Length and width should the rectangle have so that its area is a maximum are 4.242 and 2.121 respectively.
From the question, we have
Area = A = xy
A = xsqr(9-x^2)
Taking the derivative and set = 0
A' = (x/sqr(9-x^2)(-2x) + sqr(9-x^2) = 0
A' = -x^2 + 9 -x^2 = 0
-2x^2 =-9
x^2 = 9/2
x = 3/sqr2 = (3/2)sqr2 = 4.242
y = sqr(9-x^2) = sqr(9-9/2) = 3sqr2/2 = 2.121
Dimensions of the rectangle are 4.242 and 2.121 respectively
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
Complete question:
A rectangle is bounded by the x-axis and the semicircle y = radical 9 − x^2 (see figure). What length and width should the rectangle have so that its area is a maximum?
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Seventh grade > R.12 Simplify expressions by combining like terms JJG
Simplify the expression:
7z+-6z + 10z
Answer:
11z
Step-by-step explanation:
7z+(-6z)= 1z or z
1z + 10z = 11z
The period T (in seconds) of a pendulum is given by T = 2 √(), where L stands for the length (in feet) of the pendulum.
If = 3.14, and the period is 9.42 seconds, what is the length?
The length of the pendulum is
feet
By using the formula for time period of a pendulum, it can be calculated that
Length of the pendulum is 72.324 feet
What is time period of a pendulum?
The time taken by a pendulum to complete one oscillation is called the time period of a pendulum.
If l is the length of the pendulum, g is the acceleration due to gravity, then time period of the pendulum is calculated by the formula
[tex]T = 2\pi \sqrt{\frac{l}{g}}}[/tex]
Here,
Time period = 9.42 seconds
g = 9.8 [tex]m/s^2[/tex]
[tex]T = 2\pi \sqrt{\frac{l}{g}}}[/tex]
[tex]9.42 = 2 \times 3.14 \sqrt{\frac{l}{9.8}}\\\\\frac{9.42}{2 \times 3.14} = \sqrt{\frac{l}{9.8}}\\\\\sqrt{\frac{l}{9.8}} = 1.5\\\\\frac{l}{9.8} = 1.5^2\\\\l = 2.25 \times 9.8\\\\[/tex]
l = 22.05 m
l = 22.05 [tex]\times[/tex] 3.28 feet
l = 72.324 feet
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I WILLL GIVE BRAINLIEST Simplify negative 4 and 3 over 4 minus 8 and 4 over 5. negative 63 over 9 negative 271 over 20 negative 13 and nine elevenths 13 and 11 over 20
Answer:
-13 11/20 = -271/20
Step-by-step explanation:
-4 3/4 - 8 4/5 =
= -4 15/20 - 8 16/20
= -12 31/20
= -13 11/20 = -271/20
The table shows the relationship between time spent running and distance traveled. A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 1, 2, 3, 4, 5. The second column is labeled distance (feet) with entries 530; 1,050; 1,600; 2,110; 2,650. Which type of model best describes the relationship? linear, because the r value for the linear model is closest to 1exponential, because the r value for the exponential model is closest to 0linear, because the rate of change between each pair of points is exactly 520exponential, because the rate of change between each pair of points is 1. 98.
The r value for the linear model is closest to 1.
We have two columns in this question, one for you to enter the time and the other for the distance. We must determine whether the relationship is exponential or linear.
I'll start by explaining the differences between linear and exponential relationships, after which we'll observe the data and find the answer, which is as follows:
linear, as the linear model's r value, is the closest to 1.
exponential and linear data
It is linear if close numbers are assumed for the absolute value of the change.
If so, the rate is exponential.
Data:
t = 1 -> d = 530
t = 2 -> d = 1050
t = 3 -> d = 1600
t = 4 -> d = 2110
t = 5 -> d = 2650
Subtractions:
2650 - 2110 = 540
2110 - 1600 = 510
1600 - 1050 = 550
1050 - 530 = 520
Divisions(rates):
2650/2110 = 1.25
2110/1600 = 1.32
1600/1050 = 1.52
1050/530 = 1.98
The rates change considerably more than the subtractions, so it is a linear relationship, and the correct option is: linear because the r value for the linear model is closest to 1.
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in a study entitled "hello from the other side", yael schneider studied the frequency, conditions of, and content of attempted electronic communications with a former significant other in the month immediately following a breakup. yael looked at messages sent via social media, text, and email of 32 individuals who had recently broken up with their significant other. her findings can be found in the almanac of questionable statistics, vol 16 (1242). what is the population in this study?
All the individuals who have recently broken up with a significant other is the population in this study answer to this question.
what is statistics?The study of statistics includes the collection, examination, analysis, and interpretation of data as well as methods for doing so. Statistics can be divided into two main categories: descriptive statistics and inferential statistics.
given,
Yael examined the texts, emails, and social media posts of 32 people who had recently split up with their partners. Her results are published in the Almanac of Doubtful Statistics.
People who just broke up with a significant other who have pledged to return to that in a moment on social media, cell phone, or internet service providers.
Keep in mind that this is about the users, not the providers, and is being done for social and behavioral science study.
All the individuals who have recently broken up with a significant other is the answer to this question.
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How much more will account X be worth more than account Y after 20 years?
The answer can be stated as, " Account X will be worth $ 248 more than account Y after 20 years."
What is simple interest?Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time.
The simple interest for account X and account Y can be calculated as follows,
For account X substitute the corresponding values in the expression as,
(P × r × t)/100
= (1800 × 1.8 × 20)/100
= 36 × 18
= 648
Similarly for account Y, interest can be calculated as,
(P × r × t)/100
= (10000 × 0.2 × 20)/100
= 40000/100
= 400
Thus, the difference between the interests is given as 648 - 400 = 248.
Hence, the account X will be $248 more than account Y.
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find each angle measure to the nearest degree tan b= 0.7536
Answer: b≈37°
Step-by-step explanation:
tg(b)=0.7536
b=arctg(0,7536)
b≈37°
Consider the inequality 1/2x−1/4<5/8 .
The required solution to the given inequality is x < 7/4.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Given that,
To determine the simplified solution of the inequality 1/2x−1/4 < 5/8.
1/2x−1/4<5/8 .
Adding 1/4 on both sides of the equality,
1/2x < 5 / 8 + 1 / 4
Multiply by 2 on both sides of equality,
1 / 2x < 7 / 8
x < 7 / 4
So, the solution of inequality lies x greater than 7/4, as of the given conditions.
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Of the 140 students 65% are girls how many are boys
Answer:
there are 22 boys and 40 girls
According to the Rational Root Theorem what are the solutions of: 2x^4 -5x^3+10x^2-9=0
The required true statement for [tex]2x^4 -5x^3+10x^2-9=0[/tex] is rational root factor of 9 divided by a factor of 2.
What is Rational root theorem?Rational root theorem states that if the equation has rational roots they will be the factors of constant term divided by factors of highest power coefficient.
The Rational Root Theorem states that any rational root of f(x) is a factor of the trailing constant divided by a factor of the leading coefficient.
In this case, a factor of 9 divided by a factor of the number 2.
[tex]2x^4 -5x^3+10x^2-9=0[/tex]
If there are any rational roots, it would be a factor of constant term of 9 divided by a factor of the high-order coefficient of 2.
Hence, The true statement is rational root factor of 9 divided by a factor of 2.
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The point 0 is the center of a regular octagon ABCDEFGH. The point X is the mid-point of the side AB.
The fraction of the area of the octagon that is shaded is [tex]\dfrac{7}{16}[/tex]
What is a fraction?A fraction is expressed as a quotient consisting of a numerator, divided by a denominator, and it is used to show the relative amount a part of an item is with regards to the whole item.
An regular octagon can be taken as comprising of eight triangles, that have a base length equal to the length of one of the sides of the octagon, and a height equivalent to the length of the apothem of the octagon, therefore;
The area of the octagon can be obtained from the sum of the area of the eight triangles in the octagon as follows;
Area of the octagon, ABCDEFGH = 8 × Area of triangle, ΔBOCThe area of the shaded region, comprises of three and a half triangles of the 8 triangles that make up the octagon, such that, we get;
Area of the shaded region = Three and a half of the eight triangles that form the octagon
Area of the shaded region = 3.5 × Area of one triangleThe fraction of the area of the octagon, represented by the area of the shaded region is therefore;
Fraction of the octagon shaded = [tex]\dfrac{3.5 \times Area \, of \, triangle \ \Delta BOC}{8 \times Area \, of\, triangle \, \Delta BOC} = \dfrac{3.5}{8}[/tex]
[tex]\dfrac{3.5}{8} =\dfrac{7}{16}[/tex]
Fraction of the area of the octagon shaded = 7/16A possible part of the question obtained from a similar online question includes to find the fraction of the octagon represented by the shaded region
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The equation for QR is 5y = -4x + 41. Is QR tangent to Circle O at R?
R (4,5)
4X
No, because the slope of OR times the slope of QR
does not equal -1.
Yes, because the slope of OR times the slope of
QR equals 1.
Yes, because the slope of OR times the slope of
QR equals -1.
No, because the slope of OR times the slope of QR
does not equal 1.
Done)
Yes, because the slope of OR times the slope of
QR equals -1.
Option C is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of QR is 5y = -4x + 41.
QR is tangent to the circle at R(4, 5) if the radius of the circle is perpendicular to QR.
This means,
The slope of the radius x Slope of the line QR = -1
Now,
The centre of the radius 0 = (0, 0)
R = (4, 5)
OR is the radius.
The slope of the radius.
= 5/4
Now,
5y = -4x + 41
y = (-4/5)x + 41
The slope of QR.
= (-4/5)
Now,
The slope of the radius x Slope of the line QR = -1
5/4 x -4/5 = -1
-1 = -1
Thus,
QR is tangent to the circle O at R(4, 5).
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Hi can I please get some help?
The length of DE from the given triangle ABC is 9. Therefore, option C is the correct answer.
What is midpoint theorem?The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side.
In the given triangle ABC, AD=DB
Here, D is the midpoint on AB so AD:DB=1:1
Now, DE=BC/2
=18/2
=9
Therefore, the length of DE is 9.
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As Monte Carlo simulation is essentially statistical sampling, the larger the number of trials used, the more precise is the result. True False
It is true that statistical sampling uses Monte Carlo simulation, where a greater number of trials are employed to obtain a precise answer.
What are the steps for Monte Carlo simulation?A mathematical method or statistical sampling called Monte Carlo simulation is used to forecast all potential outcomes of any unknown event.
As it relies on historical data to forecast future results, the accuracy increases with the number of trials.
You can review more old data to anticipate the first month's sales of any newly launched product, for instance.
It aids in more precise probability calculations.
As a result, more trials are necessary for an accurate result in Monte Carlo simulation statistical sampling.
Therefore, it is true that statistical sampling uses Monte Carlo simulation, where a greater number of trials are employed to obtain a precise answer.
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The base of a triangle is decreasing at a rate of 131313 millimeters per minute and the height of the triangle is increasing at a rate of 666 millimeters per minute. At a certain instant, the base is 555 millimeters and the height is 111 millimeter. What is the rate of change of the area of the triangle at that instant (in square millimeters per minute)?.
The rate of change of the area of the triangle at that instant is 8.5 square mm per minute.
A' = (1/2)(b'h +bh') . differentiating with respect to time
A' = (1/2)((-13)(1) +(5)(6)) = (1/2)(17) = 8.5 . . . . mm²/min
The area is increasing at the rate of 8.5 mm²/min.
Solution based on numbers
Take a look at the triangle dimensions.
01 minute before and 01 minutes after the moment of interest Previously, the base was 5 + 0.13 = 5.13 mm, while the height was 1 - 0.06 = 0.94 mm. After: base = 5 -0.13 = 4.87 mm; height = 1 +.06 = 1.06 mm; area = 2.4111 mm2. 2.5811 mm2 area
The average rate of change throughout that time period is (2.5811 -2.4111)/0.02 =.17/.02 = 8.5... mm2/min.
It should be noted that we assumed the base is dropping at a rate of 13 mm/min. We're not sure whether this isn't 1/3 mm/min because division bars frequently get lost on Brainly. At the anticipated pace, the triangle will vanish in 5/13 minutes, or around 23.08 seconds, when the base reaches zero. Of course, it only existed for 1/6 minute (10 seconds) when the height reached non-zero.
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the assumptions that z2 and z3 do not appear in the model and are uncorrelated with the error u1 are known as
z2and z3 are uncorrelated with the error u1 are known as are known as exclusion restrictions
What is Exclusion Restrictions?
Most undergraduate econometric curricula cover the use of instrumental variables as a typical method for determining a variable's causal relationship to another variable. The fundamental tenet of the approach is that it can be applied in circumstances when a source of exogenous variation in X cannot be identified. Instead, a third variable called the instrument, Z, is utilized, where Z only influences Y by acting through X.
When estimating outcomes using instrumental variables (IV) or exogenous variables, which are used in many fields of research, including statistics and economics, researchers rely on proper exclusion limits.
the assumptions that z2 and z3 do not appear in the model
Hence z2and z3 are uncorrelated with the error u1 are known as are known as exclusion restrictions.
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what is the answer to 17 divided by 1699
The answer is 99 and the remainder is 16
6. 42.3 × 1 =
42.3 x 10 =
42.3 × 10²
Answer:
Step-by-step explanation:
42.3 x 1 = 42.3
42.3 x 10= 423
42.3 x 10^2=
10 x 10 =100
42.3 x 100=4230
how many 1/6 liter savings of water are in 3 liter bottle of water
A. 2
B. 3
C 9
D. 18
ASAP PLEASE HELP A satellite orbiting Earth at an orbital radius r has a velocity v. What would the velocity be if the satellite is moved to an orbital radius of 6r?(1 point)
A. 1/6 v
B. 1/√6 v
C. √6v
D. 6v
New orbital Velocity is [tex]\frac{1}{\sqrt{6} }[/tex] times the Actual orbital velocity
What is Orbital Velocity ?The speed at which one body orbits the other body is known as the orbital velocity. The term "orbit" refers to an object's consistent circular motion around the Earth. The distance between the object and the earth's center determines the orbit's velocity.
According to the given information
When the radius given is r
Orbital Velocity = [tex]\sqrt{\frac{Gm}{r} }[/tex]
V = [tex]\sqrt{\frac{Gm}{r} }[/tex]
Here
V = orbital Velocity
G = Gravitational Constant
m = mass of Satellite
r = radius
When radius = 6r
Orbital Velocity = [tex]\sqrt{\frac{Gm}{5r} }[/tex]
New V = [tex]\frac{1}{\sqrt{6} }[/tex] × [tex]\sqrt{\frac{Gm}{r} }[/tex]
New V = [tex]\frac{1}{\sqrt{6} }[/tex] × V
So
New orbital Velocity is [tex]\frac{1}{\sqrt{6} }[/tex] times the Actual orbital velocity
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How do you make a table of values for a linear relationship?
To make a table of values for a linear relationship;
Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value
Given,
Linear relationship;
A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.
Here,
We have to make a table of values for a linear relationship;
Make the table and select a range of x values. Fill in the equation with each x value from the left side column. To determine the y value, evaluate the equation in the middle column.Since the table of values really only contains x and y pairs, you can choose to omit the middle column from your table as an optional step.Learn more about linear relationship here;
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i have pieces of strawberry candy (all identical) and pieces of rhubarb candy (all identical). find the number of ways i can distribute this candy to children, if it's ok to not give a child any candy.
If there are 8 pieces of strawberry candy and 7 pieces of rhubarb candy then I have 77 different methods to give this candy to kids who have donated $5.
Number of strawberry candy = 8 pieces
Number of rhubarb candy = 7 pieces
Find the number of ways for equally distributing candy to all 5 children
Using formula:
→ ⁿCr = n!/r(n-r)!
= 8!/5!3!
= 8×7×6×5!/5! 3 × 2 ×1
= 8×7×6/6
= 56
Calculating the distributing way to rhubarb candy:
→ ⁿCr = n!/r(n-r)!
= 7!/5!2!
= 7×6×5!/5! × 2 ×1
= 7×6/2
= 21
Adding both distributing ways:
56+21 = 77 ways
Hence we get the required answer.
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Your question is incomplete. Please find the missing content below.
I have $8$ pieces of strawberry candy (all identical) and $7$ pieces of rhubarb candy (all identical). Find the number of ways I can distribute this candy to $5$ children.
Middle School Problem: A frog stands at the number 0 on a number line and wants to hop to the number 8. He can hop 1, 2, 3 units forward in a single jump. How many different ways are there for him to reach the number 8?
Answer: There will be 3 different ways for the frog to reach the number 8
Step-by-step explanation:
It's a simple addition, just add 3+2+3 which will equal 8. You can also look at a number line and do it that way. Hope this helps!
What is the value of 5 (!)?
Answer:
120
Step-by-step explanation:
Let's assume that "5 (!)" is 5! (5 factorial)
5*4*3*2*1 = 120
How do you find the mean of 15 numbers?
To find the mean of 15 numbers, add up all of the numbers and then divide by 15. The result will be the mean of the 15 numbers.
1. Add up all the numbers
2. Divide the sum by 15
3. The result will be the mean of the 15 numbers
To calculate the mean of 15 numbers, begin by collecting all the values in the group. Sum up the values in the group by adding each number together. Once the sum is calculated, divide the sum by 15. This number will be the average of the 15 numbers. To check the accuracy of the answer, add up the 15 numbers again and divide the result by 15.
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convert 4 ounces in
to pounds
4 ounces to pounds
1 ounce = 0.0625 pounds
4 ounces * 0.625 pounds = [tex]\fbox{2.5 pounds}[/tex]
The ages of the workers at a small company are given in the table.
Find the median age of the employees.
Employees’ Ages
17 22 56 45 34
18 21 62 25 29
Median
The median In
those years is?
The median of the employees' ages is 27.
What is median?The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data point. To find the median, firstly arrange the data points in ascending order.
The ages of the workers at a small company are given.
Employees’ ages are 17, 22, 56, 45, 34, 18, 21, 62, 25, 29.
To find the median,
firstly, arrange the data points in ascending order.
17, 18, 21, 22, 25, 29, 34, 45, 56, 62.
The total element in the data set is 10.
And 10 is an even number.
Then the median is the simple average of the middle two numbers.
And the middle numbers are 25 and 29.
So, 25 + 29 / 2
= 54/2 = 27
Therefore, the median is 14.
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Select that integer that matches the following situation:
I go for a hike in Colorado. The top of the mountain is , feet above sea level.
Question 4 options:
A: 144
B: 14,000
C: -14
D: -14,000
The integer that matches the situation I go for a hike in Colorado. The top of the mountain is feet above sea level is 14000.
What is Number system?A number system is defined as a system of writing to express numbers.
Given,
I go for a hike in Colorado. The top of the mountain is ___ feet above sea level.
We need to find the suitable integer in the blank.
The top of a mountain would be a high number above sea level, 144 is around ground level above sea level therefore the top of the mountain would be 14,000 feet above sea level
Hence, the integer that matches the situation I go for a hike in Colorado. The top of the mountain is feet above sea level is 14000.
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What is the perimeter of figure I?
In geometry, the perimeter is the overall length of a shape's boundary. The perimeter of a shape is determined by adding the lengths of all of its edges and sides. 28 units make up Figure I's perimeter.
Its dimensions are expressed in linear units like centimetres, metres, inches, and feet. A rectangle in Figure I has four sides that are 8 units, 6 units, 6 units, and 8 units in length. You must total the lengths of all four sides in order to get a rectangle's perimeter. Figure I's perimeter is 8 + 6 + 6 + 8 units, or 28 units.
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Solve for X in Circle A
The value of x, if In triangle ABC, AC = 18, BC = 30 is 24.
What is circle?A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius).
Given:
In triangle ABC, AC = 18, BC = 30
As we know, if a tangent is drawn from the circle then it will form a right-angled triangle thus, ∠ ABC = 90°,
Calculate the value of x by using Pythagoras' theorem as shown below,
[tex]x^2 = BC^2 - AC^2[/tex]
x² = 30² - 18²
x = √(900 - 324)
x = √576
x = 24
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