}_1$[/tex]are the centroidal distances of the strip element from [tex]x$and $y$[/tex] axes respectively.
Step 3
The given equation of the homogenous rod is,
[tex]\begin{gathered}y=2 x^3 \\\frac{d y}{d x}=6 x^2\end{gathered}[/tex]
The given equation of the homogenous rod is,
\begin{aligned}
[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]
[tex]& d L=\sqrt{d x^2+d y^2} \\& d L=d x \times \sqrt{1+\left(\frac{d y}{d x}\right)^2} \\& d L=\sqrt{1+\left(6 x^2\right)^2} \cdot d x \\& d L=\sqrt{1+36 x^4} \cdot d x\end{aligned}[/tex]
[tex]& L=\int_{x=0}^{x=1 \mathrm{~m}} d L \\& L=\int_{x=0}^{x=1 \mathrm{~m}} \sqrt{1+36 x^4} \cdot d x \\[/tex]
[tex]& L=6 \times \int_{x=0}^{x=1 \mathrm{~m}} \sqrt{\left(x^2\right)^2+\frac{1}{36}} \cdot d x \\[/tex]
[tex]& L=6 \times\left[x^2 \sqrt{x^4+\frac{1}{36}}+\frac{1}{36} \ln \left|\left(x^2+\sqrt{x^4+\frac{1}{36}}\right)\right|\right]_0^{1 \mathrm{~m}}\end{aligned}[/tex]
Substituting the values in the above expression and solving,
[tex]& \int_L y \cdot d L=\left[\frac{\left(36 \times(1 \mathrm{~m})^4+1\right)^{\frac{3}{2}}}{108}\right]-\left[\frac{\left(0+1 \mathrm{~m}^4\right)^{\frac{3}{2}}}{108}\right] \\& \int_L y \cdot d L=\frac{224.062}{108} \mathrm{~m}^2 \\& \int_L y \cdot d L=2.075 \mathrm{~m}^2[/tex]
Now according to the formula for the center of gravity of a curve, the expression for the center of gravity of the homogenous rod is given by,
[tex]& \bar{y}=\frac{\int_L \bar{y}_1 \cdot d L}{\int_L d L} \\& \bar{y}=\frac{2.075 \mathrm{~m}^2}{2.42 \mathrm{~m}} \\& \bar{y}=0.857 \mathrm{~m}[/tex]
Therefore, the center of gravity of the given homogeneous rod is
0.857 m above the horizontal axis
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TRUE/FALSE. analysis is defined as describing the data in the sample with the use of percentages or averages.
Comparison analysis is defined as describing the data in the sample with the use of percentages or averages. Hence, option A is the most suitable answer to this question.
Comparative analysis talks about the comparison of two or more data sets, or other objects. Comparing data becomes very easy when the data is consolidated with the help of average or mean, percentages, and rounding up of the decimals.
Comparison is a very important method to check the difference in the parameters of the two data sets. Not just comparing, summarization of this data is vital for understanding what that data actually means. Hence, we can say that comparison analysis is defined as describing the data in the sample with the use of percentages or averages.
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The complete question is -
Fill in the blanks -
________ analysis is defined as describing the data in the sample with the use of percentages or averages.
A) Comparison
B) Generalization
C) Relationship
D) Summarization
E) Confidence
a manufacturer of detergent claims that the contents of boxes sold weigh on average at least 16 ounces. the distribution of weight is known to be normal, with a standard deviation of 0.4 ounce. a random sample of 16 boxes yielded a sample mean weight of 15.84 ounces. test at the 10% significance level the null hypothesis that the population mean weight is at least 16 ounces.
As there is sufficient evidence to conclude that the population mean weight is at least 16 ounces.
What is standard deviation ?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.
