The correct conclusion is:
a. f opens down on the interval 0.987 < x < 1
To determine the conclusion about the behavior of the function f, we can use the tangent line approximation and whether it overestimates or underestimates the actual value of f(0.987).
Given that the tangent line approximation at x = 1 is 2.37, and if this approximation is an overestimate of the actual value of f(0.987), it means that the function lies below the tangent line in the interval 0.987 < x < 1.
Since the tangent line has a positive slope (given that f'(1) = 4), if the function f lies below the tangent line, it must be decreasing in the interval 0.987 < x < 1.
Therefore, the correct conclusion is:
a. f opens down on the interval 0.987 < x < 1
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Complete question =
For f differentiable such that f(1) = 3 and f'(1) = 4, the tangent line approximation of (0.987) = 2.37.
If this is an overestimate, what conclusion can be made about f ??
a. f opens down on the interval 0.987 x < x < 1
b. f opens up on the interval 0.987 x < x < 1
c. f opens down at x = 0.987
d. f opens up at x = 1
(a)
The prize money from a game show is shared amongst the team in the ratio
A: B: C = 2: 5: 3. If the prize money was £1500, how much more money does person B receive than person A?
(b) Person C donates 40% of his share to charity. State the ratio of the amount
donated to charity, to the total prize money in its simplest form
Step-by-step explanation:
(a)
2:5:3 means that there are 2+5+3 = 10 units of the price money distributed between the team.
£1500 / 10 = £150 per unit.
person A gets therefore 2×150 = £300
person B gets 5×150 = £750
person C gets 3×150 = £450
so, person B gets 750-300 = £450 more money than person A.
(b)
40% of £450 = 450×0.4 = £180
so donated to total prize money is
180/1500 = 3/25
Of the following, which are solutions to the differential equation y′′−5y′+6y=0?y=e^2ty=3e^3ty=3sin(2t)I onlyII onlyIII onlyI and II only
I and II only are solutions to the differential equation y′′ − 5y′ + 6y = 0.
Let's assume y = e^2t is the solution of the given differential equation y′′ − 5y′ + 6y = 0.
Now, put y = e^2t in the given differential equation y′′ − 5y′ + 6y = 0
(e^2t)'' - 5(e^2t)' + 6(e^2t) = 0
Now differentiate it; we get
4e^2t - 10e^2t + 6e^2t = 0
0 = 0
So, here we can see that y = e^2t satisfies the equation y′′ − 5y′ + 6y = 0.
Therefore y = e^2t is the solution of the given differential equation.
Now let's assume y = 3e^3t is the solution of the given differential equation y′′ − 5y′ + 6y = 0.
Put y = 3e^3t in the given differential equation y′′ − 5y′ + 6y = 0
(3e^3t)'' - 5(3e^3t)' + 6(3e^3t) = 0
Now differentiate it; we get
27e^3t - 45e^3t + 18e^3t = 0
0 = 0
So, here we can see that y = 3e^3t satisfies the equation y′′ − 5y′ + 6y = 0.
Therefore y = 3e^3t is the solution of the given differential equation.
Similarly, let's assume y = 3sin(2t) is the solution of the given differential equation y′′ − 5y′ + 6y = 0.
Put y = 3sin(2t) in the given differential equation y′′ − 5y′ + 6y = 0
(3sin(2t)'' - 5(3sin(2t))' + 6(3sin(2t)) = 0
Now differentiate it; we get
-24cos(2t) + 30cos(2t) + 18sin(2t) = 0
-24cos(2t) + 30cos(2t) + 18sin(2t) ≠ 0
So, here we can see that y = 3sin(2t) does not satisfies the equation y′′ − 5y′ + 6y = 0.
Therefore y = 3sin(2t) is not the solution of the given differential equation.
Hence, I and II only are solutions to the differential equation y′′−5y′+6y=0.
--The given question is incorrect; the correct question is
"Of the following, which are solutions to the differential equation y′′−5y′+6y=0?
I. y = e^2t
II. y = 3e^3t
III. y = 3sin(2t)
I only
II only
III only
I and II only"--
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Mr. Gabriel borrowed $1860 to buy a computer. He will pay $71.30 per month for 30 months. Find the simple intresr rate for his loan.
The simple interest rate for his loan could be 6%
How to calculate simple interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
Given that Mr. Gabel borrowed $1860 to buy a computer. He will pay $71Mr. Gabel borrowed $1860 to buy a computer. He will pay $71.30 per month for 30 months.
To Find the simple interest rate for his loan.
P= 1860R= x
T= 30 months = 2.5 years
I = $279
Therefore, I= prt
279 = 1860 (r)(2.5)
279 = 4650r
0.06 = r
r = 6%
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need help please and thank you
Answer: B. No, the adjacent sides are not perpendicular.
Step-by-step explanation:
B(2,4), A(4, -1), C(-2, 2), D(0, -3)
Slope of BA = [tex]\frac{4-(-1)}{2-4} = \frac{5}{-2}[/tex]
Slope of CD = [tex]\frac{2-(-3)}{-2-0} =\frac{5}{-2}[/tex]
BA║CD
Slope of BC = [tex]\frac{4-2}{2-(-2)} =\frac{2}{4} =\frac{1}{2}[/tex]
Slope of AD = [tex]\frac{-1-(-3)}{4-0} =\frac{2}{4} =\frac{1}{2}[/tex]
BC║AD
Slope of BA [tex]=\frac{5}{-2}[/tex]
Slope of BC [tex]=\frac{1}{2}[/tex]
BA is not perpendicular to BC
14. Steve has a $50 gift certificate from the local bookstore. He was planning to spend the entire amount by purchasing 3 hard-cover books and 4 paperback books. However, he bought only 2 hard-cover books and 3 paperback books, and he still has $15.50 left on the gift certificate. Find the cost of a hard-cover book and the cost of a paperback book.
Answer:Let x be the cost of a hard-cover book and y be the cost of a paperback book.
We know that Steve spent 2 hard-cover books and 3 paperback books. So we can write the equation as:
2x + 3y = 50 - 15.5
2x + 3y = 34.5
We also know that he was planning to buy 3 hard-cover books and 4 paperbacks, so we can write another equation as:
3x + 4y = 50
Now we have a system of two equations with two unknowns:
2x + 3y = 34.5
3x + 4y = 50
We can use the first equation to eliminate one variable by multiplying both sides by 2 and then subtracting 3y:
4x + 6y = 69
3x + 4y = 50
x = 19.5
Now we can substitute this value of x into the second equation and find the value of y:
3(19.5) + 4y = 50
58.5 + 4y = 50
4y = -8.5
y = -2.125
Therefore, the cost of a hard-cover book is $19.5 and the cost of a paperback book is $-2.125.
Note that the cost of a paperback book is a negative value which is not possible in this case. It means that the given information does not have a solution.
Step-by-step explanation:
o the distance from p=(1,−1) to the line through the points a=(−2,2) and b=(0,−4) is
The distance from point P = (1, -1) to the line through points A = (-2, 2) and B = (0, -4) is 2.23.
What is distance ?
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
The slope of the line can be found using the coordinates of points A and B:
m = (y2 - y1) / (x2 - x1) = (-4 - 2) / (0 - (-2)) = -3
Next, we can use the coordinates of point A to find the y-intercept:
b = y - mx = 2 - (-3)(-2) = 2 + 6 = 8
m_perpendicular = -1 / -3 = 1/3
Using the coordinates of point P, we can find the equation of the perpendicular line:
y = m_perpendicular x + b_perpendicular
y = 1/3 x - 1/3
Setting the y-coordinates equal, we can find the x-coordinate of the intersection point:
-3x + 8 = 1/3 x - 1/3
-9x + 24 = x - 1/3
-10x + 24.33 = x
x = 24.33 + 10x
11x = 25.66
x = 2.33
Finally, we can find the y-coordinate of the intersection point using the equation of the perpendicular line:
y = 1/3 x - 1/3
y = 1/3 (2.33) - 1/3 = 0.77
The intersection point is (2.33, 0.77), and the distance from point P to the line is the distance between the two points:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((2.33 - 1)^2 + (0.77 + 1)^2) = sqrt(1.33^2 + 1.77^2) = sqrt(1.7769 + 3.1369) = sqrt(4.9138) = 2.23.
So, the distance from points P = (1, -1) to the line through points A = (-2, 2) and B = (0, -4) is 2.23.
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I need Help fjidsfidasfiajiujirufr
The x- intercepts in parabola is (1,0) and (5,0).
What do you mean by parabola?A parabola is a type of symmetrical, U-shaped curve that is a graph of a quadratic function. It is defined by the equation y = ax² + bx + c, where a, b, and c are constants. The shape of the parabola is determined by the value of the coefficient "a". If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.
Parabolas are used in many areas of mathematics and science, including physics, engineering, and economics. For example, they are used to model the trajectory of objects under the influence of gravity, to describe the motion of objects in space, and to analyze the behavior of systems that exhibit parabolic patterns.
The vertex of a parabola is the point that represents the highest or lowest point on the curve, and the axis of symmetry is a line that separates the curve into two congruent halves.
The x-intercepts of a parabola can be found by setting the y-value to 0 and solving for x. In this case, the y-coordinate of the x-intercepts will be 0, so we have:
y = 0
To find the x-intercepts, we can use the information given in the coordinates of the parabola: (1,0), (5,0), and (0,6).
From the coordinates (1,0) and (5,0), we can see that the x-intercepts are at 1 and 5.
From the coordinate (0,6), we can see that the y-intercept is at (0,6).
So, the x-intercepts of the parabola are (1,0) and (5,0).
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Making an inference is the first part of the process of investigating a question
using data.
OA. True
OB. False
Answer:
A. True
Making an inference is the first part of the process of investigating a question using data. Making an inference is the process of drawing a conclusion based on evidence and reasoning. It is the first step in the process of data analysis, as it allows us to make a prediction or understand the relationship between variables, before any analysis is done.
Step-by-step explanation:
What percentage of health care workers (including physicians) that do not wash their hands before examining patients?
A. 20%
B. 75%
C. 48%
D. 15%
Option D is correct. Around 15% of health care workers (including physicians) that do not wash their hands before examining patients.
According to a study published in the Journal of Hospital Infection, an estimated 15% of healthcare workers do not consistently wash their hands before examining patients. This is a concerning statistic, as hand hygiene is one of the most important ways to prevent the spread of healthcare-associated infections.
Handwashing helps to remove dirt, bacteria, and viruses from the skin, reducing the risk of transmitting these harmful organisms to patients. Improving hand hygiene among healthcare workers is a critical component of patient safety, and many hospitals and healthcare organizations have implemented programs to increase handwashing rates and prevent the spread of infections.
Despite these efforts, the 15% figure highlights the continued need for education and training to promote hand hygiene among healthcare workers, and to ensure that all healthcare workers understand the importance of washing their hands before and after patient interactions.
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on average, an individual's bmr decreases approximately 3 to 5 percent per decade after what age? a. 20 b. 50 c. 30 d. 70
An individual's BMR decreases approximately 3 to 5 percent per decade on an average after the age of option C. 30.
BMR is known as basal metabolic rate which decreases when the age of a person increases.As metabolism factor slow down with the increase in age.After the age of 30 metabolism rate decreases which effect basal metabolic rate every decade by round about 3 to 5 percent.At the young age expenditure of the daily energy is quiet more compare to older age.On an average after the age of 30 BMR is decreases approximately by 3 to 5 percent.
Therefore, on an average individuals BMR is approximately decreases by round about 3 to 5 percent per decade after the age of option c. 30.
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Points K and M are points of tangency. Find the value of x
If the points K and M are points of tangency, then the value of x is, 4
What is a circle?In mathematics, the circle is a two dimensional rounded figure which has no corner edges.
Standard form = (x - a)² + (y - b)² = r²
Given that,
A circle, having two pair of lines JK & JM
It is known that,
theorem of a circle,
Lengths of the tangents on the circle from the same point are equal
Length of JK = Length of JM
6x + 5 = 37 - 2x
8x = 32
x = 4
Hence, the value of x is 4
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what is the unsigned decimal equivalent (with 5 digits after the decimal point, truncated, e.g., 12.34567) of the following unsigned base 9 value? 1101.101
The decimal equivalent of 1101.101 in base 9 is 729.1184.
The decimal equivalent of an unsigned base 9 value is simply the number represented in the decimal system.
To find the decimal equivalent of 1101.101 in base 9, we need to convert each digit to its decimal equivalent.
First, we'll convert the whole number portion of 1101.101.
1101 in base 9 is equivalent to
=> 9³ + 1 = 729
Now, we'll convert the fractional portion.
The first digit after the decimal point, 1, represents 1/9.
The next digit, 0, represents 0/9².
The last digit, 1, represents 1/9³.
Adding these values together, we get
=> 729 + 1/9 + 1/729 = 729.1184
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Find the missing lengths of the sides.
W = 12
L = 8
so multiply 8 and 12
Bert and Ernie are solving the inequality 2x²+5x-3
problem 3-67 when Bert has an idea. "Can't we change this into one parabola and solve our
inequality that way?", he asks.
Ernie asks, "What do you mean?"
"Can't we determine the solutions by looking at the graph of f(x)=x²+x-6?", Bert replies.
a. Where does Bert get the equation f(x)=x²+x-6?
b. Try Bert's idea. Make a sketch of the parabola and show how it can be used to solve the
original inequality.
Answer:
Step-by-step explanation:
Given equation: f(x)=x^2+x-6
The roots of the equation, set the equation equal to zero.
[tex]x^2+x-6=0\\x^2+3x-2x-6=0\\x(x+3)-2(x+3)=0\\ (x+3)(x-2)=0\\ x=-3,2[/tex]
Therefore, the roots of the equation are x=-3 and x=2
Solve the system using the substitution method.
10x - 16y = 17
3x + 3y = 9
a flat screen television is advertised as being 47 inches on its diagonal. if the tv is 19 inches tall, then how wide is the screen?
Answer:
42.85 inches wide
Step-by-step explanation:
You must use the Pythagorean theorem
width^2+19^2=47^2
width^2=47^2-19^2
width=square root of (2209-361)
width=square root of (1848)
width= 42.85 inches
A square pool has a side length of s feet. How many 2-foot square tiles does it take to tile the border of the pool?
Answer:
2s
Step-by-step explanation:
sq pool so total length = 4s
so need 4s/2 = 2s tiles
an individual has been driving a passenger vehicle to work, averaging 60 60 miles a week in a car that averages 22 22 miles per gallon. the individual plans to purchase a hybrid vehicle that averages 50 50 miles per gallon. if the individual drives to work 50 50 weeks a year, how much gas will they save if they switch to a hybrid vehicle for their commute?
The individual can save about 76 gallons of gas when switching to a hybrid vehicle.
A motor vehicle's fuel efficiency is calculated in miles per gallon (mpg). Miles traveled divided by gasoline consumed is the formula used to calculate mpg.
The gallons used by the vehicle a year when it travels 60 miles per week are given by,
[tex]\begin{aligned}\text{gallons used}&=\mathrm{\frac{50\;weeks\times 60\;miles}{22\;miles/gallon}}\\&=\mathrm{136\;gallons}\end{aligned}[/tex]
The gallons used by the hybrid vehicle a year when it travels 50 miles per gallon is given by,
[tex]\begin{aligned}\text{gallons used}&=\mathrm{\frac{50\;weeks\times 60\;miles}{50\;miles/gallon}}\\&=\mathrm{60\;gallons}\end{aligned}[/tex]
Then, the gas they have saved is calculated by subtracting fuel consumed by both vehicles, 136-60=76 gallons.
The required answer is 76 gallons.
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Use the Midpoint Rule with n = 4 to approximate the area of the region bounded between the curves y = sin2(πx/4) and y = cos2(πx/4) for 0 ≤ x ≤ 1.
The area of the region bounded between the given curves is =0.640675 unit square.
The center point of a straight line can be located using the midpoint formula. You may occasionally need to determine the difference between two specific numbers. The average of the two numbers is what you find there. In a similar way, we obtain the halfway number (or point) between two coordinates using the midpoint formula in coordinate geometry.
The midpoint rule states that you can calculate the area under a curve by using the formula:
[tex]M_n=\frac{b-a}{2}[f(\frac{(x_0+x_1)}{2})+f(\frac{x_1+x_2}{2})+....+f(\frac{x_{n-1}+x_n}{2})][/tex]
In our case a=0 ,b=1 ,n=4
[tex]x_0=0 ,x_1=1/4,x_2=1/2, x_3=3/4\ and \ x_4=1[/tex]
Therefore, we have-
[tex]M_4=\frac{1}{4}[f(\frac{1}{8})+f(\frac{3}{8})+f(\frac{5}{8})+f(\frac{7}{8}][/tex]
now to evalute f(x),
[tex]f(x)=cos^{2}(\frac{\pi x}{4})-sin^{2}(\frac{\pi x}{4})\\ \\f(x)= cos(\frac{\pi x}{2})\\\\f(1/8)=cos(\frac{\pi}{16})=0.9807\\\\f(3/8)=0.8314\\\\f(5/8)=0.5555\\\\f(7/8)=0.19509[/tex]
hence the value of integral is equal to -
M4= 2.56279÷4=0.640675
The area of the region bounded between the given curves is =0.640675 unit square.
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the owner of a garden supply store wants to construct a fence to enclose a rectangular outdoor storage area by using part of one side of the store, which is 270 feet long, as one of the sides of the enclosed area. there are 500 feet of fencing available for the other three sides of the enclosure. find the dimensions of the outdoor enclosure with the most area.
The dimensions of the outdoor enclosure with the most area is 250 feet and 125 feet.
One side of the store is 270 feet long
There are 500 feet of fencing available for the other three sides of the enclosure.
The Perimeter of rectangular outdoor storage = 2x + y
2x + y = 500
To maximize the area
y = 500 - 2x...............(1)
Area of rectangle;
A = xy
Now putting the value of y
A = x(500 - 2x)
Solve
A = 500x - 2x^2...................(2)
To finding the value of x differentiating on both side with respect to x.
dA/dx = 500 - 4x...................(3)
Equating dA/dx = 0
500 - 4x = 0
Subtract 4x on both side, we get
4x = 500
Divide by 4 on both side, we get
x = 125
Now putting the value of x in equation 1
y = 500 - 2(125)
y = 500 - 250
y = 250
Differentiating equation 3 again with respect to x
d^2A/dx^2 = -4 < 0 (Maximum)
Hence, for the maximum storage area
Length parallel to the store wall = 250 feet
Length perpendicular to the store wall = 125 feet
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Sydney i cutting the crut from the edge of her andwich. The dimenion, in centimeter, of the andwich i hown. A rectangle labeled andwich. The right ide i labeled 2 x quared 9. The bottom ide i labeled 2 x quared 8. Which expreion repreent the total perimeter of her andwich, and if x=1. 2, what i the approximate length of the crut?
Repone
4x217; 21. 8 centimeter
4 x quared plu 17 ; 21 point 8 centimeter
8x234; 43. 6 centimeter
8 x quared plu 34 ; 43 point 6 centimeter
8x234; 45. 52 centimeter
8 x quared plu 34 ; 45 point 5 2 centimeter
4x217; 22. 76 centimeter
The total perimeter will be 4x^+17 and length be 22.76 cm
As per the data given in the questions,
We have, the shape of the sandwich be rectangular.
We know that, perimeter of the rectangle can be determined by using formula: 2(l+b),
where, l = length of the rectangle
and, b = breadth of the rectangle
The expression for the perimeter of the sandwich would be:
2 (2x^2 + 9) + 2 (2x^2 + 8)
= 4x^2 + 26
Now for finding the length of the crust,
we will put the value of x=1.2,
So, the value of the approximate length of the crust would be:
=4x^2 + 26
= 4 * 1.2^2 + 26
= 22.76 centimetres.
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There are 32 Year 11 pupils in a rugby club, out of a total of 85 pupils.
Write this proportion as a percentage.
Give your answer correct to 1 decimal place when appropriate. 26% of an amount.
Answer:
32/85=26/100
Step-by-step explanation:
find a parametrization of the tangent line to ()=(ln()) −10 10 at the point =1.
The tangent line to the curve y = ln(x) - 10 at the point (1, -9) is parametrized by x = t and y = t - 10
To find the tangent line to the curve y = ln(x) - 10 at the point (1, -9), we need to find a parametrization of the line. We can do this by finding the slope of the tangent line and the point at which the tangent line intersects the y-axis.
First, we find the slope of the tangent line by taking the derivative of the function y = ln(x) - 10 at x = 1:
dy/dx = d/dx ln(x) = 1/x
So, the slope of the tangent line at (1, -9) is m = 1/1 = 1.
Next, we find the y-intercept of the tangent line. This can be found by using the point-slope form of a line:
y - y1 = m(x - x1)
Substituting in the values for m, x1, and y1, we get:
y - (-9) = 1(x - 1)
Simplifying, we find:
y + 9 = x - 1
y = x - 10
So, the y-intercept of the tangent line is -10.
Putting everything together, we find that the parametrization of the tangent line to the curve y = ln(x) - 10 at the point (1, -9) is given by:
x = t
y = x - 10 = t - 10
So, the tangent line to the curve y = ln(x) - 10 at the point (1, -9) is parametrized by x = t and y = t - 10.
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A certain type of coffee brand costs $5.99 for 12.4 ounces. What is the unit rate?
The unit rate of the coffee is found as $0.483.
Define the term unit rate?A proportion between two amounts, one of which has a score of 1. A rate and even a unit rate are two different ways to compare two separate units of measurement, whereas a unit rate is the comparison of two independent units of measurement for a single thing.For the given question:
cost of 12.4 ounce of coffee = $5.99.
For the unit rate, divide both sides by 12.4.
cost of 1 ounce of coffee = $5.99/12.4
cost of 1 ounce of coffee = $0.483
Thus, the unit rate of the coffee is found as $0.483.
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By the congruent complements theorem, which angle is congruent to angle4? angle1 angle2 angle3 angle5
From the figure , and by using congruent complements theorem, the angle that is congruent to angle4 is (a) angle1 .
The "Congruent Complements Theorem" states that if two angles are complementary to same angle, then they are congruent. In other words, if two angles add up to 90 degrees, and they both complement the same third angle, then they are equal in measure.
The ∠4 and ∠5 are the complements and ∠1 and ∠5 are complements.
Which proves that : ∠1 and ∠4 are complimentary to the same angle that is ∠5.
Therefore, the ∠ 1 is congruent to angle 4 .
The given question is incomplete , the complete question is
From the figure below , the angle 4 and angle 5 are complements and angle 1 and angle 5 are complements , By using the congruent complements theorem, which angle is congruent to angle4 ?
(a) angle1
(b) angle2
(c) angle3
(d) angle5
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In a circle with radius 4, an angle intercepts an arc of length 8\pi8π. Find the angle in radians in simplest form.
The required Angle in radian in simplest form is 2π.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
Explain angle in radian with arcs of circle.The centre angle of one radian (s = r) subtends an arc length of one radius. One radian has the same value for all circles because they are all alike. The central angle of a circle is measured by its arc, which is 360 degrees, and its radian measure, which is 2 radians.
According to question:Radius = 4 unit, arc = 8π
We know that
angle = arc/radius
angle = 8π/4
angle = 2π radian.
Thus, required angle in radian is 2π.
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solution a is prepared using a stock solution with a concentration of 0.300 m by a dilution factor of 10. what is the concentration of solution a?
The concentration of solution A after dilution by a factor of 10 would be 0.0300 M.
The dilution factor is defined as the ratio of the final volume to the initial volume of the solution.
If a solution is diluted by a factor of 10, it means that the final volume of the solution is ten times greater than the initial volume. As a result, the concentration of the solute in the final solution will decrease by a factor of 10.
Therefore, if the initial concentration of the stock solution is 0.300 M, then the concentration after dilution by a factor of 10 of solution A would be
= 0.300 M / 10
= 0.0300 M
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How does tetrahedron WXYZ looks like?
The four-sided geometric object known as a tetrahedron (WXYZ) has four triangle faces that are joined to one another at their edges. Its vertices are all linked, and its faces are all equilateral triangles.
The three-dimensional geometric structure known as a tetrahedron (WXYZ) has four triangle-shaped faces. The edges of each of the tetrahedron's faces are joined to one another. All of the faces are triangular shapes with equal sides, or equilateral triangles. The tetrahedron is a solid shape because all of its vertices are joined together. The tetrahedron's four vertices are joined to one another, forming a pyramid-like shape. The tetrahedron's four vertices are the only points that do not form the triangle faces. The tetrahedron's four faces come together to produce a point in the middle of the shape. The apex of the tetrahedron is where this point is located. The faces of the tetrahedron are all congruent, or identical, as they are a regular polyhedron.
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given the quadratic function y=x^2+ax+b, the minimum value is -3, and the graph passes through point (1,1). find the values of the consists a and b.
suppose two researchers want to estimate the proportion of american college students who favor abolishing the penny. they both want to have about the same margin of error to estimate this proportion. however, researcher 1 wants to estimate with 95% confidence and researcher 2 wants to estimate with 99% confidence. which researcher would need fewer students for her study in order to obtain the desired margin of error?
A.Researcher 1: Since increases for a higher level of confidence, the researcher 1 would need larger sample size.
About probabilityThe benefits of studying probability are very useful for making the right decisions, because there is no certainty in life in the world, so it is necessary to know what is the probability that an event will occur. Probability is expressed as a fractional number between 0 and 1 or as a percentage. Some important terms in probability are (a) trial, (b) outcome, and (c) event.
There are three approaches in determining probability namely (a) the classical approach which gives the same probability, (b) a relative approach that pays attention to events that have occurred and (c) a subjective approach based on individual judgment.
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