To find the volume of the solid generated by revolving about the y-axis the region under the curve y = 5e^-2x in the first quadrant, we can use the method of cylindrical shells.
The formula for the volume generated by a cylindrical shell is V = 2πrh Δx, where r is the radius of the shell, h is the height of the shell, and Δx is the thickness of the shell.
In this case, we are rotating about the y-axis, so our cylindrical shells will have a height of y and a thickness of Δy. The radius of each shell will be the distance from the y-axis to the curve, which is x.
We can solve for x in terms of y by rearranging the equation y = 5e^-2x:
y/5 = e^-2x
ln(y/5) = -2x
x = -ln(y/5)/2
So the volume of each cylindrical shell is:
V = 2πx * y * Δy
Substituting for x:
V = 2π(-ln(y/5)/2) * y * Δy
V = -πln(y/5) * y * Δy
To find the total volume, we need to integrate this expression from y = 0 to y = infinity:
V = ∫[0,∞] -πln(y/5) * y dy
Using integration by parts:
u = ln(y/5), dv = y dy
du = 1/y dy, v = 1/2 y^2
∫[0,∞] -πln(y/5) * y dy = [-π(1/2y^2 ln(y/5) - 1/4y^2)] [0,∞]
= [π/4]
Therefore, the volume of the solid generated by revolving about the y-axis in the region under the curve y = 5e^-2x in the first quadrant is π/4, which is a finite value.
Hence, the answer is 0.7854 (rounded to four decimal places).
Instead of throwing next snowball, Max decides to kick it off the ground He can kick it at a speed of 24 feet per second.
How long will it take for
Max's kicked snowball to
hit the ground, and what
is its maximum height.
Answer:
To solve this problem, we can use the equations of motion for a vertically launched object. First, we need to find the initial velocity of the snowball when it is kicked off the ground. We know that its speed is 24 feet per second, but we also need to take into account the angle at which it is kicked. Let's assume that Max kicks the snowball at a 45-degree angle. Using trigonometry, we can find that the horizontal velocity of the snowball is also 24 feet per second, and the vertical velocity is 24 feet per second times the sine of 45 degrees, which is approximately 16.97 feet per second. Now we can use the following equation to find the time it takes for the snowball to hit the ground: h = vi*t + 0.5*a*t^2 where h is the maximum height, vi
How would the shape of the distribution change if the salesman decides to also deal in cars priced under $5,000 and in cars priced from $45,000 to $50,000 and projects sales of 200 cars in each category?
The distribution will exhibit symmetry. The solution has been obtained by using the histogram.
What is a histogram?
A graph known as a histogram uses rectangles to show the frequency of numerical values. The vertical axis of a rectangle's height (which represents the distribution frequency of a variable) (the amount, or how often that variable appears).
The given histogram's form demonstrates that the distribution's shape exhibits symmetry (i.e. the shorter bars are to the left and to the right while the longer bars are in the middle).
Sales of vehicles under $5,000 and those between $45,000 and $50,000, with expected sales of 200 vehicles each, will be added, resulting in bars at both ends of the histogram that are the same size as the shortest bar.
Due to the distribution's continued symmetry, this won't change the histogram's initial shape of the distribution.
Hence, the first option is the correct answer.
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The complete question and the figure is attached below.
Question: A salesman sells cars with prices ranging from $5,000 to $45,000. the histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.
How would the shape of the distribution change if the salesman decides to also deal in cars priced under $5,000 and in cars priced from $45,000 to $50,000 and projects sales of 200 cars in each category?
a. the distribution will exhibit symmetry.
b. the distribution will exhibit a positive skew.
c. the distribution will exhibit a negative skew.
d. the distribution will uniform throughout.
how do you think the use of quantitative methods relates to these advantages and disadvantages? new york times
Using quantitative techniques in the context of The New York Times has both advantages and disadvantages.
The advantages are:
accuracy:
Quantitative techniques can provide more precise and accurate data, which can lead to more accurate reporting and analysis of news articles.
Data-Driven Insights:
Quantitative techniques help identify trends and patterns in data and help journalists make informed decisions about what to report on.
Objectivity:
Quantitative techniques help reduce bias and subjectivity in reporting by relying on data rather than personal opinions or interpretations.
The disadvantages include:
Lack of context:
Quantitative methods can oversimplify complex issues, resulting in misleading or inaccurate reporting.