The following null and alternative hypotheses need to be tested
H0 : µ = 16
Hα : µ < 16
This corresponds to a left-tailed test , for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is α = 0.1, and the critical value for the left-tailed test is [tex]Z_{c}[/tex] = -1.28
The rejection region for this left-tailed test is R = {z : z < -1.282}
The z-statistics is computed as follow
[tex]z = \frac{X - µ _{0} }{sigma / \sqrt{n} }[/tex]
= (15.84 - 16) / (0.4 / √16)
= -1.6
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the following data on price () and the overall score for stereo headphones that were tested by consumer reports were as follows. the estimated regression equation for these data is . brand price score bose 180 77 scullcandy 150 72 koss 85 62 phillips/o'neill 80 58 denon 80 40 jvc 35 26
The estimated regression equation for these data is Ŷ = 23.194 + 0.318x for every i=1,...,6.
What is meant by regression equation?
In math, the linear regression analysis output delivers some important information, which helps the researcher to predict the estimation, accuracy, and efficiency of the model.
Here we have the data on price and the overall score for stereo headphones that were tested by consumer reports were as follows.
And we need to find the estimated regression equation for these data.
Here let us consider x be the price in dollars of the stereo headphones of brand ii (the independent variable). and let y be the overall score of the stereo headphones of brand ii (the dependent variable).
Here first, we will compute the value of SSE.
The formula is given by
= > SSE = 1∑n (yi − y)²
Therefore, we will show the table of values of xi, Ŷ, Ŷ, (yi−Ŷ) and (yi−Ŷ)².
Now, we have to calculate the value of yi^, plug in the value of xi in the equation
=> Ŷ = 23.194 + 0.318x for every i=1,...,6.
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The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine.
What is the rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled? Place your answer in the box:
The rate of change (slope) of the distance in feet below sea level with respect to time that the submarine traveled is 11 feet .
Given :
The table below shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine .
From the table:
Take any two points ( 0 , 380 ) and ( 15 , 545 )
slope m = 545 - 380 / 15 - 0
= 165 / 15
= 33 / 3
= 11 / 1
= 11 feet
Hence the slope m is 11 feet .
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4(2x-1)+3(2x+15) what is the answer to this question
Answer:
14x+41
Step-by-step explanation:
Answer:
14x + 41
Step-by-step explanation:
4(2X - 1) + 3(2X + 15) distribute the 4 and 3.
8x - 4 + 6x + 45 Combine like terms
14x + 41 This is your answer simplified.
One of the methods forensic investigators use for estimating the age at death of a human, or the age of a living individual (for example for legal reasons or to verify identity) is based on measurement of the biochemical changes in amino acids within the teeth or bones. As bones and teeth age the ratio (R/L) of two amino acids, denoted simply as R and L, increases. The biochemical changes that occur over time in these amino acids follow an exponential law. The age t, in years, can be estimated from (R/L) using the equation t = b0 + b1*LN((1+R/L)/(1-R/L))^(), where LN denotes the natural logarithm (logarithm base e). This Excel file has data on the ratio (R/L) from the teeth of human subjects of known age. Question 1. Use the data to find the least squares intercept b0 and slope b1 in the equation t = b0 + b1*LN((1+R/L)/(1-R/L))^(). intercept b0 slope b1 Question 2. While tending to his flower garden, Sherlock Holmes discovers a body buried in his backyard. Forensic analysis yields the value 0.045 for the ratio (R/L). Use the least squares equation to estimate the age of Sherlock Holmes' surprise garden visitor. years Question 3. Calculate a 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor. lower bound upper bound Question 4. Several years ago a man in Sherlock Holmes's neighborhood mysteriously disappeared. At the time of the disappearance the man was 35 years old. Do you think that this is the body of that man? No Yes
Age as a Function of R/L
R/L
LN[(1+(R/L))/(1-(R/L))]
Age(yrs)
0.0253
14
0.026
18
0.0314
21
0.0302
21
0.0343
25
0.0327
25
0.0317
26
0.0312
26
0.0342
26
0.0338
27
0.0325
28
0.0334
28
0.0334
29
0.0333
30
0.0362
33
0.0359
33
0.0401
36
0.0375
36
0.0398
37
0.0424
38
0.0424
38
0.0404
41
0.0489
49
0.0498
53
0.0518
57
0.0526
63
0.0588
69
0.0579
69
1)The regression equation is Age--26.7+809 LN [(1+(R/1))/(1-(R/L))]. Hence, the value of the regression coefficients by is-26.7 and by is 809
2)The forecasted value for 0.0901 LN [(1+(RL)) (1- (RL))) is 46.103.
