Answers
The parametric equations graph as a portion of a parabola. The initial point is (5,0), and the terminal point is (3,4). The vertex of the parabola is (2,9). Arrows are drawn along the parabola to indicate motion right to left.
How to determine parametric equation?Parametric equations are a way of expressing a set of equations that define the coordinates of a point in terms of a third variable (parameter) that varies over a certain range. In the given problem, the parametric equations:
x(t) = 2 - t
y(t) = (t+3)²
To visualize the graph of these equations, we can substitute different values of t and plot the corresponding points (x(t), y(t)) on a coordinate plane. Since t ranges from -4 to 0, we can choose a few values of t such as t=-4, t=-2, and t=0 to get the corresponding points.
When plotted these points, a portion of a parabola that opens upwards. The vertex of the parabola is at the point (3, 4) where x=2-t and y=(t+3)² intersect. The initial point of the graph is when t=-4, which gives the point (6, 1) and the terminal point is when t=0, which gives the point (2, 9). The arrows are drawn along the parabola to indicate the direction of motion, which is from right to left in this case.
Find out more on parametric equations here: https://brainly.com/question/30451972
#SPJ1
Related Questions
What is m∠a?
A straight angle divided by a ray into two angles. The smaller angle has a measure of 50 degrees.
40°
50°
90°
130°
Answers
To find the answer look at the procedures
X+50 degree=180 degree
X=180 degree-50 degree
X=130 degree
An engine does 62 J of work each cycle as it absorbs 2 times as much heat as it discharges to the environment. A) Determine the efficiency of the engine in percent. B) What quantity of heat is discharged to the environment each cycle in Joules?
Answers
Answer:
A) 150%
B) 20.67 J
Step-by-step explanation:
A) To determine the efficiency of the engine, we can use the formula:
efficiency = (work output / heat input) x 100%
In this case, the engine does 62 J of work each cycle, so the work output is 62 J. We're also given that the engine absorbs 2 times as much heat as it discharges to the environment, so we can express the heat input as 2 times the heat discharged:
heat input = 2 x heat discharged
Therefore, we can rewrite the efficiency formula as:
efficiency = (62 J / (2 x heat discharged)) x 100%
Simplifying this expression, we get:
efficiency = 31 J / heat discharged
Now we need to determine the value of heat discharged. We know that the engine absorbs 2 times as much heat as it discharges, so the net heat input is 3 times the heat discharged:
net heat input = heat input - heat discharged = 2 x heat discharged - heat discharged = heat discharged
Therefore, we can express the net heat input as:
net heat input = 3 x heat discharged
Now we can use the first law of thermodynamics, which states that the net heat input is equal to the work output plus the heat discharged:
net heat input = work output + heat discharged
Substituting the given values, we get:
3 x heat discharged = 62 J + heat discharged
Solving for heat discharged, we get:
heat discharged = 20.67 J
Now we can calculate the efficiency:
efficiency = 31 J / 20.67 J = 1.50 or 150%
Therefore, the efficiency of the engine is 150%.
B) To determine the quantity of heat discharged to the environment each cycle in Joules, we can use the value we calculated above for heat discharged:
heat discharged = 20.67 J
Therefore, the quantity of heat discharged to the environment each cycle is 20.67 J.
Hope this helps!
A sum of money has a value of$3000 eight-
een months from now. If money is worth 6%
compounded monthly, what is its equivalent value
(a) now?
(b) one year from now?
(c) three years from now?
Answers
Answer:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where A is the future value, P is the present value, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
(a) To find the present value of the money, we need to solve for P in the formula above. We are given that A = $3000 and t = 18/12 = 1.5 years. The interest rate is 6% per year, compounded monthly, which means n = 12. Substituting these values into the formula, we get:
3000 = P(1 + 0.06/12)^(12*1.5)
Simplifying and solving for P, we get:
P = 3000 / (1 + 0.06/12)^(12*1.5)
P = $2,572.39
Therefore, the equivalent value of the money now is $2,572.39.
(b) To find the equivalent value of the money one year from now, we need to calculate the future value of $1 after one year, and then multiply it by the present value we found in part (a). The future value of $1 after one year, at 6% per year, compounded monthly, is:
FV = 1*(1 + 0.06/12)^(12*1)
FV = $1.06168
Multiplying this by the present value we found in part (a), we get:
$2,572.39 * $1.06168 = $2,735.92
Therefore, the equivalent value of the money one year from now is $2,735.92.
