a visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an island. the island is 7 miles due south of the shoreline. the visitor plans to travel from the cottage to the island by running and swimming. if the visitor runs at a rate of 5 mph and swims at a rate of 3 mph, how far should the visitor run to minimize the time it takes to reach the island?
Answers
The visitor should run 1.2 miles to minimize the time it takes to reach the island.
Consider the following figure.
Let us assume that x (CD) represents the distance covered when visitor runs at a rate of 5 mph
So, the time taken by visitor would be:
t₁ = x/5
Let the distance covered 10 - x when visitor swims at a rate of 3 mph
From figure consider right triangle ABC.
Using Pythagoras theorem,
BC² = 7² + (10 - x)²
BC = [tex]\sqrt{49 + (10-x)^2}[/tex]
Now the times taken by visitor when he swims at a rate of 3 mph,
t₂ = [tex]\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]
so, the total time would be:
t = t₁ + t₂
[tex]t=\frac{x}{6}+\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]
Differentiating with respect to x we get,
[tex]\frac{dt}{dx}=\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}[/tex]
consider dt/dx = 0
[tex]\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}=0[/tex]
If we solve above equation for x we get, x = 11.2 and x = 8.8
The distance the visitor should run to minimize the time would be:
10 - 8.8 = 1.2 miles
Therefore, the required distance is 1.2 miles
Learn more about the Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ4
Related Questions
Area = ______ in^2
Help please!
Answers
Answer:
Area = 50 in^2
Step-by-step explanation:
Area = B x H
The dotted line is saying that the left and right sides of the triangle are 5 inches
So just multiply 10 x 5 and get 50in^2
Juan Carlos claims that he cannot graph a point at (- 3.25, 6.5) because his coordinate plane only has whole numbers on the axis.
Answers
The intersection of two numerical axes creates a two-dimensional plane known as a coordinate plane. The x-axis, which is a horizontal number axis, and the y-axis, which is a vertical number axis, are two different types of number axes.
The French mathematician René Descartes enhanced the coordinate plane that had been created centuries earlier. The system is occasionally referred to as the Cartesian coordinate system in his honor. You can doodle points and lines on coordinate planes. With the aid of this method, we may generate and communicate algebraic concepts as well as visually express algebraic relations.
The coordinate plane has a horizontal axis, a vertical axis, and a right angle where numerous straight lines intersect. In a coordinate plane, the horizontal axis is represented by the x axis. The vertical axis is referred to as the y-axis. The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0.
As ordered pairs, positions on the coordinate plane are described.
By connecting the position of the point along the x-axis (the first value in the ordered pair) and the y-axis (the second value in the ordered pair), an ordered pair reveals the location of the point.
The first value in an ordered pair, like (x, y), is referred to as the x coordinate, and the second value is referred to as the y coordinate. The x coordinates are presented before the y coordinates; take note of this. The ordered pair of the origin is represented as (0, 0), since it has an ordinate and abscissa of 0.
Learn more about Coordinate Plane:
brainly.com/question/13611766
#SPJ4
Complete Question:
Juan Carlos asserts that he is unable to graph a point at coordinates (-3.25,6.5) because his coordinate plane's axis only contains whole numbers. Correcting Juan Carlos's reasoning and elaborating on how to graph this point will help. Juan Carlos claims that he cannot graph a point at (-3.25,6.5) because his coordinate plane only has whole numbers on the axis. Help Juan Carlos by correcting his thinking and explaining how to graph this point.
If RT is greater than BA, which correctly compares
angles C and S?
O mzC=mZS
O mzC
O m2C> mZS
O mzC ≥ m/s
Answers
As angle Z is bigger than angle Y and angle C must be greater than angle S, we also cannot say that mzC >mZS. The accurate disparity is: mZS >mZC .
how can you describe angle ?An angle is just a geometric shape made up of two rays or splines that meet at a point in the middle known as the vertex. The angle's sides or legs are the rays or dotted lines that make up the angle. T
he standard unit of measurement for angles is the degree, with 360 degrees being one entire circle. Acute angles are those that are less than 90 °, right angles are those that are exactly 90 degrees, obtuse angles are those that are higher than 90 degrees but much less than 180 degrees, & straight angles are those that are exactly 180 degrees.
given
The right response is "mZC > mZS".
