Jane should land 1.5 mi down the shoreline and walk the remaining 4.5 mi to the village to minimize her travel time.
Let x = distance travelled along the shore over water.
Then, 6 − x = distance travelled along the shore over land.
Let T = the total time taken to reach the destination.
T = distance/velocity = √(4 + x²)/3 + (6-x)/5 on [0, 6].
Note that T must be non negative and that x = 6 means the destination
is reached solely by rowing and without the benefit of faster land
travel. In actual fact, T is valid over [0, ∞) but [0, 6] is reasonable here.
T' = x/3√(4 + x²) - 1/5 = 5x - 3√(4 + x²) = 0
⇒5x = 3√(4 + x²)
⇒25x² = 9(4 + x²)
⇒16x² = 36
⇒x = ±6/4 = ±1.5
The negative x value is discarded since it does not belong to [0,6].
T(0) = 28/15 = 1.8667
T(1.5) = 1.733
T(6) = 2.1082
Therefore, Jane should land 1.5 mi down the shoreline and walk the
remaining 4.5 mi to the village to minimize her travel time.
Her minimum travel time will be T(1.5) = 1.733 hrs. or 1hr 44 min.
--The given question is incomplete, the correct question is
"Jane is 2 mi, offshore in a boat and wishes to reach a coastal village 6 mi, down a straight shoreline from the point nearest the boat. She can row at 3mph and can walk at 5 mph. Where should she land her boat to reach the village in the least amount of time?"--
To know more about destination, here
https://brainly.com/question/14693696
#SPJ4
need help with #7 a and b. i’m in Algebra 1 and this is lesson 5 Exponential Algebra and Functions.
There is no upper limit if the ratio raises x to a higher power. The limit is 0 if the ratio causes the power of x to be reduced to zero.
A ratio is what?A ratio is an expression for an ordered pair of numbers, a and b, where b is not equal to zero and the expression is written as a/b. A ratio is created by combining two ratios. Assuming a ratio of one boy to three girls, this would suggest that 3/4 of the population is female and only 1/4 is male. A part can be an amount, a percentage, or the difference between two or more objects.
Here,
The ratio of, say, the highest-degree words serves as the upper bound as x grows.
There is no upper bound on how much the ratio can raise the power of x. The limit is 0 if the ratio causes the power of x to be reduced to zero.
To know more about ratio visit:
brainly.com/question/13419413
#SPJ1
express √832 in the form 4n where n is the integral
We can express √832 as 4(2√13).
What is definite integral?A definite integral of a function can be represented as the signed area of the region bounded by its graph.
Given is the root of 832 or √832.
Assume that {4n} is equal to {y}. So, we can write -
y = 4n
Squaring both sides, we get -
y² = (4n)² = (√832)²
y² = 16n² = 832
16n² = 832
n² = (832/16)
n² = 52
n = √52
n = 2√13
So, we can write (√832) as 4(2√13).
Therefore, we can express √832 as 4(2√13).
To solve more questions on expressing numbers, visit the link below -
https://brainly.com/question/9562264
#SPJ1
Which figure could be the result of dilating the trapezoid with a scale factor between 0 and 1?
10
9-
8
7
6
5
4
$
0
7
6
5
4
3
1 2 3 4 5 6 7 8 9
O
x
घ
A trapezoid will appear smaller than the original trapezoid if it is dilated with a scale factor between 0 and 1.
What shape is a trapezoid?An open, flat shape with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.
What are a trapezoid's three characteristics?What three characteristics do trapezoids have? An isosceles trapezoid has equal base angles and diagonals. The midpoints of the two opposing sides are parallel to the point where the diagonals intersect. An isosceles trapezoid has opposite sides that are congruent to one another or have the same length.