Data limit:
Quantitative methods are data-dependent and results may not be reliable if data are incomplete or inaccurate.
Overall, it is very useful for the journalists in the New York Times to use quantitative techniques
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what is (x - 8) (x - 3) (x + 9)?
A.x^2-2x-59
B.x^2-2x-59
C.2x^2-2x-59
D.2x^2+2x-59
Answer:
We can use the distributive property of multiplication to expand the given expression as follows:
(x - 8) (x - 3) (x + 9) = (x - 8) (x^2 + 6x - 27) [Using (a - b)(a + b) = a^2 - b^2]
= x(x^2 + 6x - 27) - 8(x^2 + 6x - 27) [Using distributive property]
= x^3 + 6x^2 - 27x - 8x^2 - 48x + 216 [Using distributive property]
= x^3 - 2x^2 - 75x + 216
Therefore, the answer is (B) x^2-2x-59
Hope This Helps!
On the graph of a quadratic function, the x-intercepts are (4, 0) and (8, 0), and the vertex is (6, −4). Which equation represents the function?
Answer:
A
Step-by-step explanation:
given the x- intercepts x = a and x = b then the corresponding factors are
(x - a) and (x - b)
the equation of the quadratic is then the product of the factors , that is
y = a(x - a)(x - b) ← a is a multiplier
here the x- intercepts are x = 4 and x = 8 , then factors are
(x - 4) and (x - 8 ) , so
y = a(x - 4)(x - 8)
to find a substitute any other point on the graph into the equation
given vertex = (6, - 4 ) , then
- 4 = a(6 - 4)(6 - 8)
- 4 = a(2)(- 2) = - 4a ( divide both sides by - 4 )
1 = a , then
y = (x - 4)(x - 8) ← expand using FOIL
y = x² - 12x + 32
how did copper transment the currents
When a voltage is applied across a copper wire or conductor, the electric field generated by the voltage pushes the free electrons in the copper atoms, causing them to move in the direction of the electric field.
This creates an electric current that flows through the wire or conductor.
Copper is a popular material used for transmitting electrical currents because of its excellent properties.
How copper transmits electrical currents:
Conductivity:
Copper has high electrical conductivity, which means it allows the flow of electrons with minimal resistance.
This property enables it to transmit electrical currents efficiently.
Ductility:
Copper is a ductile material, making it easy to form into thin wires without breaking.
This property allows for the creation of long and flexible copper cables that can be installed in various environments for transmitting electrical currents.
Low electrical resistance:
The low resistance of copper minimizes energy loss in the form of heat when transmitting electrical currents.
This helps to maintain the efficiency and performance of electrical systems.
Availability:
Copper is a relatively abundant material, making it an accessible and cost-effective choice for transmitting electrical currents in various applications.
Durability:
Copper is resistant to corrosion and wear, which means it can maintain its performance over time.
This makes it a reliable material for transmitting electrical currents in both short-term and long-term installations.
In summary, copper transmits electrical currents effectively due to its high conductivity, ductility, low electrical resistance, availability, and durability.
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as the degrees of freedom increase, what distribution does the student's t distribution become more like? uniform chi-square standard normal (z) binomial
As the degrees of freedom increase, the Student's t distribution becomes more like the standard normal (z) distribution. Correct option is C.
The Student's t distribution is a probability distribution that is used to estimate the mean of a population when the sample size is small or when the population standard deviation is unknown. It is similar to the standard normal distribution, but it has heavier tails and more spread out.
As the degrees of freedom increase, the t-distribution approaches the normal distribution because the shape of the t-distribution becomes more and more similar to the normal distribution.
This is due to the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches the normal distribution.
When the degrees of freedom is large, the t-distribution becomes less variable, and the tails become less heavy, approaching the normal distribution. Therefore, the standard normal (z) distribution is the limiting distribution of the Student's t distribution as the degrees of freedom increase.
Therefore, Correct option is C.
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complete question is:
As the degrees of freedom increase, what distribution does the student's t distribution become more like?
a) uniform
b) chi-square
c) standard normal (z)
d) binomial
what is the equation of a rational function that has a y-intercept at (0,-4), vertical asymptote at x=-2, and horizontal asymptote at y=3?