3)The 95% prediction interval for the age at death of Sherlock Holmes' surprise garden visitor is 41.013,51.193.
4)Yes, a man in Sherlock Holmes's neighborhood thought that the body because; the man's age comes under the age in years that is, the smaller age is 14 and the larger age is 69. Thus, this is the body of that man.
Exponential law=The first law states that to multiply two exponential functions with the same base, we simply add the exponents. The second law states that to divide two exponential functions with the same base, we subtract the exponents.
MINITAB procedure:
Choose Stat > Regression Regression
Step 2: In Responses, enter the column of Age (yrs)
Step 3: In Predictors, enter the column of LN [(1+(R/L))/ (1-(R/1))] Step 4: In Options, enter the value of Prediction interval for new observation as 0.0901
The regression equation Age (year 26,7 809 28(13+1/233/4-1-26.7252.025 -13.20 0.00025.61 31.37 0.000)
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Complete the proof of the identity by choosing the Rule that justifies each step. Sin^2x + 4cos^2x = 4 -3sin^2x To see a detailed description of a Rule in the Rule menu, select the corresponding question mark. Statement Rule sin^2 x + 4cos^2 x sin^2 x + 4 (1 -sin^2 x) Rule? sin^2 x + 4 -4sin^2 x Rule? 4 -3sin^2 x Rule? Reciprocal identities: sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u Quotient identities: tan u = sin u/cos u cot u = cos u/sin u Pythagorean identities: sin^2u + cos^2u = 1 tan^2u + 1 = sec^2 u cot^2 u + 1 = csc^2 u Odd/Even function identities: sin(-u) = -sin(u) cos(-u) = cos(u) tan(-u) = -tan(u) csc(-u) = -csc(u) sec(-u) = sec(u) cot(-u) = -cot(u)
Previous question
Find a function f whose graph is a parabola with the given vertex and that passes through the given point.
vertex (−1, 8) point (−2, −1)
f(x) =?
Answer:
y=-7(x+1)^2 +8
Step-by-step explanation:
Vertex as shown in vertex form, and solve for the coefficient by plugging in the point.
y=-9(x+1)^2+8
start with the vertex form of a parabola:
y=a(x-h)^2+k , "h" and "k" are the vertex coordinates, and "a" is the leading coefficient.
1. plug in the vertex coordinates
y=a(x+1)^2+8
2. to find "a", plug in the point coordinates in the function from step 1 for x and y
-1=a(-2+1)^2+8
when you solve this equation, you will find that a=-9
3. substitute "a" value in the equation from step 1
Done
find a polynomial f(x) 3 of degree that has the following zeros. 0,-5,4
The polynomial f(x) of degree 3 is
f(x) = x³ + x² - 20x
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The zeroes of the polynomial are 0, -5, and 4.
This can be written as,
x = 0, x
x = -5, (x + 5)
x = 4, (x - 4)
x(x + 5)(x - 4)
(x² + 5x)(x - 4)
x³ - 4x² + 5x² - 20x
x³ + x² - 20x
Thus,
The polynomial is f(x) = x³ + x² - 20x
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many partitional clustering algorithms that automatically determine the number of clusters claim that this is an advantage. list two situations in which this is not the case. g'
When the data set is extremely small, the algorithm might fail to detect the inherent clusters in the data set. When the data set has a high degree of overlap between clusters, the algorithm might generate too many clusters and fail to capture the underlying structure of the data.