(c) To find the equivalent value of the money three years from now, we need to calculate the future value of $1 after three years, and then multiply it by the present value we found in part (a). The future value of $1 after three years, at 6% per year, compounded monthly, is:
FV = 1*(1 + 0.06/12)^(12*3)
FV = $1.19102
Multiplying this by the present value we found in part (a), we get:
$2,572.39 * $1.19102 = $3,066.63
Therefore, the equivalent value of the money three years from now is $3,066.63.
Find the value of x. Then find the area of the triangle.
Answers
Answer:
it would be 3 or 2
Step-by-step explanation:
Juliet tell her in Israel our volunteer firefighters on Saturday to volunteer fire department hell is annual coin drop fundraiser at street light after one hour Keller had collected $42.50 more than Julia. Israel had collected $15 less than Keller. The three firefighters collected $125.95 in total. How much did each person collect?
Part A: Choose all equations that represents this problem. J= the amount Julia collected, K= the amount Keller collected, I = the amount Israel collected.
Options:
A: 125.95=J+(42.5+J)+(J+15)
B: 125.95=K+42.5+K-15
C: 125.95=I+(1+15)+(I-27.5)
D: 125.95=K+(K-42.5)+(K-15)
Part B: Keller collected 42.50 more than Julia, and Israel had collected 15 less than Keller. The three firefighters collected $125.95 in total. How much did each person collect?
Options:
$125.95
$61.15
$46.15
$42.50
$64.80
$18.65
$15.00
Answers
Part A: A
Part B: Julia collected 18.65, Keller collected 61.15, and Israel collected 45.15
Jungle John participates in a reality TV show that features fitness and agility competitions. In order to beat the competitors, John needs to swing from tree A to tree B, completing an arc of at least 60 feet with a central angle of 115∘.
What length of rope (radius) will he need to accomplish this activity?
Round your answer to the nearest foot, and please show your work.
Answers
The length of rope Jungle John will he need to accomplish this activity is 30 feet.
How do we calculate?
the formula for arc length is
L = rθ
where L = length of the arc,
r =e radius of the circle,
θ = central angle of the arc in radians.
θ = (115∘/180∘)π = 2.0089 radians
60 feet = r(2.0089 radians)
r = 60 feet / 2.0089 radians
r = 29.85 feet
r is approximated to 30 feet
Therefore, Jungle John will need a rope with a length of at least 30 feet to swing from tree A to tree B and complete an arc of at least 60 feet with a central angle of 115∘.
Learn more about arc length at: https://brainly.com/question/30582409
#SPJ1
factorise 9x^2 + 3x^3
Answers
Answer:
[tex]9 {x}^{2} + 3 {x}^{3} [/tex]
[tex]3 {x}^{2} (3 + x)[/tex]
[tex]3 {x}^{2} (x + 3)[/tex]
The lateral area of a cone is 587 pi symbol cm^2. The radius is 32cm. Finf the slant height to the nearest tenth.
Answers
Answer:
The lateral area of a cone is given by the formula:
L = πrs
Where r is the radius of the base, s is the slant height, and π is pi.
We are given that the lateral area L is 587π cm^2 and the radius r is 32 cm. Substituting these values into the formula, we get:
587π = π(32)s
Simplifying, we can cancel the π on both sides of the equation:
587 = 32s
Dividing both sides by 32, we get:
s = 18.34375
Rounding to the nearest tenth, we get:
s ≈ 18.3 cm
Therefore, the slant height is approximately 18.3 cm.
Step-by-step explanation:
Does anybody know this? I am a bit confused and please answer it right cause if you don't know it don't bother
Answers
The number of different passwords, considering 2 digits and 2 letters, is given as follows:
A. 6,760,000.
B. 3,276,000.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The password is composed by:
Four digits.Two letters.With repetition, we have that:
Each of the four digits have 10 possible outcomes.Each of the two letters have 26 possible outcomes.Hence the number of passwords is given as follows:
10^4 x 26² = 6,760,000.