Step-by-step explanation:
let's see.
first, let's deal with the asymptotes.
the vertical asymptote at x = -2.
it means that for x getting close to that value y is getting enormously larger and larger, so that for x = -2 we would get what we call y = infinity. we could even accept +infinity or -infinity. in both cases we get the same asymptote
I personally think using both +infinity and -infinity is easier to define. because coming from the left (negative direction) and from the right (positive direction) we can use the same expression and don't need to worry about the sign.
so, I go for something like
y = 1/(x + 2)
or even better considering we need a horizontal asymptote too :
y = x/(x + 2)
this will divide by 0 for x = -2 creating the asymptote.
now for the horizontal asymptote of y = 3.
it means that for x getting close to infinity (+infinity and/or -infinity) y has to get closer and closer to this finite value (3).
we achieve this by dividing a dimension of x by the same dimension of x.
so, for large values of x any additive parts of the terms become irrelevant for the limit.
as we had above
y = x/(x + 2)
the limit for x going to +infinity AND to -infinity would be
x/x = 1.
but we need the limit of 3.
so, all we need to do is to multiply the expression by 3 :
y = 3x/(x + 2)
now the limit for x going to +/- infinity is
3x/x = 3
and now for the y-intersect at (0, -4) :
we need to do something, so that y = -4 for x = 0.
let's look at what we have so far :
y = 3x/(x + 2)
-4 = 3×0/(0 + 2) = 0/2 = 0
clearly, that is wrong and therefore still not covered.
imagine, we keep the denominator of the fraction unchanged.
what do we need to do on the numerator side to create -4 as result ?
in other words, we need to find an n so that
-4 = (3x + n)/(x + 2)
for x = 0
-4 = n/2
n = -8
and we get as final result
y = (3x - 8)/(x + 2)
that includes the point (0, -4), and has the asymptotes at x = -2 and y = 3.
can i get some help please
Answer:
144 sq. units
Step-by-step explanation:
Area of Square =[tex][side] ^{2}[/tex]
f(x)= a (x - h)² + k
vertex axis of symmetry
h(x) = (x + 2)²
g(x) = (x-3)²
j(x)=(x-3)² + 2
y-intercept
Vertex of h(x) is (-2, 0), and the axis of symmetry is the line x = -2, vertex of g(x) is (3, 0), and the axis of symmetry is the line x = 3, vertex of j(x) is (3, 2), and the axis of symmetry is the line x = 3.
What is axis of symmetry?
In mathematics, the axis of symmetry is a line that divides a given shape into two symmetrical parts, such that each part is a mirror image of the other.
We can use the standard form of a quadratic function, which is given by:
[tex]F(x) = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola and the axis of symmetry is the line x = h.
For [tex]h(x) = (x + 2)^2[/tex], we have:
h = -2 (since x + 2 = 0 when x = -2)
k = 0 (since the square of any real number is non-negative)
Therefore, the vertex of h(x) is (-2, 0), and the axis of symmetry is the line x = -2.
For [tex]g(x) = (x - 3)^2[/tex], we have:
h = 3
k = 0
Therefore, the vertex of g(x) is (3, 0), and the axis of symmetry is the line x = 3.
For [tex]j(x) = (x - 3)^2 + 2[/tex], we have:
h = 3
k = 2
Therefore, the vertex of j(x) is (3, 2), and the axis of symmetry is the line x = 3.
To find the y-intercept of each function, we can simply plug in x = 0:
For h(x):
[tex]h(0) = (0 + 2)^2 = 4[/tex]
Therefore, the y-intercept of h(x) is 4.
For g(x):
[tex]g(0) = (0 - 3)^2 = 9[/tex]
Therefore, the y-intercept of g(x) is 9.
For j(x):
[tex]j(0) = (0 - 3)^2 + 2 = 11[/tex]
Therefore, the y-intercept of j(x) is 11.
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simplify:
(-212)+384-(-137)
Answer:
309
Step-by-step explanation:
Turn - and - into +:
-212 + 384 + 137
Then add:
172 + 137
= 309
4. the center of the confidence interval is determined by the and the width of the confidence interval is determined by the . a. margin of error; sample statistic b. population parameter; margin of error c. sample statistic; population parameter d. population parameter; sample statistic e. sample statistic; margin of error
(a) margin of error; sample statistic.
How to find confidence interval?The center of the confidence interval is determined by the sample statistic, and the width of the confidence interval is determined by the margin of error.
Therefore, the correct option is (a) margin of error; sample statistic.
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cory ships two paperback books. one weighs 3/8 pound and the other weighs 3/4 pound. which weight is greater than 1/2 pound?