The right side of the figure is longer than the left side if RT is bigger than BA. Angle X is greater than angle W, and angle Z is greater than angle Y as a result.
Angles C and S will have the same measure if the triangles are identical because they are matching angles (they are in the same place in each triangle). We are unsure, nevertheless, whether the triangles are comparable.
We cannot therefore assert that mzC = mZS.
As angle Z is bigger than angle Y and angle C must be greater than angle S, we also cannot say that mzC >mZS. The accurate disparity is: mZS >mZC .
To know more about angles visit:
brainly.com/question/14569348
#SPJ9
Question 3
Identify the equation of a line that passes through (1, 10) and (-4,-5).
O A)x1= 3(y - 10)
O B) y 1 = 3(x - 10)
OC) y-10=(x - 1)
O D) y 10 = 3(x - 1)
Answers
Answer:
y = 3x - 7
Step-by-step explanation:
We can use the two-point form formula to find the equation of a line that passes through two given points (x1, y1) and (x2, y2):
y - y1 = (y2 - y1) / (x2 - x1) * (x - x1)
where (x1, y1) and (x2, y2) are the two points and (x, y) represents any point on the line.
Using the given points, we have:
x1 = 1, y1 = 10
x2 = -4, y2 = -5
Substituting these values into the formula, we get:
y - 10 = (-5 - 10) / (-4 - 1) * (x - 1)
Simplifying the equation, we have:
y - 10 = 3(x - 1)
Expanding and rearranging, we get:
y = 3x - 7
Therefore, the equation of the line that passes through (1, 10) and (-4, -5) is y = 3x - 7
chatgpt
Which model best represents the relationship between time and volume?
OA linear model would best represent the relationship because scatterplot A is fairly linear.
O An exponential model would best represent the relationship because scatterplot B is fairly linear.
A power model would best represent the relationship because scatterplot C is fairly linear.
A linear model would best represent the relationship because scatterplot C is fairly linear.
Answers
The answer is C: A power model would best represent the relationship because scatterplot C is fairly linear.
What is a power model?In this the rate of change of the dependent variable is proportional to the power of the independent variable. In other words, when the independent variable increases, the dependent variable increases at a rate that is proportional to the power of the independent variable. This type of model is often used to describe phenomena such as population growth, economic growth, and physical processes such as diffusion.
When looking at the graph of scatterplot C, it is clear that the relationship between time and volume follows a power model.
The data points in the graph are fairly linear, meaning that as the log of time increases, the log of volume increases at a rate that is proportional to the power of the log of time.
This indicates that a power model would best represent the relationship between time and volume, making C the correct answer.
For more questions related to log
https://brainly.com/question/30452067
#SPJ1
Answer:
the obvious
Step-by-step explanation:
What is the image of (−12,−12) after a dilation by a scale factor of 1 4 centered at the origin?
Answers
the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin is (-3, -3).
How to find?
To find the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin, we can use the following formula:
(x', y') = (kx, ky)
where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, and k is the scale factor.
In this case, the scale factor is 1/4 and the center of dilation is the origin (0, 0). Therefore, we have:
x' = (1/4) × (-12) = -3
y' = (1/4) × (-12) = -3
So the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin is (-3, -3).
To know more about coordinated related questions, visit:
https://brainly.com/question/29151766
#SPJ1
The diagram shows a solid cuboid with base 10 cm by 6 cm.
The height of the cuboid is x centimetres.
x
10
6
(a) Find an expression, in terms of x, for the total surface area of the cuboid.
(b) The total surface area of the cuboid is 376 cm².
Form an equation in x and solve it to find the height of the cuboid.
Answer (a)
(b)
cm² [1]
cm [2]
Answers
The answers to both the subparts of the given cuboid:
(A) The expression: (SA)=120+32x
(B) The height x=4.875
What is a cuboid?A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces.
Cuboid is short for "like a cube."
A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.