Without repetition, we have that:
Digits: 10, 9, 8 and 7 outcomes.Letters: 26 and then 25 outcomes.Hence the number of passwords is given as follows:
10 x 9 x 8 x 7 x 26 x 25 = 3,276,000.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751
#SPJ1
5. Jennifer solved a math problem. The answer. to her problem was in square inches. Which formula did Jennifer most likely use to solve her problem?
A P=(2xl) + (2xw)
B V=SxSxS
C P= 4xs
D A= SXS
Answers
Answer:
D. A = s × s
Step-by-step explanation:
D. A = s × s is an area formula. Area is side times side. This is an area formula for a square. The units of area are square units. Since Jennifer has square inches in her answer, she was working on an area problem.
A. and C. are perimeter formulas. Perimeter is the distance around the outside of a shape. The units of perimeter are straight up plain, one-dimensional units like inches (or feet, meters, miles, km)
B. is a volume formula. The units of volume is cubic units or units to the third power.
The answer is D.
100 Points! Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Photo attached. Please show as much work as possible. Thank you!
Answers
f(4) = 537. and f(-3) = 363. To find f(-3), we replace x with -3 in the expression similarly for x=4.
what is expression ?
In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.
In the given question,
To find f(-3), we replace x with -3 in the expression:
f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3
= 3(81) - 4(-27) + 3(9) + 15 - 3
= 243 + 108 + 15 - 3
= 363
Therefore, f(-3) = 363.
To find f(4), we replace x with 4 in the expression:
f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3
= 3(256) - 4(64) + 3(16) - 20 - 3
= 768 - 256 + 48 - 23
= 537
Therefore, f(4) = 537.
To know more about expression , visit:
https://brainly.com/question/14083225
#SPJ1
Find the circumference
Answers
Answer:
25.12 m (or 25.13 m)
Step-by-step explanation:
Recall the formula for the circumference of a circle:
[tex]2\pi r[/tex]
where r is the radius.
We are given that the radius is 4 m, so let's plug that into our formula:
[tex]2\pi r=\\2\pi *4=\\8\pi[/tex]
[tex]\pi[/tex] is approximately 3.14, so let's multiply 8 m by 3.14. We get:
25.12
So, the circumference is about 25.12 m.
(if you multiply by pi itself using a calculator, the answer is about 25.13 m)
Help pls
Stuck on this question
Answers
Answer:
x = 35
Step-by-step explanation:
since the figures are similar then the ratios of corresponding parts are in proportion, that is
[tex]\frac{x}{10}[/tex] = [tex]\frac{14}{4}[/tex] = [tex]\frac{7}{2}[/tex] ( cross- multiply )
2x = 7 × 10 = 70 ( divide both sides by 2 )
x = 35
Determine the measurement of KL.
KL=8.58
KL=9.36
KL=10.13
KL=9.84
Answers
Therefore , the solution of the given problem of angles comes out to be KL has a measurement of 19.49.
What does an angle mean?The largest and smallest walls of a skew are found at the intersection of the pathways connecting its ends. Two pathways could meet at a crossroads. Another result of two entities interacting is an angle. More than anything else, they resemble dihedral shapes. Two line beams can be arranged in a variety of ways between their endpoints to produce a two-dimensional curve.
Here,
It looks to be a right-angled triangle with the sides identified as KL, KM, and LM based on the photograph provided. The measurements are as follows:
=> KL = 8.58
=> KM = 9.36
=> LM = 10.13
=> KM + LM = KL
Since KM and LM are the two sides that make up KL, we may sum them to find the measurement of KL.
=> KM + LM = 9.36 + 10.13 = 19.49
KL thus has a measurement of 19.49.
To know more about angles visit:
https://brainly.com/question/14569348
#SPJ1
24. Which description describes the solutions to this inequality?
9 > 52
A. all the possible numbers that are smaller than twenty-five
B. all the positive numbers that are greater than ten
C. all the positive numbers that are larger than twenty-five
D. all the possible numbers that are smaller than ten
Answers
The description describes the solutions to this inequality in all the positive numbers that are greater than ten. The correct option is B.
What is inequality?Relationships between two expressions that aren't equal to one another are known as inequalities. Social justice theories are fundamentally based on the idea of inequality, which is the condition of not being equal, especially in terms of status, rights, and opportunities.