The book that weighs 3/4 pounds is greater than 1/2 pounds.
To compare the weights of the two books with 1/2 pound, we need to convert 1/2 pound into a fraction with a common denominator as the given weights. The common denominator of 8 and 4 is 8. So, we can convert 1/2 pound to 4/8 pound.
Now we can compare the weights of the two books with 4/8 pounds. The weight of the first book is 3/8 pounds, which is less than 4/8 pounds. The weight of the second book is 3/4 pounds, which is greater than 4/8 pounds.
Therefore, the book that weighs 3/4 pounds is greater than 1/2 pound.
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How many hours does each person in our class do homework each night? Statistical or Non Statistical
Answer:
Non-statistical I think
Step-by-step explanation:
Write in standard notation 6.15x10^2
Please help me find X and Y.
2x - 4y = 36
4x + 3y = -5
A: (-7, 4)
B: (7, -4)
C: (-4, 7)
D: (4, -7)
Answer: B: (7, -4)
Step-by-step explanation:
To solve for x and y, we can use either substitution or elimination method. Here, we'll use the elimination method to solve for x and y:
2x - 4y = 36 (Equation 1)
4x + 3y = -5 (Equation 2)
To eliminate y, we can multiply Equation 1 by 3 and Equation 2 by 2, and then add the two resulting equations:
6(2x - 4y) = 6(36) (Multiplying Equation 1 by 3)
2(4x + 3y) = 2(-5) (Multiplying Equation 2 by 2)
Simplifying, we get:
12x - 24y = 216
8x + 6y = -10
Adding the two equations, we get:
20x = 206
Dividing both sides by 20, we get:
x = 10.3
Now, substituting x = 10.3 into Equation 1 or Equation 2, we can solve for y. Let's use Equation 1:
2x - 4y = 36
2(10.3) - 4y = 36
20.6 - 4y = 36
-4y = 15.4
y = -3.85
Therefore, the solution to the system of equations is (x,y) = (10.3,-3.85).
Rounded to the nearest integer, the solution is approximately (x,y) = (10,-4).
So, the answer is option B: (7, -4).
Answer:
D. (4, 7)
Step-by-step explanation:
2x - 4y = 36
4x + 3y = -5
2(4) - 4(-7) = 36
4(4) + 3(-7) = -5
A rectangular container 6.5 ft long, 3.2 ft wide, and 2 ft high is filled with sand to a depth of 1.3 ft. How much sand is in the container?
I'll give thanks or mark as brainliest if you can figure out how much more sand the container can hold
There are 26.24 cubic feet of sand in the rectangular container based on volume.
We must determine the volume of sand in the rectangular container in order to determine how much is there.
Let's start by determining the container's volume:
Container volume equals length, width, and height
Container volume: 6.5 feet by 3.2 feet by two feet
Container volume is 41.6 cubic feet.
The amount of sand in the container's volume must then be determined. We can determine the volume of sand by using the following formula because it fills the container to a depth of 1.3 feet:
Sand volume is determined by its length, width, and depth.
Sand volume = 6.5 feet by 3.2 feet by 1.3 feet
Sand volume = 26.24 cubic feet
As a result, the container contains 26.24 cubic feet of sand.
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In this lesson, you learned how a compass and straightedge are used to create constructions related to circles. In this assignment, you will use those tools to complete those constructions on your own.
As you complete the assignment, keep this question in mind:
How do you perform constructions related to circles?
Directions
Complete each of the following constructions, reading the directions carefully as you go. Be sure to show all work and insert an image of each construction. If you are unable to take and insert screenshots of the constructions, print this activity sheet and create them by hand using a compass and straightedge.
Your teacher will give you further directions about how to submit your work. You may be asked to upload the document, e-mail it to your teacher, or print it and hand in a hard copy.
Now, let’s get started!
Step 1: Construct a circle through three points not on a line.
a) Construct a circle through three points not on a line using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a circle through three points not on a line by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
Step 2: Construct regular polygons inscribed in a circle.
a) Construct an equilateral triangle inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct an equilateral triangle inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
b) Construct a regular hexagon inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a regular hexagon inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
c) Construct a square inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a square inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
Step 3: Construct tangent lines to a circle.
a) Construct a tangent to a circle through a point on the circle using the construction tool. Insert a screenshot of the construction here. Alternatively, a tangent to a circle through a point on the circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
b) Construct a tangent to a circle through a point outside the circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a tangent to a circle through a point outside the circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
Use circumcenter to draw a circle through three non-collinear points.
a) Draw diameter, construct equilateral triangle with one vertex at center and other two on circle.
b) Draw diameter, construct regular hexagon with one vertex at center and other vertices on circle.