So, we have the values:
x, 10 and 6
Total surface area formula:
(SA)=2lw+2lh+2hw
Now, insert values to form the expression:
(SA)=2lw+2lh+2hw
(SA)=2(10*6)+2(10*x)+2(x*6)
(SA)=120+20x+12x
(A) The expression: (SA)=120+32x
Now, the height would be:
376=120+32x
32x = 376-120
32x=156
x=156/32
(B) x=4.875
Therefore, the answers to both the subparts of the given cuboid:
(A) The expression: (SA)=120+32x
(B) The height x=4.875
Know more about cuboid here:
https://brainly.com/question/26403859
#SPJ1
there are 4 baseball games during the week. the probability of a rainout is 10% for each game. assuming the weather each day is independent, what is the probability for at least one rainout
Answers
The probability that at least one game will be rained out during the week is 0.3439
To calculate the probability of at least one rainout, we need to calculate the probability that all four games will be played and then subtract it from 1.
The probability that a game will not be rained out is 1 - 0.1 = 0.9.
Therefore, the probability that all four games will be played is
= 0.9 x 0.9 x 0.9 x 0.9
Multiply the numbers
= 0.6561
So the probability that at least one game will be rained out is
= 1 - 0.6561
Subtract the numbers
= 0.3439
Learn more about probability here
brainly.com/question/11234923
#SPJ4
Graph the image of T(10, – 2) after a reflection over the x-axis.
Answers
Answer:
To graph the image of T(10, -2) after a reflection over the x-axis, you simply need to flip the point vertically so that it lies on the opposite side of the x-axis.
The x-coordinate of the point will stay the same, and the y-coordinate will change sign.
Starting with the point T(10, -2), reflect it over the x-axis to obtain the image point T'(10, 2), which is 10 units to the right of the y-axis and 2 units above the x-axis.
So the graph of T(10, -2) after a reflection over the x-axis is the point T'(10, 2), as shown in the following diagram:
|
|
|
|
|
------T'(10, 2)
|
|
------x-axis------
|
|
|
|
|
|
|
Note that the x-axis is the line that runs horizontally through the middle of the diagram, while the y-axis is the line that runs vertically through the middle of the diagram. I hope this helps.
During a sale, colour pencils were being sold in packs of 24 each and crayons in
packs of 32 each. If you want full packs of both and the same number of pencils
and crayons, how many of each would you need to buy?
Answers
Answer:
96 ÷ 32 = 3 packs of crayons.
Step-by-step explanation:
given the parent function f(x) equals 2^x which  graph shows FX plus one 
Answers
Step-by-step explanation:
You didn't show us any choices for answers, but this should help you:
The population of a town is decreasing at a rate of 2% per year. In 2000 there were 1100 people. Question 1 Part A Find an exponential decay function to model this situation
Answers
Answer:
bot
Step-by-step explanation:
Ambitious
HELP WILL GIVE BRAINLIEST TO WHOEVER CAN SOLVE ALL OF THEM PLEASE
Answers
The function f(x) = |-x| is an even function, the equation of the parabola that has vertex at (2, 7) and passes through the point (-1, 3) is y = (-4/9)(x - 2)^2 + 7.
What is an odd or even function?An odd function is a function that satisfies the property f(-x) = -f(x) for all values of x in the function's domain. Geometrically, this means that an odd function is symmetric about the origin.
To determine if the function f(x) = |-x| is an odd or even function, we can use the definition of odd and even functions.
First, let's check if f(-x) = f(x) for all values of x in the domain of the function:
f(-x) = |-(-x)| = |x|
f(x) = |-x|
Since |x| is equal to |-x| for all values of x, we have f(-x) = f(x) for all x in the domain. This means that f(x) is an even function.
2. There are different methods to find the equation of a parabola given its vertex and another point on the curve. One possible way is to use the standard form of the equation of a parabola:
y = a(x - h)^2 + k
where (h, k) is the vertex and a is a constant that determines the shape and orientation of the parabola.
To find a, we can use the fact that the point (-1, 3) lies on the parabola:
3 = a(-1 - 2)^2 + 7
3 = 9a + 7
9a = -4
a = -4/9
Substituting this value of a and the vertex (h, k) = (2, 7) into the equation, we get:
y = (-4/9)(x - 2)^2 + 7
Therefore, the equation of the parabola that has its vertex at (2, 7) and passes through the point (-1, 3) is:
y = (-4/9)(x - 2)^2 + 7
3. To determine whether the function f(x) = 25 - x^3 is even, odd, or neither, we need to find f(-x) and -f(x):
f(-x) = 25 - (-x)^3 = 25 + x^3
-f(x) = -(25 - x^3) = -25 + x^3
Now, let's compare f(-x) and -f(x):
f(-x) = 25 + x^3 ≠ f(x) and f(-x) ≠ -f(x)
-f(x) = -25 + x^3 ≠ f(x) and -f(x) ≠ -f(x)
Since neither f(-x) = f(x) nor f(-x) = -f(x) hold for all x in the domain of f, the function f(x) = 25 - x^3 is neither even nor odd.
4. To determine whether the function f(x) = 72 - x^4 is even, odd, or neither, we need to find f(-x) and -f(x):
f(-x) = 72 - (-x)^4 = 72 - x^4
-f(x) = -(72 - x^4) = -72 + x^4
Now, let's compare f(-x) and -f(x):
f(-x) = 72 - x^4 = f(x)
-f(x) = -72 + x^4 ≠ f(x) and -f(x) ≠ -f(x)
Since f(-x) = f(x) for all x in the domain of f, the function f(x) = 72 - x^4 is even. This means that its graph is symmetric with respect to the y-axis.
Learn more on odd or even function here;
https://brainly.com/question/29220653
#SPJ1
Patrick left home at 4:20 p.m. on Sunday. He returned 36.3 hours later. what day and time was it when he got home?
Answers
First, we need to convert 36.3 hours into days and hours. Since there are 24 hours in a day, we can divide 36.3 by 24 to get the number of days, and take the remainder to get the number of hours:
36.3 hours ÷ 24 hours/day = 1 day and 12.3 hours
So, Patrick returned 1 day and 12.3 hours later.
Adding 12.3 hours to the time he left at 4:20 p.m. on Sunday, we get:
4:20 p.m. + 12.3 hours = 4:20 p.m. + 12 hours + 0.3 hours
= 4:20 a.m. on Tuesday
Therefore, Patrick arrived home at 4:20 a.m. on Tuesday.
Answer: 4 o'clock am on Tuesday
Step-by-step explanation: 4pm on Sunday+36 hours which gets you to Monday 4 pm + 12 hours= 4 am on Tuesday.
(I hope this helps
while bowling with freinds, bradly rolls a stirke in 8 out o f10 frames. what is the experimental probabillty that bradly will role a stike in the first frame of the next game?
Answers
The experimental prοbability οf Bradley rοlling a strike in the first frame οf the next game is alsο 0.8 οr 80%.
What is prοbability?The likelihοοd οr chance that an event will οccur is quantified by prοbability. It is a number between 0 and 1, where 0 indicates an imprοbable event and 1 indicates a certain event. A given event's prοbability is determined by dividing the number οf pοssible οutcοmes by the number οf ways the event cοuld οccur.
The experimental prοbability is the ratiο οf the number οf times an event οccurs tο the tοtal number οf trials.
In this case, Bradley rοlls a strike in 8 οut οf 10 frames, sο the experimental prοbability οf him rοlling a strike in a single frame is 8/10 οr 0.8.
Hence, each frame is independent οf the οthers, the experimental prοbability οf Bradley rοlling a strike in the first frame οf the next game is alsο 0.8 οr 80%.
To know more about probability visit :
https://brainly.com/question/13604758
#SPJ9
Peter’s gym membership costs $23 per month. Which table shows the sum of the amounts that Peter will pay for his gym membership over the next 4 months?
Answers
Whats the width of a rectangle if the perimeter is 130 ft and the length is 45 but there's no area
Answers
Answer:
Step-by-step explanation:
I hope this helps
True or false? To begin an indirect proof, you assume the inverse of what you
intend to prove is true.
OA. True
OB. False
PLEASE HELP ASAP
Answers
Answer:
the answer is A. true
Step-by-step explanation:
I had this question before
i’m very confused need help Asap
Answers
The opposite angles formed when two lines intersect are vertically opposite angles.
It should be noted that the value of x based on the information given about the perpendicular lines will be A. 28°.
How to calculate the value of angle xBased on the information given, it should be noted that the total value of the angle on a straight line is 180°.
Therefore, the value of x will be calculated thus:
55 + 2x - 49 + 90 + x = 180
3x + 96 = 180
Collect the like terms
3x = 180 - 96
3x = 84
Divide through by 3
3x / 3 = 84 / 3
x = 28
The value of the angle is 28°.
Learn more about angles on:
brainly.com/question/25716982
#SPJ1
How do you find the surface area for this? Anything helps, thank you!
Answers
Answer:
99
Step-by-step explanation:
Take the whole shape apart, now, multiply every part on it using the formulas for each.
The area of the two triangle parts is 7.5+7.5=15
the side on the left would be found by doing 5*6=30
the middle side would be 6*6=36
and the right side would be 6*3=18
Add it all up to get 15+30+36+18=
15+66+18=
81+18=
99
circular cloud of poison gas from a factory explosion is expanding so that hours after the explosion the radius of the cloud is meters. how fast is the area of the cloud increasing hours after the explosion?
Answers
The rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the square of the radius of the cloud.
Therefore, the rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the radius of the cloud. The rate of expansion can be calculated using the equation . Therefore, the rate at which the area of the cloud is increasing can be calculated as .
The area of a circle is determined by the square of its radius. Thus, when the radius of the cloud is expanding at a rate, the area of the cloud is increasing at a rate that is proportional to the square of its radius.
Therefore, in order to calculate the rate at which the area of the cloud is increasing, we must calculate the rate of expansion of the radius of the cloud and then multiply it by the square of the radius of the cloud. To calculate the rate of expansion of the radius of the cloud, we can use the equation .
After we have calculated the rate of expansion, we can then multiply it by the square of the radius of the cloud to calculate the rate at which the area of the cloud is increasing.
To know more about equation click on below link:
https://brainly.com/question/29657992#
#SPJ11
There are 8 students on the curling team and 11 students on the badminton team. What is the total number of students on the two teams if 4 students are members on both teams
Answers
Well the first 4 you can see there is for the players who are only in curling team, the second 4 is for players on both teams, the 7 is for players in only badminton team
So the answer is 4 + 7 + 7 = 15
Find the value of :
[tex]5 { }^{2} +2 {}^{5} [/tex]
Answers
5^2 = 25
2^5 = 32
So, 5^2 + 2^5 = 25 + 32 = 57.
Therefore, the value of 5^2 + 2^5 is 57.
*square the numbers (multiply them times itself)
25+32
*add
Final Answer: 57
You are solving this system of equations by eliminating y first. Which of the following options below
shows the correctly multiplied pair of equations?
12x + 6y = 10
2x + 3y = 8
a. 12x+6y=10
-12x + (-36y) = -48
b. 12x+6y= 10
-12x + (-18y) = -48
c. 12x+6y= 10
-24x + (-6y) = -16
d. 12x+6y=10
-4x + (-6y) = -16
Answers
The correctly multiplied pair of equations that shows the system of equations by eliminating y first.
d. 12x+6y=10 and -4x + (-6y) = -16.
Explain about the method of elimination?There are either two or three equations with two or three variables when there is a system of linear equations. In this session, we'll be dealing for both x and y while using a two-equation system.
To create an equation in one variable using the elimination approach, you can either add as well as subtract the equations.To eliminate a variable, add the equations when the coefficients about one variable are in opposition, and subtract the equations when the coefficients among one variable are in equality.Given equation are:
12x + 6y = 10 ...eq 1
2x + 3y = 8 ...eq 2
To eliminate the y first, multiply eq 2 by -2.
-2(2x + 3y = 8)
-4x + (-6)y = -16 eq 3
On solving both eq1 and eq 3
8x = -6
x = -3/4
Thus, the correctly multiplied pair of equations that shows the system of equations by eliminating y first.
d. 12x+6y=10 and -4x + (-6y) = -16.
Know more about the method of elimination
https://brainly.com/question/25427192
#SPJ1
Does the table below represent a linear relationship? If so, write an equation for that relationship. If not, explain
TABLE BELOW
Answers
Answer:
Yes
Step-by-step explanation:
Imagine that time is x and distance is y. 0x+11=11 for the first equation.
3x+11=17 for the second. So x is 2, plug it in for the 3rd, then you see that it is linear. The equation is 2x+11=y
Smith's Produce sells packages of pre-cut vegetables. The company has a tolerance level of less than or equal to y grams for a 250-gram package. Which graph could be used to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x?
Answers
The answer of the given question based on the graph could be used to determine the variance levels that would result in a package of vegetables is histogram.
What is Histogram?A histogram is a bar graph-like representation of data that groups data into ranges, called bins, and displays the frequency of data within each bin. In this case, the x-axis of the histogram would represent the weight of the vegetable packages, and the y-axis would represent the frequency of packages that fall within each weight bin.
To determine variance levels that would result in package of vegetables being rejected because of its weight, histogram would need to be constructed based on tolerance level of company. The histogram would show distribution of package weights, and any packages that fall outside of the acceptable weight range would be considered rejected. By analyzing the histogram, the company could determine the variance levels that would result in package rejection and make necessary adjustments to their production process.
A histogram would be the most appropriate graph to use in this situation to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x.
To know more about Frequency visit:
https://brainly.com/question/30053506
#SPJ1
the graph that could be used to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x, is a normal distribution curve with a mean of 250 grams and a standard deviation of y.
What is a graph?
In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).
To determine the graph that could be used to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x, we need to understand the tolerance level of the company.
The company has a tolerance level of less than or equal to y grams for a 250-gram package. This means that any package of vegetables that weighs less than 250-y grams or more than 250+y grams will be rejected.
To graph this, we can plot the weight of the package on the x-axis and the probability of the package being rejected on the y-axis. The graph will have a normal distribution curve with a mean of 250 grams and a standard deviation of y.
Therefore, the graph that could be used to determine the variance levels that would result in a package of vegetables being rejected because of its weight, x, is a normal distribution curve with a mean of 250 grams and a standard deviation of y.
To learn more about graph from the given link:
https://brainly.com/question/17267403
#SPJ1
What is the measure of each exterior angle of a regular decagon
Answers
Answer: Hence, a regular decagon has each exterior angle 36∘ and each interior angle as 144∘.
What is the measure of each interior angle of a regular octagon? 45º 60º 120º 135º
Answers
The measure of each interior angle of a regular octagon is 135°.
An octagon is an eight-sided polygon with eight interior angles, and a regular octagon is an eight-sided polygon with eight interior angles of equal measure (congruent angles) and eight sides of equal length (congruent sides).
An octagon is composed of eight angles that sum to 1080 degrees.
The sum of the interior angles of a polygon with n sides is (n-2)×180°.
To get the interior angle, you must divide the sum of the interior angles by the number of sides.
A regular octagon has eight sides, so to find the measure of each interior angle of a regular octagon, divide the sum of
the interior angles by eight.
Sum of interior angles = (n-2)×180°
= (8-2)×180°
= 6 × 180°
= 1080°
Measure of each interior angle of a regular octagon = 1080°/8= 135°
Therefore, the measure of each interior angle of a regular octagon is 135°.Answer: 135°.
for such more question on regular octagon
https://brainly.com/question/16973814
#SPJ11
Answer: The answer is D 135º
Step-by-step explanation: it is show below
A tabletop in the shape of a trapezoid has an area of 7,722 square centimeters. Its longer base measures 131 centimeters, and the shorter base is 85 centimeters. What is the height?
Answers
By answering the presented question, we may conclude that Therefore, trapezium the height of the trapezoid is 71.5 centimeters.
What is trapezium?A trapezium is a two-dimensional geometric figure with four sides, one pair parallel to the other. It is also called as a trapezium in certain locations. The parallel sides are known as bases, whereas the non-parallel sides are known as legs. The distance between the two bases is the trapezoid's height or altitude. The area of a trapezium is given by A = 0.5 * (b1 + b2) * h, where b1 and b2 are the lengths of the two bases and h is the height.