The given equation is 9 > 52.
everything that is positive and bigger than 10
Therefore, the correct option is B. All the positive numbers are greater than ten.
Learn more about inequality, here:
https://brainly.com/question/30238773
#SPJ1
The circle is divided into equal parts.
What fraction of the area of the circle is shaded?
+0
e
1
4
w|1
1
-
2
13% Complete
AZ
Answers
according to the given information we can say that the fraction of the area of the circle that is shaded is 1/4 or 0.25.
What is circle?Every point in a horizontal surface that is a certain distance above another point forms a circle (centre). It is a circle made out of point that are separated from each other in a horizontal direction as a result. At all angles, it is rotating symmetric about the centre. In the closed, two-dimensional plane of a circle, each pair of points is evenly separated from the "centre." A line that pierces the circle creates a specular symmetrical line. At all angles, it rotates symmetrically about the centre.
given,
If the circle is divided into two equal parts and one of them is shaded, then the shaded area is half of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/2 or 0.5.
If the circle is divided into four equal parts and one of them is shaded, then the shaded area is one-fourth of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/4 or 0.25.
Therefore, the answer depends on how many equal parts the circle is divided into and the number of shaded parts.
To know more about circle visit:
https://brainly.com/question/29142813
#SPJ1
Damon recorded the snowfall in his town for each day of January. This line plot shows the distribution.
Snowfall in January
0
1
2
3
4
5
6
7
Inches
Complete the sentences.
The distribution of snowfall amounts is best described as
. So, the
is a more appropriate measure of variation than the
.
Answers
The distribution of snowfall amounts is best described as bimodal, with modes at 2 inches and 7 inches. So, the range is a more appropriate measure of variation than the standard deviation.
What is a bimodal distribution?A bimodal distribution can be identified in a histogram when two distinct groups can be seen there. A bimodal distribution actually has two modes or two different data clusters.
In a bimodal distribution, no particular data value has the highest frequency of occurrence, rather two data values have the highest frequency.
The line plot of the distribution by Damon has two modes and is, therefore, bimodal.
Learn more about bimodal distributions at: https://brainly.com/question/30071486
#SPJ1
Pete is twice as old as chris. Seven years ago the sum of their ages was 31. Find their ages now
Answers
Answer:
Step-by-step explanation:
Answer: Pete is twice as old as Chris.p = 2c Seven years ago the sum of their ages were 31.(p-7) + (c-7) = 31p + c - 14 = 31p + c = 31 + 14p + c = 45Find their ages now replace p with 2c2c + c = 453c = 45c = 45/3c = 15 is Chris's agethenp = 2(15)p = 30 is Pete's age::Check solutions in the statement"Seven years ago the sum of their ages were 31"30-7 + 15-7 = 31
Find the balance in the account after the given period.
$4000 principal earning 7% compounded annually, 8 years
Answers
The balance in the account after the given period is [tex]\$6,872.74[/tex]
we know that
The compound interest formula is equal to
[tex]\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]\text{t}= 8 \ \text{years}[/tex]
[tex]\text{P}=\$4,000[/tex]
[tex]\text{r}=0.07[/tex]
[tex]\text{n}=1[/tex]
substitute in the formula above
[tex]\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74[/tex]
Graph the circle ( x − 5 ) 2 + ( y − 6 ) 2 = 4
Answers
The circle has a radius of 2 and is centred at the coordinates (5, 6). On the circle's x-axis, the points (3, 6) and (7, 6) are two points .
What is circle ?A circle is a closed shape made up of all elements in a plane that are indistinguishable from a predetermined point known as the centre. The radius (r) of a circle is the separation between the circle's centre and any other point on the circumference.
given
These procedures can be used to graph the circle :
Determine the circle's centre. The point in this instance serves as the centre (5, 6).
Determine the circle's radius. The circle's diameter is 4/2, or two.
Place the circle's centre on the coordinate plane.
Plot points that are 2 units distant from the centre in all directions to form the circle.
The circle has a radius of 2 and is centred at the coordinates (5, 6). On the circle's x-axis, the points (3, 6) and (7, 6) are two points, and the points (5, 4) and (5, 8) are two points on the circle's y-axis.