Partitional clustering algorithms can automatically determine the number of clusters, which is often perceived as an advantage. However, this is not always the case. For example, when the data set is small the algorithm might be unable to detect the true clusters in the data set. Additionally, when the data set has high levels of overlap between clusters, the algorithm might generate too many clusters and fail to recognize the underlying structure of the data. In these cases, the automatic determination of the number of clusters can be disadvantageous as it fails to capture the true structure of the data.
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Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n1 = 37 and n2 = 45. The appropriate distribution to use is the:
rev: 12_26_2015_QC_CS-36924
t distribution with df = 81.
t distribution with df = 82.
t distribution with df = 41.
t distribution with df = 80.
The appropriate distribution to use is t distribution with df = 80.
Variance
The variance of a random variable is the expected squared deviation from its population mean or sample mean. Variance is a measure of dispersion, which means it measures how far apart a set of numbers is from their average value.Distribution
A probability distribution is a mathematical function that calculates the chances of various possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and event probabilities (subsets of the sample space).Given that:
n1 = 37
n2 = 45
The variances of the populations are not know so we can use t distribution
Degree of freedom = n1 + n2 - 2
= 37 + 45 - 2
= 80
Therefore, t distribution with df = 80
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Select the correct answer.
What is the circumference of this circle?
OA. 4 1/2 pi
B. 9 pi
c. none of the above
d. 2 1/4 pi
e. 20 1/4 pi
The circumference of this circle is 2π
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
The arc is the circumference.
C = 2πr
C = 2x πx 6
C = 12π
A circle is 360 degrees. The arc is covering 60 degrees
60/360 = 1/6
The arc is 1/6 of the circle, so it will be 1/6 of the circumference
1/6 C = 1/6 (12π)
arc = 2π
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HELP PLEASEEEEEEEEEEEEEE
Answer:
A) [tex]g(x) = (x - 2 )^{2}[/tex]
Explanation:
Since the equation g(x) is similar to f(x), but translated horizontally, then we can conclude that there is a change in the x value.
Since, the equation g(x) is slide to the right by 2 factor, then there will be a change in x value by -2 factor.
For equation B, the graph will move to the left of f(x) by two factor.
For equation C, the graph will move up of f(x) by two factor.
For equation D, the graph will move down of f(x) by two factor.
A triangular ramp has a diagonal incline with a length of 153 inches. The ramp’s incline makes an angle of X/4 from the floor. How high off the ground is the top of the ramp’s incline? Round your answer to the nearest hundredth inch.
High off the ground the top of the ramp’s incline is 108.19 inch
Trigonometric ratios are what?
Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.
Given that :
hypotenuse = 153 inch
and angle is pi/4
Let h be the height
so sin pi/4 = h/153
h = 153 . sqrt 2/2
h = 108.19
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Calculate the difference and enter below. -4 + (-4)
[tex]-4-4[/tex]
[tex]-4+(-4)[/tex]
[tex]=\fbox{-8}[/tex]
[tex]-4+(-4)[/tex] on a number line:
which of the following statements are true regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable? select all that apply. multiple answers: multiple answers are accepted for this question select one or more answers and submit. for keyboard navigation...show more a f(x)
The true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable is 0 < F(x) < 1. and F(x) = 1 for at least one value of x, F(x) = 1 for all values of x > a, where a is a constant.
What is meant by probability density function?
In math, probability density function refers most commonly associated with absolutely continuous univariate distributions.
Here we need to find the true statement regarding the probability density function f(x) and the cumulative density function f(x) of a continuous random variable.
In order to find the correct statement, we must know the definition of the cumulative density function also.
The cumulative density function means the probability function that X will take a value less than or equal to x.
Based on the both definition option (A), (B) and (C) are true.
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Calculate the difference and enter below. -9 - (-10)
Answer:
1
Step-by-step explanation:
subtract the two numbers
Answer: 19
Step-by-step explanation: Imagine a number line -9 is on the left side and 10 is on the other. Now you have to clculate how many jumps or spaces it takes to reach 10. Which is 19, or 9 + 10.
I hope this helps.
1. 50x2=
2. 60x3=
3. 75x8+3=
And then add then all together
Answer:
1. 50 x 2 = 100
2. 60 x 3 = 180
3. 75 x 8 + 3 = 603
603 + 180 + 100 = 883
Step-by-step explanation:
Just multiply and add.
using traditional methods it takes 90 hours to receive an advanced driving license. a new training technique using computer aided instruction (cai) has been proposed. a researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. after performing the test on 190 students, the researcher fails to reject the null hypothesis at a 0.02 level of significance.
The conclusion is that there is insufficient proof that the new training method increases training time at the 0.02 level of significance.
What is meant by Hypothesis test?Hypothesis test: Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H₀
The average amount of time required to obtain an advanced driving license using conventional techniques is μ=90 hours.
According to the researcher, the new method can result in a longer training period.
A researcher tests the hypothesis with 190 pupils.
At the significance threshold of α=0.02, the researcher fails to reject the null hypothesis.
To put to the test
H₀:The average amount of time required for the new method to obtain an advanced driving license is 90 hours, or μ=90
Hₐ: The new method often requires more than 90 hours, or μ>90, to obtain an advanced driving license.
Failure to reject the null hypothesis indicates that there was insufficient data in our sample to draw a conclusion on the existence of the effect. The absence of data, however, does not demonstrate that the effect is unreal.
The new method takes fewer than 90 hours on average to get an advanced driving license as a result.
Therefore, the researcher's assumption that the new method would increase training time was unfounded.
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Two random samples of professional baseball players were selected and the number of home runs hit were recorded. One sample was obtained from the National League, and the other sample was obtained from the American League. Ata -0.10, is there a difference in the means? Use the critical value method with tables. National League American League 18 18 12 25 24 Download data Use μ 1 for the mean number of home runs from the National League. Assume the variables are normally distributed and the variances are unequal. Part 1 out of 5 State the hypotheses and identify the claim with the correct hypothesis. H0:#1 (select) | ▼ Ma (select) H2:A9 (select) μ2 (select) This hypothesis test is a (select) test
Hypotheses: H0: μ1 = μ2 and H1: μ1 ≠ μ2.This hypothesis test is a two-tailed test.
Calculate the pooled standard deviation of the two samples.
Let x1 and x2 be the sample means of the National League and American League, respectively. Let s1 and s2 be the sample standard deviations of the National League and American League, respectively. Let n1 and n2 be the sample sizes of the National League and American League, respectively.
Pooled standard deviation = √[( (n1 - 1)s1^2 + (n2 - 1)s2^2 ) / (n1 + n2 - 2)]
s1 = 6.9282
s2 = 6.3246
n1 = 2
n2 = 2
Pooled standard deviation = √[( (2 - 1)6.9282^2 + (2 - 1)6.3246^2 ) / (2 + 2 - 2)]
Pooled standard deviation = 6.6759
Calculate the degrees of freedom (df).
Degrees of freedom (df) = n1 + n2 - 2
df = 2 + 2 - 2
df = 2
Calculate the t-statistic.
Let μ1 and μ2 be the population means of the National League and American League, respectively.
t-statistic = (x1 - x2 - (μ1 - μ2)) / √(s^2 / n1 + s^2 / n2)
x1 = 18
x2 = 19
μ1 = μ2
s2 = 6.6759
n1 = 2
n2 = 2
t-statistic = (18 - 19 - (μ1 - μ2)) / √(6.6759^2 / 2 + 6.6759^2 / 2)
t-statistic = (-1) / (4.4518)
t-statistic = -0.2244
At a significance level of 0.10,
The critical value for a two.
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a norman window has the shape of a rectangle surmounted by a semicircle. (thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) a window with the shape of a rectangle surmounted by a semicircle. the diameter of the semicircle is equal to the width of the rectangle. the rectangle has width x. if the perimeter of the window is 32 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.
The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft
According to the question,
A norman window has the shape of a rectangle surmounted by a semicircle.
Let The width of rectangle be x and height be y
It is given that the diameter of the semicircle is equal to the width of the rectangle
Therefore , Diameter of circle = x
Radius = x/2
Perimeter of window = 32 = Perimeter of rectangle + Perimeter of semi-circle
=> 32 = Width + 2height + πr
=> x + 2y + πx/2 = 32
=> 2x + 4y + πx = 64
Solving for y,
=> 4y = 64 - 2x - πx
=> y = 64 - 2x - πx/ 4 ----------(1)
Area of the window = Area of rectangle + area of semi-circle
=> A = Width × hiegth + πx²/8
=> A = xy + πx²/8
Substituting the value of y from equation (1)
=> A = x ( 64 - 2x - πx/ 4 ) + πx²/8
[tex]A = x ( \frac{64 - 2x -\pi x}{ 4} ) + \frac{\pi x^2}{8}\\A = ( \frac{ 64x - x^2 ( 2 + \pi)}{4 } ) + \frac{\pi x^2}{8}[/tex]
Differentiating A w.r.t x
=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4}[/tex]
Now , To find a maximum area
dA/dx = 0
=> [tex]\frac{dA}{dx} = (\frac{64 - 2x(2 + \pi)}{4} ) + \frac{\pi x}{4} = 0[/tex]
Solving for x ,
64 - 4x - 2π + πx = 0
=> x = 64 / 4 + π ------(2)
Differentiating A again w.r.t x
=> d²A / dx² = -2(2 + π)/4 + π/4
=> -π+4 / 4 which is less than zero
Therefore,
Area is maximum when x = 64 / 4 + π
The exact value of x (in ft) so that the greatest possible amount of light is admitted is 8.96 ft
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08
En completes an exercise program at a fitness center The graph shown below represents
the percentage of her exerclee program 09 Erin has completed when she has exerched for
*minutes
Erin's Exercise Program
felpaydung
2882882822
100
0 8 10 15 20 25 30 35 40 45 50 558 00 08
Time (minutes)
Based on the graph what does the value of the y-coordinate represent when x = 15
A Bin has completed ON of her exercise program
8
Bin has completed 25% of her exercise program
0
Bin has completed 0 minutes of her exercise program
D. Ein has completed 28 minutes of her exercise program
The meaning of the y-coordinate of the graph when x = 15 is given as follows:
B. Erin has completed 25% of her exercise program.
What is shown by the graph?The graph is a relation that represents a function between two variables.
The variables for this problem are given as follows:
Variable x: time that Erin spent exercising.Variable y: percentage of the exercise program that Erin has completed, considering that she has been exercising for x minutes.One ordered pair for the graph in this problem is given as follows:
(15, 25).
This means that when Erin spends 15 minutes exercising, she has completed a percentage of 25% of her exercise program, and thus option B is correct.
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Sue borrows $3500 and will be charged 0.8% simple interest per year. How much will she owe in 5 years?
Answer:
$14000
Step-by-step explanation:
= (3500 x 0.8 x 5) / 100
= $14000
I hope my answer helps you.
Quick! Which expression is equivalent? I think either D or C but I’m a bit confused, please help!