To know more about diagonals visit:-
brainly.com/question/12274248
#SPJ1
FIND THE SUM OF ALL NATURAL NUMBERS FROM 1 TO 100 (ARITHMETIC PROGRESSION)
Answer:
According to arithmetic progression, natural numbers can be written down as 1, 2, 3, 4, 5, 6, 7, and 8 to 100. Basically, the sum of the first 100 natural numbers is equal to 5050.
find the value of x
answer options
9,15,10,14
Answer:
14
Step-by-step explanation:
Hope this helps
What is the difference of the first and third quartiles in 1. 96, 2. 09, 01. 79, 1. 61, 1. 75, 2. 11, and 1. 84
The difference is quartiles 3 - quartiles 1 = 2.05 - 1.79 = 0.26
What is the difference of the first and third quartiles ?The first quartile (Q1) is the 25th percentile of a dataset, which separates the lowest 25% of the data from the rest. The third quartile (Q3) is the 75th percentile of a dataset, which separates the lowest 75% of the data from the highest 25%. To find the difference between Q1 and Q3, you would subtract Q1 from Q3.
In this specific dataset, you would need to sort the values first in increasing order:
1.61, 1.75, 1.79, 1.84, 1.96, 2.09, 2.11
The first quartile (Q1) is the median of the lowest half of the dataset, which is 1.79
The third quartile (Q3) is the median of the upper half of the dataset, which is 2.05
so the difference is Q3 - Q1 = 2.05 - 1.79 = 0.26
To know more about quartiles visit: https://brainly.com/question/17198478
#SPJ4
What relationship exists between Nand K?
Given:
KLMN is a parallelogram.
Helppppp meee
The relationship exists between N and K are the endpoints of the side KN.
A parallelogram is a geometric object with sides that are parallel to one another in two dimensions.
It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length.
we know that for a parallelogram KLMN is a quadrilateral whose two sides are parallel to each other and has two non-parallel sides.
for N and K we could say that the two are endpoints of the line segment KN; which is one of a side of a parallelogram KLMN.
Therefore, The relationship exists between N and K are the endpoints of the side KN.
To learn more about parallelogram visit : brainly.com/question/29147156
#SPJ4
Please give me a step by step explanation
Answer:
[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]
Step-by-step explanation:
The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].
[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]
We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].
Now add these equations together to get our equation.
[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]
Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].
=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]
There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 that are different in colour?
Northlake High School has two lunch periods. Students can eat their lunch in the cafeteria or on an outside patio. About 35% of students who have first lunch eat outside. Compare this with the percentage of second-lunch students who eat outside.
Select the true statement.
A. A smaller percentage of second-lunch students (24%) eat outside.
B. A greater percentage of second-lunch students (39%) eat outside.
c. A greater percentage of second-lunch students (41%) eat outside.
D. A smaller percentage of second-lunch students (18%) eat outside.
A / P / E / X
B. A greater percentage of second-lunch students (39%) eat outside.
From the table above, the percentage second-lunch students who eat outside is calculated as follows:
%= number of students who eat outside/total number of students who have second lunch × 100/1
%=18/46 x 100/1
%=39.1%
What is PercentPercent is usually used to describe data in percentage form. This mathematical science is often used when calculating population percentages, discounts, interest rates, and so on. Percent is a number that represents part or all of the value or goods by forming a ratio of one hundred. Percent has an infinitely high value, while its lowest value is 0 percent. The amount of the percentage is denoted by "%".
History of Percent NumbersThis number was born in ancient Rome to be precise from the collection of auction taxes by using a fraction of 1/100 of the auction value or called centesima rerum venalium. the percent symbol has changed several times. Originally the Latin word percento was used. However, in the next generation, the word percento was changed to two symbols, namely the word per which changed to "/" and cento which changed to "00". Until finally the symbol "%" was known.
Percent formulaThe simple formula for calculating percent is: Percentage (%) = (Total parts)/(Total amount) X 100%. The general percentage formula for calculating the percentage of a number that is considered as part of the whole is written in percent or 100%.
Learn more about percentage at https://brainly.com/question/29306119.
#SPJ4
What is the volume of the rectangular prism? 5/4 5/2 3
The rectangular prism's volume is equal to [tex]$V=9.375 \mathrm{~m}^3$[/tex]. Prism volume (V) is equal to B ×h, where h is the prism's height and B is the area of the base.