To know more about circle visit:
brainly.com/question/29142813
#SPJ1
The relationship between the actual air temperature x (in
degrees Fahrenheit) and the temperature y adjusted for wind
chill (in degrees Fahrenheit, given a 30 mph wind) is given by
the following formula:
y = -26 +1.3x
Estimate the actual temperature if the temperature adjusted
for wind chill is -35 degrees Fahrenheit.
Answers
The estimated actual temperature (x) when the temperature adjusted for wind chill (y) is -35 degrees Fahrenheit =
approximately -6.92 degrees Fahrenheit.
How do we estimate the actual temperature?To estimate the actual temperature (x) when the temperature adjusted for wind chill (y) is given as -35 degrees Fahrenheit using the formula y = -26 + 1.3x, we can substitute y with -35 and solve for x.
-35 = -26 + 1.3x
Adding 26 to both sides to isolate the x term:
-35 + 26 = 1.3x
-9 = 1.3x
Dividing both sides by 1.3 to solve for x:
x = -9 / 1.3
x ≈ -6.92
Thus, the estimated actual temperature (x) when the temperature adjusted for wind chill (y) is -35 degrees Fahrenheit would be approximately -6.92 degrees Fahrenheit.
Learn more about temperature at brainly.com/question/27944554
#SPJ1
The estimated actual temperature is -6.92 degrees Fahrenheit.
The estimated temperatureWe can use the given formula to solve for x when y is known. Rearranging the formula, we get:
x = (y + 26) / 1.3
Substituting y = -35 into this formula, we get:
x = (-35 + 26) / 1.3
x = -6.92 (rounded to two decimal places)
Therefore, the estimated actual temperature is -6.92 degrees Fahrenheit.
The term actual temperature typically refers to the true or measured temperature of an object, substance, or environment. It is the temperature that is currently present in a given location or situation, as opposed to a predicted or estimated temperature. The actual temperature can be measured using a thermometer or other temperature sensing device.
Learn more on calculations on temperature here https://brainly.com/question/25677592
#SPJ1
anyone know what the area of triangle ABC is?
Answers
The area of triangle ABC is 6cm²
What is a triangle?A triangle is a three-sided polygon that consists of three edges and three vertices. It is also known as the trigon and has special names such as the hypotenuse (opposite the right angle) and legs (the other two sides). It can also refer to a percussion instrument consisting of a rod of steel bent into the form of a triangle open at one angle.
The area of the triangle is given as
Area= 1/2absinC
But the CosB = Adj/Hypo
Cos60 = Adj/12
1/2 = Adj/12
corss and multiply to have
2A = 12
Therefore Adj = 6
Therefore base = 6*2 = 12
Applying the formula we have Area= 1/2acsinB
Area = 1/2* 12*12*Cos60
Area = 12*1/2 =6cm²
Learn more about the area of a triangle on https://brainly.com/question/19305981
#SPJ1
what is the value of sec^-1(1.4)
Answers
The calculated value of sec^-1(1.4) is 44.41 degrees
What is the value of sec^-1(1.4)The inverse secant function, denoted as sec^-1(x), returns the angle whose secant is x.
In other words, if secθ = x, then sec^-1(x) = θ.
To find the value of sec^-1(1.4), we need to find the angle whose secant is 1.4.
However, we know that the range of the secant function is [-∞, -1] ∪ [1, ∞], which means that sec^-1(x) is only defined for values of x that fall within this range.
Uisng a graphint tool, we have
sec^-1(1.4) = 44.41
Read more about trigonometry function at
https://brainly.com/question/24349828
#SPJ1
The cat____under the table when the veterinarian came into the examining room.
Which of these words would indicate that the
cat was afraid of the veterinarian?
A sulked
B cowered
C reclined
D strolled
Answers
Answer: B
Step-by-step explanation:
The word that would indicate that the cat was afraid of the veterinarian is "cowered." "Cowered" means to crouch down in fear or shame. So, the sentence would be: "The cat cowered under the table when the veterinarian came into the examining room."
81 smartphones is 45% of what number of smartphones? Please show work
Answers
Answer:
Let s be the number of smartphones.