To find the height of the trapezoid,
Area = (b1 + b2) × h / 2
h = 2 × Area / (b1 + b2)
h = 2 × 7722 / (131 + 85)
h = 2 × 7722 / 216
h = 71.5
Therefore, the height of the trapezoid is 71.5 centimeters.
To know more about trapezium visit:
https://brainly.com/question/8208556
#SPJ1
which number has which number has the lowest value? 1/6 1/3 - 1/9 1/3 - 1/6 1/4 - 1/6the lowest value?
Answers
the fraction with the lowest value is 1/12.
Company revenue quadratic function.
Angel
The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:
r(x) = a(x - h)^2 + k
where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
We can use the given revenue values to set up a system of three equations:
2.7 = a(0 - h)^2 + k
3.4 = a(1 - h)^2 + k
2.7 = a(6 - h)^2 + k
Subtracting the first equation from the second, and the first equation from the third, we get:
0.7 = a(1 - h)^2
0 = a(6 - h)^2
Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:
6 - h = 10
which gives us h = -4.
Substituting h = -4 into the first equation, we get:
2.7 = a(0 - (-4))^2 + k
2.7 = 16a + k
Substituting the revenue value for 2005, we get:
3.9 = a(3 - (-4))^2 + k
3.9 = 49a + k
Solving for a and k, we get:
a = -0.1
k = 4.3
Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:
r(x) = -0.1(x + 4)^2 + 4.3
The vertex of this function is at (-4, 4.3).
Angel
What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?
We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:
3 - 4 + 5 - 6 + ... + 101
We can group the terms into pairs:
(3 - 4) + (5 - 6) + ... + (99 - 100) + 101
Each pair of terms adds up to -1, so we can simplify the expression to:
-1 -1 -1 ... -1 + 101
where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:
-50 + 101 = 51
Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.
Angel
What is 12 7/8 - 56/17?
To subtract mixed numbers like 12 7/8, we first need to convert it to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction, and adding the result to the numerator. This gives us:
12 7/8 = (12 × 8 + 7)/8 = 103/8
Now we can subtract 56/17 from 103/8. To do this, we need to find a common denominator for the two fractions. The least common multiple of 8 and 17 is 136, so we can rewrite the fractions with this denominator:
103/8 = (103/8) × (17/17) = 1751/136
56/17 = (56/17) × (8/8) = 448/136
Now we can subtract the two fractions:
1751/136 - 448/136 = (1751 - 448)/136 = 1303/136
We can simplify this fraction by finding a common factor to divide both the numerator and denominator. Since both 1303 and 136 are relatively prime, we cannot simplify it any further. Therefore, the final answer is:
12 7/8 - 56/17 = 1303/136
Angel
A circle in the xy-plane has a diameter with endpoints (2,4) and (2,14). An equation of this circle is (x-2)^2+(y-9)^2=r^2 ,where r is a positive constant. What is the value of r?
The center of the circle is the midpoint of the diameter, which is at (2, (4+14)/2) = (2, 9). We can substitute this center point into the equation of the circle to get:
(x - 2)^2 + (y - 9)^2 = r^2
(2 - 2)^2 + (9 - 9)^2 = r^2
0 + 0 = r^2
So we see that r = 0. Therefore, the equation of the circle is just:
(x - 2)^2 + (y - 9)^2 = 0
This describes a single point in the xy-plane, which is the center of the circle. Note that this point is already on the given diameter, so it makes sense that the radius is zero.
Angel
which number has which number has the lowest value? 1/6 1/3 - 1/9 1/3 - 1/6 1/4 - 1/6the lowest value?
To compare these fractions, we can first find a common denominator for all of them. The least common multiple of 2, 3, and 4 is 12, so we can rewrite the fractions with this denominator:
1/6 = 2/12
1/3 - 1/9 = (3/12) - (1/12) = 2/12
1/3 - 1/6 = (2/6) - (1/6) = 1/6
1/4 - 1/6 = (3/12) - (2/12) = 1/12
So the fractions can be ordered as follows, from least to greatest:
1/12 < 1/6 < 2/12 = 1/3 - 1/9 < 1/3 - 1/6
Therefore, the fraction with the lowest value is 1/12.