What is the formula to rectangular prism?1.25 metres in length, 2.5 metres in width, 3 metres in height, and a diagonal length of 4.10030487 metres make up the total surface area. [tex]$\mathrm{S}_{\text {tot }}[/tex]=[tex]28.75 \mathrm{~m}^2$[/tex] , Latitudinally exposed area [tex]$S_{\text {lat }}=22.5 \mathrm{~m}^2$[/tex] , maximum surface area is [tex]$S_{\text {top }}=3.125 \mathrm{~m}^2$[/tex] , surface area of the ground is [tex]$S_{\text {bot }}=3.125 \mathrm{~m}^2$[/tex] so that the volume is [tex]$V=9.375 \mathrm{~m}^3$[/tex]
When determining the volume of a rectangular prism , we multiply its length, width, and height. The base's area multiplied by the height gives the rectangular prism its volume. Length, width, and height are the cubic units that make up a rectangular prism's volume. Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. Size times width equals the base's area, B.
To learn more about rectangular prism refer to :
https://brainly.com/question/24284033
#SPJ1
The graph of y = x2 has been translated 7 units to the left. The equation of the resulting parabola is _____.
The equation of the parabola after the translation is:
g(x) = (x - 7)^2
What is the equation for the resulting parabola?We know that we start with a parabola of the form:
y = x^2
Now we know that the parabola has been translated 7 units to the left.
Remember tht for a general function y = f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
If N > 0, the translation is to the left.if N <0, the translation is to the right.So a translation of 7 units to the left is written as:
g(x) =f(x - 7)
g(x) = (x - 7)^2
That is the equation of the parabola after the translation.
Learn more about translations:
https://brainly.com/question/24850937
#SPJ1
The circumference of a circle is 13.3(pi symbol) ih eget is the radius of the circle
A)3.9in
B)5.75 in
C) 6.15 in
D)10.1 in
Answer:
I think 6.15in is the answer (hope u get it right)
Step-by-step explanation:
Simplify algebraic expression
Answer:
1
Step-by-step explanation:
To start, we will substitute 8 in for w. So, we get:
[tex]5 - \frac{32}{8}[/tex]
Then, we simplify our fraction, giving us:
5 - 4
Then, 5 - 4 = 1. So our answer is 1.
Hope this helped!
Answer:
5 - (32/w) = 1
Step-by-step explanation:
Given expression,
→ 5 - (32/w)
Now we have to use,
→ w = 8
Let's solve the expression,
→ 5 - (32/w)
→ 5 - (32/8)
→ 5 - (4)
→ 5 - 4
→ 1 => final value
Therefore, the answer is 1.
find x pah lease and thank you
Answer: x=4
Step-by-step explanation: x+3=2x-1, then you do simple algebra
Calculate the area of a circle with a radius of 2.3 cm.
Answer:
16.62 cm²
Step-by-step explanation:
A = πr² is the appropriate equation here.
If r = 2.3 cm, then A = π(2.3 cm)² = 16.62 cm²
Two points (2, 10) and (-4,4) lie on a
line. What is the y-intercept of that
line?
Answer:
The y-intercept is 8.
Step-by-step explanation:
[tex]\frac{2+4}{10-4\\} \\\frac{6}{6} =1\\\\\\slope=1\\1(2)+y=10\\2-2+y=10-2\\y=8[/tex]
x2 - 4x + 4 = 20 please helpppppppp
Answer:
6.472
Step-by-step explanation:
Answer:
x = 2 ± 2√5 Exact solution
x = {-2.472, 6.472} Decimal approximation
Step-by-step explanation:
x² - 4x + 4 = 20
Subtract 4 from both sides
x² - 4x = 16
Complete the square using half the x coefficient, (-4/2 = -2), as the complete the square term
(x - 2)² = (-2)² + 16
(x - 2)² = 20
Take the square root of both sides
x - 2 = ±√20
x - 2 = ±2√5
Add 2 to both sides
x = 2 ± 2√5 Exact solution
x = {-2.472, 6.472} Decimal approximation
---------------------
Note this could also be solved using the quadratic formula
Ordena el siguiente Polinomio de forma ascendente con relacion a x: x4y – 7x2y3 – 5x5 + 6xy4 + y5 – x3y2
Answer:
El polinomio ordenado de forma ascendente y con relación a [tex]x[/tex] es [tex]p(x,y) = y^{5}+6\cdot y^{4}\cdot x -7\cdot y^{3}\cdot x^{2}-y^{2}\cdot x^{3}+x^{4}\cdot y -5\cdot x^{5}[/tex].