81 = .45s, so s = 180
Answer:
36.45
Step-by-step explanation:
You make 45 into a percentage, which is 0.45%. Then, multiply 0.45 by 81 and you get 36.45. Hope this helps! And if you’re incorrect I deeply apologize. I tried my best and I’m 95% sure that I’m correct.
Solve for m 5(20 - m) = 40
Answers
Answer: 12
Step-by-step explanation: distribute 5 to 20 and -m which gives you
100 - 5m = 40. Subtract 100 on both sides which gives you -5m = -60. Divide both sides by -5 which gives you m = 12
Find the circumference of the circle. Round to the nearest tenth.
A. 148.4 m
B. 169.6 m
C. 84.8 m
D. 54.0 m
Answers
Answer:
C. 84.8 m
Step-by-step explanation:
Circumference of circle = D x 3.14
D = 27 m
Let's solve
27 x 3.14 = 84.78 m
So, the circumference of the circle is C. 84.8 m
What is tan(A)?
Remember to rationalize the denominator.
(Please Help)
Answers
Answer:
[tex]\frac{2 \sqrt{5}}{5}[/tex]
Step-by-step explanation:
As given by SOH-CAH-TOA
tan is equal to opposite/adjacent.
therefore for A, the opposite would be equal to 2, and adjacent would be equal to [tex]\sqrt{5}[/tex] as the hypotenuse is never referred to as an adjacent side. so the answer would be tan(A) = [tex]\frac{2}{\sqrt{5}}[/tex] however, to rationalize the denominator you must multiply the fraction by [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex] .
[tex]\frac{2}{\sqrt{5}} *\frac{\sqrt{5}}{\sqrt{5}} = \frac{2 * \sqrt{5}}{\sqrt{5} *\sqrt{5}}[/tex]
then simplify
[tex]\frac{2 \sqrt{5}}{5}[/tex]
Find an Euler path for the graph. Enter your response as a sequence of vertices in the order they are visited, for example, ABCDEA.
Answers
The given graph's Euler path is represented as a series of vertices visited in the following order: EBADCFEACBE.
What is Euler's path?A path in a finite graph known as an Euler path is one that traverses each edge precisely once while yet allowing for the revisiting of vertices.
A similar Euler trace that begins and finishes at the same vertex is known as an Euler circuit or cycle. When Leonhard Euler found a solution to the Seven Bridges of Konigsberg puzzle in 1736, it was first brought up for discussion.
A path known as an Euler path is one that utilises every edge in the graph once and only once. It doesn't have to return to the starting point because it is a path. A circuit that utilises every edge in the diagram once is known as an Euler circuit. As it is a circle, it should start and terminate at the same vertex.
If a graph has no more than two vertices of odd degree, it has an Euler path.
If every vertex has an even degree, the graph has an Euler circuit.
To know more about Euler path, visit:
https://brainly.com/question/14948056
#SPJ1
23
A train travelled along a track in 110 minutes, correct to the nearest 5 minutes.
Jake finds out that the track is 270 km long.
He assumes that the track has been measured correct to the nearest 10 km.
Could the average speed of the train have been greater than 160 km/h?
You must show how you get your answer.
Answers
Answer: To answer this question, we need to calculate the maximum possible speed of the train based on the given information and check if it is greater than 160 km/h.
First, let's use the given information to find the range of possible speeds of the train. The time taken by the train is given as 110 minutes, correct to the nearest 5 minutes. This means that the actual time taken by the train could be anywhere between 107.5 minutes and 112.5 minutes.
Converting the time to hours, we get:
Lower bound of time = 107.5 minutes = 107.5/60 hours = 1.792 hours
Upper bound of time = 112.5 minutes = 112.5/60 hours = 1.875 hours
Now, let's use the given distance of 270 km, correct to the nearest 10 km, to find the range of possible average speeds of the train. The lower bound of the distance is 265 km, and the upper bound is 275 km.
Lower bound of speed = 265 km / 1.875 hours = 141.3 km/h
Upper bound of speed = 275 km / 1.792 hours = 153.5 km/h
Therefore, based on the given information, the maximum possible speed of the train is 153.5 km/h, which is less than 160 km/h.
So, we can conclude that the average speed of the train could not have been greater than 160 km/h.
Step-by-step explanation: