Based on the graph, we can see that the relationship between the number of stuffed animals and the number of action figures is proportional since the line passes through the origin (0, 0), which is a characteristic of proportional relationships.
What are proportional relationships?Mathematical relationships between two variables that have a constant multiple of one another are known as proportional relationships. This implies that when one variable rises or falls by a particular factor, the other variable rises or falls by the same amount as well.
In other words, a straight line on a graph that runs through the origin (0, 0) can be used to illustrate a proportionate connection. This is due to the fact that they are proportional, therefore when one variable is equal to zero, the other variable must likewise be zero.
To graph the linear relationship between the number of stuffed animals, x, and the number of action figures, y, we can use the two given data points: (20, 15) and (60, 45).
First, we can find the slope of the line that passes through these two points using the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (20, 15) and (x2, y2) = (60, 45)
slope = (45 - 15) / (60 - 20) = 30 / 40 = 0.75
Next, we can use the point-slope form of the equation of a line to write the equation of the line that passes through the two points:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) = (20, 15)
y - 15 = 0.75(x - 20)
y - 15 = 0.75x - 15
y = 0.75x
Now we can graph the line by plotting the two given points and drawing a straight line passing through them:
Linear relationship graph
Based on the graph, we can see that the relationship between the number of stuffed animals and the number of action figures is proportional, since the line passes through the origin (0, 0), which is a characteristic of proportional relationships.
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help me solve |ax-b|>c c>=0
Answer: |ax-b| > c
c >= 0
Solve equation log(x) +log(x+4)=(32) for x
The value of x for the given equation is x = e³² - 4 / 2.
What is logarithm?The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 is equal to 103, its logarithm in base 10 is 3, or log10 (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, as in big O notation, the logarithm of x to base b is written as logb (x), logb x, or even without the explicit base, log x.
The given equation is log(x) +log(x+4)=(32).
Raise both sides of the equation to the power of e:
[tex]e^{\log x} + e^{\log (x+4)} = e^{32}[/tex]
x + x+ 4 = e³²
2x = e³² - 4
x = e³² - 4 / 2
Hence, the value of x for the given equation is x = e³² - 4 / 2.
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $14.69 and the monthly cost for 57 minutes is $17.68 . What is the monthly cost for 39 minutes of calls?
The monthly cost for 39 minutes of calls is $15.34.
According to given conditions :We can use the two given data points to form two equations and then solve for the unknown coefficients of the linear function.
Let the monthly cost (in dollars) be denoted by C, and let the total calling time (in minutes) be denoted by T. Then we can write:
C = aT + b
where a is the slope of the line (representing the rate of change of cost per minute of calling time), and b is the y-intercept of the line (representing the fixed monthly cost).
Using the given data points (34, 14.69) and (57, 17.68), we can form the following two equations:
14.69 = 34a + b (equation 1)
17.68 = 57a + b (equation 2)
Subtracting equation 1 from equation 2, we get:
17.68 - 14.69 = 57a - 34a + b - b
2.99 = 23a
a = 2.99/23
a = 0.13 (rounded to two decimal places)
Substituting the value of a into equation 1 (or 2), we get:
14.69 = 34(0.13) + b
b = 14.69 - 4.42
b = 10.27
Therefore, the linear function that represents the monthly cost in terms of total calling time is:
C = 0.13T + 10.27
To find the monthly cost for 39 minutes of calls, we can substitute T = 39 into this function:
C = 0.13(39) + 10.27
C = 5.07 + 10.27
C = $15.34 (rounded to two decimal places)
Therefore, the monthly cost for 39 minutes of calls is $15.34.
What is cost price ?The cost price (CP) is the original price paid to purchase a product or asset. It is the total cost incurred to acquire or produce the item, including all direct and indirect costs such as the cost of raw materials, labor, overhead expenses, transportation, taxes, etc.
The cost price is an important factor in determining the profitability of a business or investment, as it directly affects the profit margin. The profit margin is the difference between the selling price (SP) and the cost price (CP), expressed as a percentage of the cost price.
Profit Margin = (SP - CP) / CP * 100%
For example, if a product is sold for $100 and the cost price is $70, then the profit margin is:
Profit Margin = ($100 - $70) / $70 * 100%
Profit Margin = 30%
This means that for every $1 of cost, the business makes a profit of $0.30. The profit margin can be used to evaluate the efficiency and competitiveness of a business, and to compare the profitability of different products or investments.
