dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x²+y²=16.
What is implicit differentiation?The method of finding an implicit function's dependent variable's derivative by differentiating each term individually, symbolizing the derivative, and then solving the resulting expression for the symbol.
Without having to solve the provided equation for y, you may use the implicit differentiation technique to determine the derivative of y with respect to x.
Because we assume that y may be written as a function of x, the chain rule must always be applied when differentiating the function y.
So, the dx/dt will be:
The circle's equation is: x² + y² = 16
Assuming that x = 2, then:
2² + y² = 16
y² = 12
y = ±√12
Hence, the first quadrant is positive:
y = √12
y = 2√3
When implicit differentiation is used, we get that:
2x dx/dt + 2y dy/dt = 16
If fracdydt = -3, as is the case, then
2(2) dx/dt - 12√3 = 16
4 dx/dt = 16 + 12√3
dx/dt = 16+12√3/4
dx/dt = 4+3√3
Therefore, dx/dt = 4+3√3 in the case of the circle with radius 4 and the equation x² + y² = 16.
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In the diagram below, mZCIH = 100° and mZBGD = 42°. Find m/FHG.
Step
1
2
try
Angle
m/CIH 100°
m/BGD = 42°
mz
B.
42% G
Select a Reason
Reason
Given
Given
F
H
E
100°
A
C
A triangle is a plane figure that consists of three sides and three internal angles. Thus m<FHG is [tex]122^{o}[/tex].
How to illustrate the triangleA triangle is a family of polygon which is bounded by three straight sides, thus forming three internal angles. The sum of the internal angles of a trigon is [tex]180^{o}[/tex]. While exterior angles are angles which are outside the edges of a triangle.
From the given question;<IGH = <BGD = 42° (vertically opposite angles)<HIG = 180 - <CIH = 180 - 100<GIH = [tex]80^{o}[/tex]
Thus, we can conclude that;<IGH + <GIH + <GHI = [tex]180^{o}[/tex]42 + 80 + <GHI = [tex]180^{o}[/tex]<GHI = [tex]180^{o}[/tex] - 122 = 58<GHI = [tex]58^{o}[/tex]So that;m<FHG
= [tex]180^{o}[/tex] - M<GHI = [tex]180^{o}[/tex] - 58
= [tex]122^{o}[/tex]m<FHG
= [tex]122^{o}[/tex]
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(4,0)(2-9) simplest radical form
The distance between two points (4, 0) and (2, -9) is √85 units in the simplest radical form.
What is meant by distance between two points?The length of the line segment connecting two points in a plane is defined as the distance between them. The formula for calculating the distance between two points is commonly presented as √(x₂-x₁)²+(y₂-y₁)².
Distances in geometry are usually positive, unless when the points coincide. We consider two points A(a, b) and B to obtain the formula for the distance between two points in the plane (c, d).
The given two points are (4, 0), (2, -9).
Distance between two points is given by,
Distance=√(x₂-x₁)²+(y₂-y₁)²
Where x₁, x₂, y₁, y₂ are the points.
So, the distance between (4, 0) and (2, -9)
=√(2-4)²+(-9-0)²
=√4+81
=√85 units
Therefore, the distance between two points (4, 0) and (2, -9) is √85 units in the simplest radical form.
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a car is driving at 100 kilometers per hour. how far, in meters, does it travel in 2 seconds? meters
A car travels 500/3 meters in 2 seconds.
What is speed?
The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.
Here, we have
Speed of car = 100 KM/ hour
1 km= 1000m
1 hour = 3600 seconds
Let's find the speed of the car in Meters/second
Speed of car in m/sec = 100*1000 m/3600 second
Here we have taken 1000 for km and 3600 for an hour
Speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second
Speed of car in m/sec = 250/9 m per sec
We know that
Distance = speed*time
Speed = 250/9 m per sec
Time = 2 second
Distance = 250/9 * 2 meters = 500/3 meters
Hence, a car travels 500/3 meters in 2 seconds.
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Geometry.....Solve for each variable. Show your work and explain in paragraph form how you solved each problem.
Base Angles Theorem
Converse to Base Angles Theorem
Corollary
Converse to the corollary
Sum of Interior Angles
Exterior angles
The value of x is 35 and the value of y is 82.
What is an isosceles riangle?In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Given that the three angles of the triangle are 40, 2x and y-12. The value of x and y will be calculated as,
2x = y-12
2x + y-12 + 40 = 180
2x + y =180-40+12
2x + y = 152
2x - y = -12
___________
4x = 140
x = 35
y = 2x + 12
y = 2 x 35 + 12
y = 82
Therefore, the value of x is 35 and the value of y is 82.
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b. if we want to get a 80% confidence interval with a small margin of error, say only 8%. how many people do you need to sample?
The number of people needed will be approx 65.
Margin of error = Critical value x Standard deviation for the population.
Margin of error = Critical value x Standard error of the sample.
Given, Margin of error (m) = 0.08
z (at 80% confidence level)=1.282
Sample size(n) = (z/m)^2 p (1-p)
In order to find the sample size, we must know the value of proportion.
The value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.
p = 0.5
∴ Sample size = (z/m)^2 p (1-p)
= (1.282/0.08)^2 × 0.5 × (1-0.5)
= 65
Inferential statistics is a statistical method that deduces from a small but representative sample the characteristics of a bigger population. In other words, it allows the researcher to make assumptions about a wider group, using a smaller portion of that group as a guideline.
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Keiko is using metric units of capacity to find an equivalent measure for 3 gallons. She records the liquid volume using milliliters and deciliters. Which unit will give a more precise measure? Explain.
If she records the liquid volume using milliliter and deciliter, then the deciliter gives more precise measure
The total capacity = 3 gallon
Convert the gallon to milliliter
We know
1 gallon = 3.785 ml
The total capacity in milliliter = The total capacity × 3.785
Substitute the values in the equation
= 3 × 3.785
= 11.355 milliliter
Convert the gallon to deciliter
We know,
1 gallon = 37.854 deciliter
Total capacity in deciliter = The total capacity × 37.854
Substitute the values in the equation
= 3 × 37.854
= 113.562 deciliter
Here deciliter is much smaller than millimeter
Therefore, deciliter gives more precise measure
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Simplify the expression 4(x+7) using combining like terms or distributive property.
Answer:
4x+28
4 multiplied by x is just 4x and 4x7 is 28
how many square feet of cement would be needed for a 7-foot wide continual sidewalk around the outside edge of a 60 foot by 90 foot corner lot?
Using mathematical operations, we know that 1,099ft² of cement would be needed.
What are mathematical operations?A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.
There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.
Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.
So, square feet of cement needed:
A: 60' x 7' = 420SF.
90' x 7' = 630SF on side B.
Keep in mind that the corner is 49 SF (7'x7') in size.
The three components are added together as follows:
1,099 square feet = 420SF + 630SF + 49SF.
Therefore, using mathematical operations, we know that 1,099ft² of cement would be needed.
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please help precalculus. Given the following piecewise function:
The values of the functions defined in the piecewise function are f(0) = 5 and f(-4) = 11
How to evaluate the piecewise function?From the question, we have the following piecewise function that can be used in our computation:
f(x) = | x + 5 x < -2
x² + 2x + 3 x ≥ -2
Evaluating the function f(0)
In this function, we have the x value to be
x = 0
This x value is at the domain x < -2
So, we make use of
f(x) = x + 5
Substitute 0 for x in f(x) = x + 5
f(0) = 0 + 5
Evaluate
f(0) = 5
Evaluating the function f(-4)
In this function, we have the x value to be
x = -4
This x value is at the domain x ≥ -2
So, we make use of
f(x) = x² + 2x + 3
Substitute -4 for x in f(x) = x² + 2x + 3
f(-4) = (-4)² + 2(-4) + 3
Evaluate
f(-4) = 11
Hence, the value of f(-4) is 11
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The perimeter of the rectangle and the triangle shown are the same. Write an equation to represent this situation, and solve for x. Then, find the perimeter of each shape.
An equation to represent this situation is 16x - 5 = 14x + 1. The value of x is equal to 3.
The perimeters of the rectangle and triangle are equal to 43 units.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this equation;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.An equation for the perimeter of this rectangle is given by:
P = 2[(5x - 2) + (3x - 0.5)]
P = 2(8x - 2.5)
P = 16x - 5.
Mathematically, the perimeter of a triangle can be calculated by using this equation:
P = a + b + c
Where:
P is the perimeter of a triangle.a, b, and c are the side length of a triangle.P = (2x + 3) + (2x + 3) + (10x - 5)
P = 14x + 1
Since the perimeter of both geometric figures are the same, we can calculate the value of x as follows:
16x - 5 = 14x + 1
2x = 6
x = 3
For the perimeter of this rectangle, we have:
P = 16x - 5.
P = 16(3) - 5.
P = 43 units.
For the perimeter of this triangle, we have:
P = 14x + 1.
P = 14(3) + 1.
P = 43 units.