What is diameter?Step 1: To construct a circle through three points not on a line, we can use the circumcenter of a triangle. We first construct the perpendicular bisectors of any two sides of the triangle. The point where these two lines intersect is the circumcenter of the triangle. We can then draw a circle with this point as the center, which passes through all three vertices of the triangle.
Step 2:
a) To construct an equilateral triangle inscribed in a circle, we can draw a diameter of the circle and then construct an equilateral triangle with one of the endpoints at the center of the circle and the other two endpoints on the circle itself.
b) To construct a regular hexagon inscribed in a circle, we can draw a diameter of the circle and then construct a regular hexagon with one of the vertices at the center of the circle and the other vertices on the circle itself.
c) To construct a square inscribed in a circle, we can draw a diameter of the circle and then construct a square with one of the vertices at the center of the circle and the other vertices on the circle itself.
Step 3:
a) To construct a tangent to a circle through a point on the circle, we can draw a radius of the circle to the point of tangency, and then construct the perpendicular bisector of this radius. The line where the perpendicular bisector intersects the circle is the tangent line.
b) To construct a tangent to a circle through a point outside the circle, we can draw a line from the point to the center of the circle, and then construct the perpendicular to this line at the point of tangency. The line where the perpendicular intersects the circle is the tangent line.
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fossils found in deeper layers of sediment are
Answer:
older than those found in shallower layers of sediment. This is because sedimentary rock layers form over time, with the oldest layers at the bottom and the newest layers at the top. As sedimentary rocks form, they often trap the remains of plants and animals, which then become fossils. The deeper layers have been buried for a longer period of time, so they contain older fossils. This principle is known as the law of superposition and is an important tool for dating fossils and determining the relative ages of different rock layers.
Solve the system of equations
Answer:
(-1, 2)
Step-by-step explanation:
1.) The way to use elimination is to add or subtract both of the equations together to eliminate a variable. If we add the two equations together, the -6x and 6x cancel out. Since we added the equations together, -12y and 10y would add up to -2y, and -18 and 14 would add up to -4
2.) Now, we have the equation -2y = -4. By dividing by -2 on both sides, we get y=2.
3.) Next, we need to substitute y back in to get the x value. If you use the first equation, we get -6x - 12 * 2 = -18.
4.) By simplifying, you get that -6x - 24 = -18. If you add 24 on both sides, you get -6x = 6, and by dividing by -6 on both sides, you get x = -1.
5.) Finally, you have to put the answer in form of a point. -1 would be the x-coordinate and 2 would be the y-coordinate. Therefore, the point is (-1, 2)
Marci performed a division.
175
was the dividend,
5
was the divisor, and
35
was the quotient. Which is a correct representation of this problem?
Answer:
35
Step-by-step explanation:
A line has endpoints (4.25, 6.25) and (22, 6.25). What is the length of the line segment.
Answer:
[tex] \sqrt{(22 - 4.25)^{2} +(6.25 - 6.25) ^{2} } \\ [/tex]
[tex] \sqrt{(15.75)^{2} } [/tex]
=15.75 units
Please help with this question
An estimate for the mean daily energy output is 5 kw/h.
What is the mean?The mean is the average value of a data set.
The mean is computed as the quotient of the total value divided by the number of data items.
Energy Output Frequency Cumulative Cumulative
(kw/h) Frequency Energy Output
1 1 1 1
2 1 2 3
3 1 3 6
4 4 7 22
5 4 11 42
6 3 14 60
7 2 16 74
8 2 18 90
Mean Daily Energy Output = 5 (90 ÷ 18)
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Suppose you send about 8 text messages a day, and your older sister sends more text messages than you do. Together, you send a total of about 21 messages per day. About how many text messages does she send a day? Write an equation that contains the unknown value, x, and solve for the unknown value.
PLS HURRY THIS IS A PROJECT
Answer:
21 - 8 = x
21 - 8 = 13
Step-by-step explanation:
because you send a total of 21, and you send 8, just do 21 - 8 and thats how many text messages she sends
What is the measure of ∠EKY in this figure?