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What is the solution?
Answer:
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line is a measure of how steep the line is, and it is defined as the change in y divided by the change in x between any two points on the line. In other words, if we choose two points (x1, y1) and (x2, y2) on the line, then the slope of the line is:
m = (y2 - y1) / (x2 - x1)
The y-intercept of a line is the point where the line crosses the y-axis. In other words, it is the value of y when x = 0. To find the y-intercept of a line given in slope-intercept form, we simply look at the constant term (the term with no x) in the equation.
In the given equation, y = -6x - 7, we can see that the coefficient of x is -6, which means that the slope of the line is -6. This tells us that as we move along the line from left to right, the y-value will decrease by 6 units for every 1 unit that the x-value increases. In other words, the line is sloping downwards from left to right.
To find the y-intercept of the line, we look at the constant term, which is -7. This tells us that when x = 0, y is equal to -7. So the y-intercept is the point (0, -7), which means that the line crosses the y-axis at the point (0, -7).
To summarize, the slope of the line y = -6x - 7 is -6, which means that the line is sloping downwards from left to right. The y-intercept of the line is (0, -7), which means that the line crosses the y-axis at the point (0, -7).
What is the equivalent expression to 4(9+3)
Answer:
4(9+3) = 48
Step-by-step explanation:
To simplify the expression 4(9+3), we need to perform the addition inside the parentheses first and then multiply the result by 4.
9+3 = 12, so we can substitute this into the expression as follows:
4(9+3) = 4(12)
Now we can perform the multiplication:
4(12) = 48
Therefore, the equivalent expression to 4(9+3) is simply 48.
In the circle below, c is the center, FE is a diameter, GD intersects the
circle at E, and KH intersects the circle at E and 1. Use this information to
fill in the blanks. (need help urgently!!)
The following terms are;
Chord = EJ
Tangent line; GD
Secant line ; KH
What is arc in a circle and what are its classifications?For a circle, take two points on its circumference. That divides the circumference of the assumed circle in two parts. Those both parts are called arcs of the circle. The bigger part will be called the major arc, and the smaller one will be called the minor arc.
WE are given that c is the center, FE is a diameter, GD intersects the
circle at E, and KH intersects the circle at E and 1.
Here we have to find the following;
If the assumed circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting the line segment AB.
Chord = EJ
Tangent line; GD
Secant line ; KH
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What is the input value other than -7, for which h(x)=3
The input value is 7 for which h(x) = 3x-14 is equal to 0.
Describe Graph?Graphs are visual representations of data that show how any two variables relate to one another. Without requiring a lot of words, they are frequently used to communicate complex and large amounts of data. A specific amount of data must be gathered through surveys or experiments before a graph may be created.
The graph's vertices
y is the coordinate
3, (−7,3), (5,3)
Otherwise put,
h(−7)=h(5)=x
The correct answer is x=5.
Essential Elements of a Graph.
choosing a graph that can accurately depict the kind of data generated
The horizontal axis (X-axis indicates the independent variable) and the vertical axis are the axes and scales (Y-axis represents the dependent variable).
Equally significant is the graph's caption, which explains the premise on which the graph was created without offering any interpretation or analysis of the data.
Pie charts are used to display data in groupings. The percentage of values is used to divide the full pie chart into segments. When there are only a few groups—say, six or fewer—pie charts are utilized.b
In a bar graph, both horizontal and vertical columns are used to plot the data. Higher values are represented by bars with longer lengths. As an illustration, consider the rising crop yield each year. When there are significant variances across categories, bar graphs are typically employed.
Line graph - A line graph is similar to a scatter plot, with the exception that it uses a continuous variable along the X-axis, such as time, temperature, height, and weight. For instance, a person's weight gain over a period of weeks.
The points on the graph
y -coordinate is 3, (−7,3), (5,3)
In other words,
h(−7)=h(5)=x
We are asked for an input value other than −7
so the answer is x=5
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The complete question is:
In one day, there are two high tides and two low tides in equally spaced intervals. The high tide is observed to be 6 feet above the average sea level. After 6 hours pass, the low tide occurs at 6 feet below the average sea level. In this task, you will model this occurrence using a trigonometric function by using x as a measurement of time. Assume the first high tide occurs at x = 0.
Determine these key features of the function that models the tide:
1.amplitude
2.period
3.frequency
4.midline
5.vertical shift
6.phase shift
Answer:
1. The amplitude of the function is 12 feet, since it moves from 6 feet above to 6 feet below the average sea level.
2. The period of the function is 12 hours, since it takes 12 hours for the tide to go from high to low and back again.
3. The frequency of the function is 0.5 (1/12), since it takes 12 hours for the function to repeat itself.
4. The midline of the function is the average sea level.
5. There is no vertical shift.
6. The phase shift is 0, since the first high tide occurs at x = 0.
What is the answer to this problem?
3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x=?
Answer:
10x -25
Step-by-step explanation:
You want to simplify the expression ...
3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x
SimplifyFirst, we use the distributive property to eliminate parentheses:
3x+6+x-2+8x-24+-4-4+x+1+-2x-4+6+7x+-8x
Now, we group x-terms and constant terms:
(3 +1 +8 +1 -2 +7 -8)x +(6 -2 -24 -4 -4 +1 -4 +6)
Finally, we perform the sums:
10x -25
__
Additional comment
This sort of problem can be described as "tedious, but not difficult."
I need help graphing this equation
The graph of the piecewise function is attached at the end.
What is piecewise function?A piecewise function is a function that is defined on a sequence of intervals. For example -
[tex]$|x| =\left \{ {{-x\;\;\;\;x < 0} \atop {x\;\;\;\;x > 0}} \right.[/tex]
Given is the piecewise function as -
[tex]$f(x) =\left \{ {{-x-1\;\;\;\;x < 3} \atop {-x+1\;\;\;\;x \geq 3}} \right.[/tex]
Refer to the graph of the piecewise function. The graph of the function is attached. The line one does not include the point {x = 3}. The second line includes the point {x = 3}
Therefore, the graph of the piecewise function is attached at the end.
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The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t.
P=$3000, r= 6%, t = 4 years
(Round to the nearest cent as needed.)
The loan's future value A, or the total amount due at time t is equal to $3,720.
How to calculate the simple interest and future value?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 3,000 × 6/100 × 5
S.I = 3,000 × 0.06 × 4
S.I = $720.
Next, we would calculate the future value as follows;
Future value, A = S.I + P
Future value, A = $720 + $3,000
Future value, A = $3,720.
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Triangle ABC is an equilateral triangle. CD bisects AB.
find x and y.
A
(4x + 2)°
C
x= type your answer.....
y type your answer...
1 point
4y
6y + 24
D
B
Answer:
Step-by-step explanation:
Given AB = AC = BC (all sides of equilateral triangle are equal)
BC = 6y + 4
AD = 4y
as D is midpoint of AB, so AB = 2 x 4y = 8y
Since AB = BC
Hence, 8y = 6y + 24
Or, 8y - 6y = 24
Or, 2y = 24
Or, y = 24/2 = 12
Now, Angle ACB = 60 degree (all angles of an equilateral triangle measure 60 degree)
And CD being bisector of side opposite C so it is angular bisector of angle ACB
So, angle ACD = 1/2 of angle ACB
Or, 4x + 2 = 30
Or, 4x = 30 - 2 = 28
Or, x = 28/4 = 7 degree
Answer:
Correct options are A) , B) and D)
A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side.
What is the meaning or the impact if the regression data residual is not normally distributed
The meaning or impact of the regression data residual not being normally distributed is that the assumptions of the regression model are not met. This can result in biased or misleading estimates of the regression coefficients and the overall fit of the model.
When the residuals are not normally distributed, it can indicate that there are other factors influencing the relationship between the independent and dependent variables that are not accounted for in the model. This can lead to incorrect predictions and unreliable conclusions about the relationship between the variables.
To address this issue, it may be necessary to transform the data or use a different type of regression model that does not assume normality of the residuals. It is also important to check for outliers and influential points, as these can also affect the distribution of the residuals.
In conclusion, the normality of the residuals is an important assumption of the regression model, and if it is not met, it can have a significant impact on the reliability and validity of the results.
Why is the numerator greater than the denominator in a fraction that is equivalent to a percent greater than 100?
When a fraction is equivalent to a percentage greater than 100, it means that the numerator represents a value that is greater than the denominator.
What is the percentage?A percentage is a way to express a number as a fraction of 100. For example, 50% is the same as 50/100, which simplifies to 1/2.
Suppose we have a fraction that is equivalent to a percentage greater than 100, such as 125%. This means that the fraction represents 125 parts out of 100, or 125/100.
To simplify this fraction, we can divide both the numerator and denominator by the greatest common factor(GCF), which is 25 in this case. This gives us:
125/100 = (125 ÷ 25)/(100 ÷ 25) = 5/4
As we can see, the numerator (5) is greater than the denominator (4). This is because the original percentage value (125%) is greater than 100%, which means the fraction must have a numerator that is greater than the denominator to reflect this increase.
In general, if a fraction is equivalent to a percentage greater than 100, its numerator will be greater than its denominator because the percentage value represents a quantity that is greater than the whole (100%).
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auntie annie is buying a duck cake and pastle cupcakes
Answer: So whats the question then
Step-by-step explanation:
What is the area of this triangle?
Enter your answer in the box.
units?
The area of the triangle DEF shown in the coordinate plane is 6 units².
What is Area of a Triangle?Area of a triangle is defined as the total region bounded by the shape of the triangle.
The formula to calculate the area of a triangle if the base length and height is given is,
Area = [tex]\frac{1}{2}[/tex] × base × height
Given is a triangle in a coordinate plane.
Base of the triangle is the side DE.
Length of DE is the length of the points (1, 1) t0 (1, 4), which is 3 units apart.
Length of base = 3 units
Height of the triangle is the perpendicular length from the vertex opposite base to the base.
That is, the distance from F(-3, 3) to (1, 3), which are 4 units apart.
Height = 4 units.
Area of triangle DEF = [tex]\frac{1}{2}[/tex] × 3 × 4
= 6 units²
Hence the area of the triangle is 6 units².
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HOW Do this please help omg omg omg omg
it would take approximately 11 hours to complete the order if the number of working machines increased by a factor of 2.
Describe Algebraic Expression?An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations, but does not contain an equals sign. Algebraic expressions are used to represent mathematical relationships and are an important tool in algebra and other areas of mathematics.
Algebraic expressions can be simple, such as x + 2, which consists of a variable (x), a constant (2), and an addition operation. More complex algebraic expressions can contain multiple variables, constants, and operations, such as 2x² + 3xy - 4.
Variables in algebraic expressions represent unknown values that can vary or change, while constants are fixed values that do not change. Mathematical operations, such as addition, subtraction, multiplication, and division, are used to combine variables and constants in algebraic expressions.
We can use the following formula to solve the problem:
(number of machines) x (time to complete the order) = constant
Let's call the constant k. If six machines working simultaneously can complete the order in 22 hours, we have:
6 x 22 = k
k = 132
Now, let's double the number of machines to 12 and find the new time it would take to complete the order:
12 x t = 132
where t is the new time it would take to complete the order with 12 machines. Solving for t, we get:
t = 132/12
t ≈ 11
Therefore, it would take approximately 11 hours to complete the order if the number of working machines increased by a factor of 2.
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Which expression has the same value as (8 x 5) + (8 × 3) ?
A.8x8
B.8 x 15
C.16 + 8
16+8
D 13+11
Sketch the region bounded by the following curves and determine the centroid of the region. y = x^2 + 3, y = 3, and x = 1| (3/8, 33/20)| (3/4, 33/10)| (33/10, 3/4)| (33/10, 3/8)| (3/8, 33/10)|
Refer to the attached image.
Ann had a total of 285 red and blue beads. She used 45 red beads and 40% of the blue bead. After that,the ratio of the number of red beads to blue beads Ann had was 1:3.
Answer:
Let's start by figuring out how many blue beads Ann had initially.
If Ann had a total of 285 red and blue beads, and she used 45 red beads, then she had 240 blue beads remaining.
If Ann used 40% of the blue beads, then she used:
0.40 x 240 = 96 blue beads
After using 45 red beads and 96 blue beads, Ann had the following number of red and blue beads remaining:
Red beads = 285 - 45 = 240
Blue beads = 240 - 96 = 144
At this point, the ratio of red beads to blue beads is:
Red beads : Blue beads = 240 : 144 = 5 : 3
However, we want the ratio to be 1 : 3. To achieve this ratio, we need to divide both the red beads and blue beads by 5. This gives us:
Red beads = 240 / 5 = 48
Blue beads = 144 / 5 = 28.8
Since we can't have a fraction of a bead, we need to round up the number of blue beads to the nearest whole number. This gives us:
Red beads = 48
Blue beads = 29
Therefore, Ann initially had 285 - 48 - 29 = 208 beads, with 48 red beads and 29 blue beads.
Step-by-step explanation:
In a school, 60% of the students are senior.
45% of the seniors have school meals.
75% of the juniors have school meals.
What percentage of the students (seniors and juniors) have school meals?
Answer:
57%
Step-by-step explanation:
Let's consider the total number of students as 100%.
60% of all students are senior, which means that the rest (40%) are juniors.
Out of all senior students, 45% have school meals.
To find the percentage of senior students who have school meals, we should do the following:
[tex]\ \frac{45\% \times60\%}{100\%} = 27\%[/tex]
This is the percentage of students who are senior and have school meals.
We need to repeat the same procedure with junior students.
To do that, we need to find the 75% of 40% out of total, which is 100%.
[tex] \frac{75\% \times 40\% }{100\%} = 30\%[/tex]
This is the percentage of junior students who have school meals.
Finally we need to add up the percentages to find the total percentage of students who have school meals.
[tex]27\% + 30\% = 57\%[/tex]
evaluate the expression. 1.25*0.9-1.25*0.3+1.25*0.4
The expression when evaluated is 1.25
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
1.25*0.9-1.25*0.3+1.25*0.4
Evaluate the products in the expression
So, we have the following representation
1.25*0.9-1.25*0.3+1.25*0.4 = 1.125 - 0.375 + 0.5
Evaluate the like terms
1.25*0.9-1.25*0.3+1.25*0.4 = 1.25
Hence the solution is 1.25
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What are the the x-intercepts for the graph of y = cos(x) over the interval [- 2pi, 2pi]
the x-intercepts will be -π/2, -3π/2, π/2, 3π/2.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The x-intercepts are locations on the coordinate plane where the y-value of the ordered pair is 0.
y = cos(x)
so the x-intercepts will be -π/2, -3π/2, π/2, 3π/2.
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Type an equation for the
following pattern.
1
2
3
4
5
21/2
9
15/2 y = - x + []
3
?
6
9/2
Enter the number that belongs in the green box. Make sure
the fraction is in simplest form.
y = -3/2 x + 24. is the equation of the line in slope intercept form.
Equation of a line in point slope formThe formula for calculating the equation of a line in point slope form is expressed as:
y - y0 = m(x - x0)
where:
m is the slope
(x0, y0) is the point on the line
Using the coordinate points (2, 9) and (4, 6). The slope is calculated as:
Slope = 6-9/4-2
Slope = -3/2
The required equation will therefore be expressed as:
y - 9 = -3/2(x - 2)
2y - 18 = -3x + 6
2y = -3x + 24
y = -3/2 x + 24
Hence the slope-intercept form of the equation is y = -3/2 x + 24.
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The following sample observations were randomly selected. (Round intermediate calculations and final answers to 2 decimal places.) x: 4 5 6 6 9 y: 3 6 5 7 7 pictureClick here for the Excel Data File 1. The regression equation is y : ______ + _____ x 2. When x is 8 this gives y: _____
The regression equation is y = 1.56 + 0.69⋅x².
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
x: 4 5 6 6 9
y: 3 6 5 7 7
Σx=28, ΣΥ=27, Σxy = 163, Σx' = 174
a = ΣΥ ΣΑΣΑ Σ ΑΥ = 27-174-28-163 = 1.558
b= 5.163 28 27 /5-174-(28)2 = 0.686
y = 1.558 + 0.686x²
Hence, The regression equation is y = 1.56 + 0.69⋅x².
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Calculus, I need help for these exercises
2) The equation of tangent line is,
⇒ y = 324x log 3 + 84 - 648 log 3
3) And, The value of x is,
⇒ x = nπ ± π/6
What is mean by Function?
A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
2) The equation of curve is,
y = 3ˣ² + 3
At x = 2
y = 3⁴ + 3
y = 84
Hence, The value of point = (3, 84)
Now, Find dy/dx as;
y = 3ˣ² + 3
dy/dx = 3ˣ² log 3 × 2x
dy/dx = 2x × 3ˣ² log 3
At x = 2
dy/dx = 2 × 2 × 81 × log 3
m = dy/dx = 324 log 3
We know that;
The slope intercept form of equation of line is,
y = mx + c
y = 324x log 3 + c
At point (x, y) = (2, 84)
84 = 324 × 2 log 3 + c
⇒ c = 84 - 648 log 3
Hence, The equation of tangent line is,
⇒ y = 324x log 3 + 84 - 648 log 3
3) We know that;
Horizontal tangent will have a slope of 0.
Hence, The derivative represent the rate of change of a function.
The equation of graph is,
y = 4x - 3 tan x
y' = 4 - 3 sec²x = 0
sec²x = 4/3
sec²x = (2/√3)²
x = nπ ± π/6
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The curved edge of the door mat below is half an ellipse, a "semi-ellipse". As shown in the figure below, the flat edge of the door mat measures 148 cm and the distance from the center (on the flat edge) to the curved edge is 58 cm. The point P is located 30 cm from the center. Find the distance from P to the curved edge.
To find the distance from point P to the curved edge of the door mat, we can use the formula for an ellipse: (x/a)^2 + (y/b)^2 = 1, where a is the semi-major axis (half the length of the flat edge) and b is the semi-minor axis (half the length of the curved edge).
In this case, a = 148/2 = 74 cm and b = 58 cm. The point P is located 30 cm from the center, so x = 30 cm. We can plug these values into the formula and solve for y:
(30/74)^2 + (y/58)^2 = 1
0.1649 + (y/58)^2 = 1
(y/58)^2 = 0.8351
y^2 = 2805.72
y = sqrt(2805.72)
y = 52.97 cm
Therefore, the distance from point P to the curved edge of the door mat is approximately 52.97 cm.
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Biking at 10 mph, it takes Kristen 1/4 hour to reach the train station to go to work. Kristen then takes the train to work, and it takes another 1/4 hour for her to get to work when the train travels 28 mph. How far does Kristen travel to work?
a- 37.5
b- 8.5
c- 19.5
d- 9.5
The requried Kristen travels 9.5 miles to work. Option D is correct.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
Here,
We can use the formula distance = rate x time to solve this problem.
When Kristen is biking, her rate is 10 mph and her time is 1/4 hour. So her distance traveled is:
distance = rate x time
distance = 10 mph x 1/4 hour
distance = 2.5 miles
When Kristen is on the train, her rate is 28 mph and her time is another 1/4 hour. So her distance traveled on the train is:
distance = rate x time
distance = 28 mph x 1/4 hour
distance = 7 miles
Therefore, the total distance Kristen travels to work is the sum of the distances she traveled while biking and on the train:
total distance = distance biked + distance on train
total distance = 2.5 miles + 7 miles
total distance = 9.5 miles
So Kristen travels 9.5 miles to work.
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The population of Placerville grew from 4360 a decade ago to 6590 today.
Answer: To find the percent increase in population, I used the following formula:
percent increase = (new value - old value) / old value * 100
In this case, the old value was the population from a decade ago (4360), and the new value was the current population (6590). So plugging these values into the formula, we get:
percent increase = (6590 - 4360) / 4360 * 100
percent increase = 51.38%
So the population of Placerville increased by approximately 51.38% over the past decade. The population of Placerville has increased by (6590 - 4360) = 2230 people over the past decade.
Step-by-step explanation:
a square of side x inches is cut out of each corner of a 9 in by 12 in piece of cardboard and the sides are folded up to form an open topped box
write the volume V as a function of its side x
The volume of the open-topped box expressed as the function is V(x) = x(9 - 2x)(12 - 2x)
How to determine the volume as a functionFrom the question, we have the following parameters that can be used in our computation:
Length = 9
Width = 12
Cut out = x
The volume as a function of x is represented as
V(x) = (Length - 2x) * (Width - 2x) * x
Substitute the known values in the above equation, so, we have the following representation
V(x) = x(9 - 2x)(12 - 2x)
Hence, the function si V(x) = x(9 - 2x)(12 - 2x)
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