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How do you decide which variable to isolate in order to
use the substitution method to solve a system of linear
equations?
Intro
Answer:
Step-by-step explanation:
it depends on the vaiable you choose to cancel out first. For example, if I had two equations:
-12x+9y=7
9x-12y=6
if you wanted first eliminate the x values, then you distribute a certain number to either equation that will cause the x values to cancel (one being negative, and the other being positive)
.2 times .2 times .2
Your answer is 8.
[tex]2x2x2=8[/tex]
A DJ added 20 more songs to his MP3 player, making the total more than 61. How many songs were originally on the player?
The number of songs that were originally on the player is 41.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this situation, a DJ added 20 more songs to his MP3 player, making the total more than 61. The number of songs will be the subtraction of the value.
This will be:
= 61 - 20
= 41
The original songs are 41.
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Given the following piecewise function,
The value of f(0) is f(0) = 3 and the value of f(-4) is f(-4) = 1
Determining the value of a functionFrom the question, we are to determine the value of the given functions
The functions are
f(0) and f(-4)
First, we will determine the value of f(0)
Since 0 ≥ -2, we will use the function
f(x) = x² + 2x + 3
Thus,
f(0) = (0)² + 2(0) + 3
f(0) = 0 + 0 + 3
f(0) = 3
Now, we will determine the value of f(-4)
Since -4 < -2, we will use the function
f(x) = x + 5
Thus,
f(-4) = -4 + 5
f(-4) = 1
Hence, f(0) = 3 and f(-4) = 1
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for a period of time, an island's population grows exponentially. if the population doubles every 17 years and the current population is 1,725, what will the population be 10 years from now?
After 10 years the population growth will be 3054, if the population doubles after every 17 years.
What is Exponential function?A mathematical function with the form f (x) = ae^x is an exponential function. "x" is a variable, and "a" is a constant that serves as the function's base and must be greater than 0. The transcendental number e, or roughly 2.71828, is the base for exponential functions that is most frequently used.
Growth rate = 100% in 17 years
In 1 year = 5.88% growth
Initial population = P₀ = 1725
Time = 17 years
So, after 10 years population
P= P₀ ( 1 + [tex]\frac{r}{100}[/tex])^t
= 1725 ( 1 + 5.88/100 )^10
=≈ 1725 * 1.77
=≈ 3054
Hence, the population growth after 10 years at the rate of 5.88 % would be 3054.
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When contructing 95% confidence interval for the mean when the parent population i right kewed and the ample ize i mall, the proportion of interval that include the population mean approache
So when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.
Explain the term confidence interval?A confidence level of both the CI refers to the likelihood that its confidence interval contains the actual population mean value.
Any confidence level can be used to determine a CI, although 95% is the most typical value.A 95% confidence interval, strictly speaking, means that if we generate a 95% confidence interval each of 100 independent samples, then about 95 of a 100 confidence intervals include the true mean value (μ).Thus, when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.
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Mark and some friends went to the movies. They bought tickets to the movies for $9 each and spent $22 at the concession stands. If they spent a total of $67, how many friends went to the movies with Mark?
Answer:
5 people total including Mark. So, 4 friends.
Step-by-step explanation:
$67 total - $22 concession stands
$45 spent on tickets
45/$9per ticket
5 tickets were purch
write the reciprocal of 3
This is a random question
The required reciprocal of 3 would be 1/3.
What is the reciprocal?The reciprocal of a number multiplied by a number is 1.
The coefficient of the inverse of the function f(x)=nx is the reciprocal of a number n. A function's inverse is the function with its points flipped.
The reciprocal of a number is the same as its multiplicative inverse.
(The multiplying opposite) It is the number 'turned upside down.
The product of a number and its reciprocal is always 1
So in this case, we can write 3 as: 3/1
The reciprocal is 1/3.
Therefore, the required reciprocal of 3 would be 1/3.
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1/3 Answer:
this is a random answer
Step-by-step explanation:
Solve for each variable. Show your work and explain in paragraph form how you solved each problem.
Base Angles Theorem
Converse to Base Angles Theorem
Corollary
Converse to the corollary
Sum of Interior Angles
Exterior angles
Answer:
can u see when i do this????
Step-by-step explanation:
First Ave.
70°
300 ft
Main St.
Canal St.
Part A:
What is the distance, in feet, on Main Street between First Avenue and Canal Street? Round your answer to the nearest hundredth.
The distance, in feet, on Main Street between First Avenue and Canal Street, using relations in a right triangle, is of:
319.25 ft.