The expression that is equivalent to 6⁻¹⁰/(6⁴)(6⁰) is (d) 1/6¹⁴
How to determine the expression that is equivalent?From the question, we have the following parameters that can be used in our computation:
6⁻¹⁰/(6⁴)(6⁰)
Express 6⁰ as 1
So, we have the following representation
6⁻¹⁰/(6⁴)(6⁰) = 6⁻¹⁰/(6⁴) * 1
Evaluate the products
6⁻¹⁰/(6⁴)(6⁰) = 6⁻¹⁰/(6⁴)
Apply the law of indices
So, we have
6⁻¹⁰/(6⁴)(6⁰) = 1/6¹⁰⁺⁴
Evaluate the differences
6⁻¹⁰/(6⁴)(6⁰) = 1/6¹⁴
Hence, the expression is (d) 1/6¹⁴
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convert the following equation into slope intercept form. 2x - 4y = 8
Answer:
hey
4y = 2x – 8
Step-by-step explanation:
2x – 4y = 8
–4y = –2x + 8
multiply both sides by (–)
–(–4y) = –(–2x + 8)
4y = 2x – 8
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Matteo bought a car that cost $12500. He put $4000 down and financed the rest at 3.8%/a compounded monthly. He wants to pay off his car in 19 months. a. How money does he need to pay each month? how much will he end up paying for his car
Answer:
a. $461.67
b. $12771.73
Step-by-step explanation:
You want to know the monthly payment and total amount paid for a car that costs $12500 when $4000 is the down payment and the interest is 3.8% for 19 months.
AmortizationThe formula for the monthly payment is ...
A = P(r/12)/(1 -(1 +r/12)^-n)
where P is the amount borrowed at interest rate r compounded monthly for n months.
Here, the down payment of $4000 reduces the loan amount to ...
$12500 -4000 = 8500
a. Monthly paymentSo, the monthly payment is ...
A = 8500(0.038/12)/(1 -(1 +0.038/12)^-19) ≈ 461.67
Matteo needs to pay $461.67 each month.
b. Total paidThe total Matteo pays for the car will be the sum of the down payment and the 19 monthly payments:
total = $4000 +19×461.67 = $12771.73
Matteo will end up paying $12771.73 for his car.
If the center of the circle is Point A, what is the difference between the circumference of the circle and the perimeter of the triangle, to the nearest tenth of a unit?
A 20.6 units
B 28.2 units
C 80.7 units
D 95.5 units
The difference between the circumference of the circle and the perimeter of the triangle is 28.2 units. (Option B)
To find the length of each side of triangle, the distance is calculated between the vertices using the formula:
d = √((x2 – x1)^2 + (y2 – y1)^2)
Hence,
AB =√((-4 – 0)^2 + (9 – 0)^2) = 9.85 units
AC = √((9 – 0)^2 + (4 – 0)^2) = 9.85 units
BC = √((9 – (-4))^2 + (4 –9)^2) = 13.93 units
Hence, the perimeter of the triangle = 9.85 + 9.85 + 13.93 = 33.6 units
As AB and AC is the radius of the circle, the circumference of the circle is:
C = 2πr = 2π(9.85) = 61.8 units.
Hence, the difference between the circumference of the circle and the perimeter of the triangle = 61.8 – 33.6 = 28.2 units.
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Help me with these pairs thank u
Answer: R(7, 9), S(6, 7), T(2, 3), U(8, 5), V(5, 5)
Solve the system of equations using elimination. 2x + 3y = −15 3x + y = 2 (0, 5) (1, −1) (3, −7) (4, −10)
The solution to the system of equations is x = 3 and y = -7. The correct option is C. (3, -7).
The system of equations is given as follows:
2x + 3y = −15 ....(1)
3x + y = 2 ....(2)
Multiply Equation 2 by 3:
9x + 3y = 6 ....(3)
Now, we can subtract Equation 1 from Equation 3 to eliminate y:
(9x + 3y) - (2x + 3y) = 6 - (-15)
9x + 3y - 2x - 3y = 6 + 15
7x = 21
x = 21/7
x = 3
Substituting the value of x into Equation 2 to solve for y:
3(3) + y = 2
9 + y = 2
y = 2 - 9
y = -7
Therefore, the solution to the system of equations is x = 3 and y = -7.
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Complete question:
Solve the system of equations using elimination.
2x + 3y = −15
3x + y = 2
A. (0, 5)
B. (1, −1)
C. (3, −7)
D. (4, −10)