A. 104º
B. 1115º
C. 129º
D.I don't know.
Answer:
104
Step-by-step explanation:
You add 65+ 39 and that gives you 104
what is the y intercept of (-6, -5), (-4, -2), (-2, 1)
A garbage can has two sections of the same size, They are both in the shape of rectangular prisms. the total volume of the two sections combined is 2,640 cubic inches. What is the length, in inches, of each section?
From given volume, length of each section is 18 inches.
What is volumes?In mathematics, ‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Let's call the length, width, and height of each section l, w, and h, respectively.
Since both sections are the same size, we can set up the following equation for their combined volume:
2(lwh) = 2640
Simplifying this equation, we get:
lwh = 1320
Now we need to find the length of each section, which is represented by the variable l. We can solve for l by dividing both sides of the equation by wh:
l = 1320/wh
We don't have enough information to determine w and h individually, but we do know that the two sections are identical, which means they have the same proportions. This means that w and h must be equal.
Let's call this common value x. Then we can rewrite the equation for l as:
[tex]l = 1320/x^2[/tex]
We can simplify this equation by multiplying both sides by [tex]x^2[/tex]:
[tex]lx^2 = 1320[/tex]
Now we can solve for x:
[tex]x^2 = 1320/l\\\\x = \sqrt{(1320/l)}[/tex]
Since w = h = x, the length of each section is:
[tex]l = 2x = 2 \sqrt{(1320/l)}[/tex]
We can simplify this expression by multiplying both sides by l:
[tex]l^2 = 4*1320/l \\l^3 = 5280\\l = 18[/tex]
Therefore, the length of each section is 18 inches.
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if tan theta equals 21/20 then find : sec theta
The value of secant theta is 29/20
How to determine the valueFirst, it is important to note the different trigonometric identities and their ratios, we have;
sin θ= opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
sec θ = hypotenuse/adjacent
From the information given, we have that;
tan θ = 21/20
Adjacent = 20
Opposite = 21
Using the Pythagorean theorem, we have;
x² = 21² + 20²
find the squares
x² = 441 + 400
add the values
x² = 841
Find the square root
x = 29
Then, sec θ = 29/20
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What are the dimensions of a square that encloses the same area as a rectangle that is 2 miles long and 1 mile wide? Answer to the nearest inch, please. 
Answer:
7467 ft 1 in = 89605 inches on a side
Step-by-step explanation:
You want the dimensions of a square with an area of 2 square miles, to the nearest inch.
Side lengthThe area of a square is given by ...
A = s² . . . . . . where s is the side length
For an area of 2 mi², the side length is ...
2 mi² = s²
√(2 mi²) = s = √2 mi
Unit conversionYou want the distance to the nearest inch, so we need to convert this to inches.
√2 mi = (√2 mi) × (5280 ft/mi) × (12 in/ft) ≈ 89604.57 in
Rounded to the nearest inch, this is
89605 inches
In feet and inches, this is
89605/12 ft = 7467 1/12 ft = 7467 ft 1 in.
Remember that arc DAB will be twice as large as m∠C. If m∠A = 105°, then what is the degree measure of arc DAB?
150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.
how can we describe an angle?The apex of the angle is the intersection of two rays that together form the geometric shape known as an angle. The component rays that make up the angle are known as the sides or arms of something like the angle.
Angles are expressed as degrees in radians, with 360 degrees or 2 radians equaling a full revolution around a point. The rotational difference between two angles' two sides determines the angle's size. Depending on their measure, angles can be categorised into various categories, including: An acute angle is one that is smaller than 90 degrees. A right angle is one that is precisely 90 degrees. The angles of a right triangle are parallel to one another.
given
We must first determine the measure of angle C because arc DAB is twice as large as angle C.
As inscribed angles of the circle, angles B and C have measurements that are equal to half those of their intercepted arcs.
m(arc BC) equals 2mB
m(arc AD) equals 2mC
Finding m(arc DAB), the product of arcs AD and AB, is what we're after.
m(arc DAB) equals m(arc AD) plus m. (arc AB)
We obtain the following by substituting the equations for the arc measures in terms of angles:
m(arc DAB)=2mC+2mB
We can use the formula we discovered for mB + mC, which equals 75 degrees, instead.
150° is equal to m(arc DAB) = 2mC + 2mB = 2(75°). As a result, the arc DAB's degree measure is 150 degrees.
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