How to obtain the distance?The situation is represented by a right triangle, hence the three trigonometric measures are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Sine of angle = length of opposite side divided by the length of the opposite side.From the image given at the end of the answer, the parameters are given as follows:
Missing Information: Hypotenuse.The side length opposite to the angle of 70º is of 300 ft.Hence the distance of the Main Street is found using the sine of the angle of 70º, as follows:
sin(70º) = 300/x
x = 300/sin(70º)
x = 319.25 ft.
Missing InformationThe right triangle is given by the image shown at the end of the answer.
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describe how the line best fit and the correlation coefficient can be used to determine the correlation between
Using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.
What is line of best fit?
Line of best fit refers to the "a line through a scatter plot of data points that best expresses relationship between those points". Lines of best fit is used to describe data and predict data where the new data will appear. Examples for lines of best fit is 'Least square method'.
Two variables are said to be correlated or to have a correlation coefficient when "changes in the value of one variable produce changes in the variable of the other variable."
In order to find the correlation between two variables on a graph, the question asks for the line of best fit and correlation coefficient.
Only when there is a linear correlation between the variables—that is, when the relationship between the variables is linear on a graph—does the correlation coefficient hold true.
Variation in "x" on the graph leads to variation in "y." Variation in "y" on the graph results in variation in "x." The variables "x" and "y" are jointly dependent on the graph.
The correlation coefficient between two variables on the graph is calculated in this manner.
Hence, using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.
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1 how fast must a ball be rolled along a 70-cm-high table so that when it rolls off the edge it will strike the floor at this same distance (70 cm) from the point directly below the table edge?
A ball must be fast rolled is 185.2cm/sec, according to the question.
What do you mean by distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
According to the given question,
We have the given information:
Table height = h = 70cm
Distance = s = 70cm
g = 9.8[tex]ms^{-1}[/tex]
Now, we have to find the time of falling,
[tex]t=\sqrt{\frac{2h}{g} }=0.378c[/tex]
Horizontal velocity,
[tex]v=\frac{s}{t}=\frac{70cm}{0.378s}=185.2cm/s[/tex]
Therefore, the required answer is 185.2cm/sec.
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2/9-2/15 in fraction form?
Answer:
4/45
Step-by-step explanation:
Jenny says the when you multiply any whole number by a fraction, the product is always less than the whole number. Do agree with Jenny Why or Why not? if no, provide an example
Answer: When multiplying a whole number by a PROPER fraction (always less then 1), the product is always less than a whole number. So yes, i agree with jenny when using proper fractions.
The greatest common factor of 48 and z, some unknown positive integer, is 12. There are two possible values for z between 10 and 30. What is the difference between these two values?.
The greatest common factor being 12, the difference between the two values is 12.
What is GCD?
The greatest common divisor (GCD) from mathematics is the largest positive integer that splits each of two or more non-zero integers.
The symbol gcd stands for the greatest common divisor of the two integers x and y.
For instance, gcd(8,12)=4 is the GCD of the numbers 8 and 12.
According to the given question:
The greatest common factor of 48 and z, some unknown positive integer, is 12. There are two possible values for z between 10 and 30.
Now there are only two numbers between 10 and 30 which has a factor of 12.
The numbers are 12 and 24.
Hence the difference between these two numbers is 24 - 12 = 12
Therefore the required value is 12.
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Solve the inequality, show all of your work:
-4x + 5 > 37
Answer:
x < -8
Step-by-step explanation:
1. Subtract 5 from both sides
-4x + 5 > 37
-4x + 5 - 5 > 37 - 5
2. Simplify
Subtract the numbers:
-4x + 5 - 5 > 37 - 5
-4x > 37 - 5
Subtract the numbers:
-4x > 37 - 5
-4x > 32
3. Divide both sides by the same factor, and flip the relation because the factor is negative
-4x > 32
[tex]\frac{-4x}{-4}[/tex] < [tex]\frac{32}{-4}[/tex]
4. Simplify
Cancel terms that are in both the numerator and denominator:
[tex]\frac{-4x}{-4}[/tex] < [tex]\frac{32}{-4}[/tex]
x < [tex]\frac{32}{-4}[/tex]
Divide the numbers:
x < [tex]\frac{32}{-4}[/tex]
x < -8
Solution:
x < -8
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
x < - 8
Step-by-step explanation:
-4x + 5 > 37
-4x > 37 - 5
-4x > 32 ( now I have to divide by -4 )
-4x > 32 / -4
x < - 8
x has to be smaller than -8 for example ( -9 or - 10 )
demonstration: -4 * (-9) + 5 > 37
36 + 5 > 37
41 > 37
the speed of a car, measured in miles per hour, was determined 10 times at random. the results are 22, 43, 35, 32, 41, 28, 29, 30, 37, and 43 miles per hour. construct a 95% confidence interval for the mean speed of this vehicle.
28.9641 ≤ x-bar(t) ≤ 39.0359.
Step-by-step explanation:1. Determine the size of the sample (n).Knowing that we have 10 different values of speed, the size of the sample is 10; n=10. Therefore, this sample is considered statistically small because n < 30.
2. Calculate the arithmetic mean of the sample.Arithmetic mean= (Sum of all values) / (Amount of values)
x-bar= (340) / (10)
x-bar= 34.0000.
x-bar= arithmetic mean.
3. Calculate the standard deviation using the formula for samples.We're going to use the Microsoft Excel tool for the standard deviation for samples (check attached image 1).
Standard deviation for samples (s)= 7.0396.
4. Calculate σ(x-bar).Check attached image 2.
σ(x-bar)= 2.2261.
5. Calculate α/2.α is the error that the confidence interval will have. Given a 95% confidence level, we know that the error is 5%; Error= 1 - Confidence.
α/2= 5%/2= 0.05/2= 0.025.
6. Find the absolute t-student value for α/2.You can either use the probability tables or the Microsoft Excel tools to find the inverse of a t-student distribution for this α/2 value (check attached image 3).
In this case we use the t-student distribution instead of the normal distribution because the sample size is small and the standard deviation of the population is unknown.
T-student value= -2.2622
Absolute t value= 2.2622.
7. Calculate the intervals.Check attached image 4 to see the formulas.
Lower limit = (34) - (2.2622*2.2261) = 28.9641
Upper limit = (34) + (2.2622*2.2261) = 39.0359
28.9641 ≤ x-bar(t) ≤ 39.0359
8. Conclude.This result means that the value of speed could be any value between 28.9641 and 39.0359, including, with a 95% confidence level. There's a 5% chance that a newly measured value of speed is outside this interval.
A park ranger claims that the average number of acres in his State Park is less than 2000 acres.
A random sample of five parks is selected and the number of acres is shown below:
959, 1187, 493, 6249, 541
Assume the variable must be normally distributed, at [tex]\alpha =0.01[/tex] is there enough evidence to support the claim? To draw your conclusion, state the hypotheses and identify the claim, find the critical value(s), label the acceptance and rejection region, calculate the test value and summarize the results.
Answer:
ypotheses:
H0: μ = 2000
H1: μ < 2000
Claim: The average number of acres in the State Park is less than 2000.
Critical Value (s): -1.645 (z-score)
Acceptance Region: z < -1.645
Rejection Region: z ≥ -1.645
Test Value: z = -3.537
Conclusion: Since -3.537 is less than -1.645, we reject the null hypothesis and accept the alternate view. There is enough evidence to support the claim that the average number of acres in the State Park is less than 2000.
Step-by-step explanation:
given the length of a human's femur, x, and the length of a human's humerus, y, would you expect a positive correlation, a negative correlation, or no correlation?
The length of a human's femur, x, and the length of a human's humerus, Y would ,positive correlation.
A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.
A scale from + 1 to -1 is used to calculate the correlation coefficient. Either + 1 or -1 represents a variable's complete connection with another. The correlation is positive when one variable rises as the other rises; it is negative when one variable falls as the other rises.
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gregory has a coupon for $1 off the purchase of 3 boxes of munchie brand cereal. the store has 5 different varieties of munchie brand cereal. how many ways can gregory choose 3 boxes of cereal?
Gregory has 10 ways to choose 3 boxes of cereal.
What do you mean by purchase?
A corporation or organization uses the purchasing process to buy products or services in order to achieve its objectives. Although many organizations make an effort to establish standards for the purchasing process, procedures can differ significantly between organizations.
According to data in the given question,
We have :
The purchase of 3 boxes and the store has 5 different varieties of munchie brand cereal.
The order in which the boxes of cereal are chosen is not important as Gregory can randomly choose any 3 different varieties. So, this is a combination problem.
Use the combination formula:
[tex]_nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Putting n=5 (5 different varieties) and r=3 (3 different varieties). So, the number of ways Gregory choose 3 boxes of cereal is:
[tex]_{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}= \frac{5.4.3.2.1}{3.2.1.2.1} _{5}C_3=\dfrac{5\cdot 4}{2\cdot 1}=10[/tex]
Therefore, the required answer is 10 ways.
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