Step-by-step explanation:
El polinomio está en términos de dos variables: [tex]x[/tex], [tex]y[/tex]. Puesto que necesitamos ordenar el polinomio con relación a
[tex]p(x, y) = \Sigma\limits_{i = 0}^{n} \,c_{i} (y)\cdot x^{i}[/tex] (1)
Where:
[tex]i[/tex] - Índice i-ésimo del polinomio asociado al polinomio i-ésimo.
[tex]c_{i}(y)[/tex] - Coeficiente i-ésimo en función de [tex]y[/tex].
[tex]x, y[/tex] - Variables independientes.
[tex]p(x,y)[/tex] - Variable dependiente.
[tex]n[/tex] - Grado del polinomio.
A partir de esto y comparando (1) con la expresión del enunciado, encontramos que el último está formado por seis monomios y tiene grado 5. Al aplicar las propiedades algebraicas correspondientes tenemos que:
[tex]p(x,y) = y^{5}+6\cdot y^{4}\cdot x -7\cdot y^{3}\cdot x^{2}-y^{2}\cdot x^{3}+x^{4}\cdot y -5\cdot x^{5}[/tex]
Music, in 2001, full-length cassettes represented 3. 4% of total music sales. Between 2001 and 2006, the percent decreased by about 0. 5% per year.
a. Write an equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006
b. Find the percent of recorded music sold as full-length cassettes in 2004
a) An equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006 : y = -0.5x + 3.4
b) The percent of recorded music sold as full-length cassettes in 2004 = 1.9%
As, between 2001 and 2006, the percent of recorded music sold was decreased by about 0. 5% per year.
This means, the slope m = -0.5
In 2001, full-length cassettes represented 3. 4% of total music sales.
This means the y-intercept would be c = 3.4
So, an equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006 would be,
y = mx + c
Substituting value of m and c,
y = -0.5x + 3.4
Now to find the percent of recorded music sold as full-length cassettes in 2004
Here, the number of years x would be
x = 2004 - 2001
x = 3
So, the percent of recorded music sold would be,
y = (-0.5 × 3) + 3.4
y = 1.9%
Learn more about an equation here:
https://brainly.com/question/649785
#SPJ4
Plz help no link PLZ NO LINKSSSS THANK YOU
Answer: HHHHHMMM DEPENDING ON MY BRAIN IT IS 6
sorry if im wrong
Step-by-step explanation:
can anyone solve it use translation if found necessary.
On solving the provided, we can say that - here in graphs by solving the equation - [tex]x^2 + y^2 = > 2^2 = > 4[/tex]
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
here from graph,
x= 0
and y = 2
so, in equation
[tex]x^2 + y^2 \\2^2\\4\\[/tex]
To know more about graphs visit:
https://brainly.com/question/11950136
#SPJ1
A tudent aid -5 i le than -4 and |n | -5 | i le than | -4 | i the tudent correct? jutify your reaoning
The student is partially correct as -5 is less than -4 but ln |-5| is not less than ln |-4|.
What is reasoning?
We can ascertain the veracity of the supplied propositions using mathematical reasoning, often known as the mathematical reasoning principle.
A student said that -5 is less than -4.
This statement is correct and the reasoning is -
According to the number line, 0 is the midpoint.
From 0 to the right side of infinity the digits increases.
So, 1 is bigger than 0, 2 is bigger than 1, 3 is bigger than 2, and so on.
Similarly, from 0 to the left side of negative infinity the digits decreases.
So, -1 is smaller than 0, -2 is smaller than -1, -3 is smaller than -2, and so on.
The student also said that ln |-5| is less than ln |-4|.
This statement is false and the reasoning is -
First simplify ln |-5| and ln |-4| -
ln |-5| = ln (5)
ln (5) = 1.6094
ln |-4| = ln (4)
ln (4) = ln (2^2)
ln (2^2) = 2 ln (2)
2 ln (2) = 1.3862
Therefore, the student is partially correct.
To learn more about reasoning from the given link
https://brainly.com/question/28432148
#SPJ4
Mia is taller than Gage. If m represents Mia’s height and g represents Gages hight write an inequity that shows the relationship between their heights. Answer plsssssssss
The inequality that shows the relationship between thier heights is; g < r or r > g
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Now we have the following parameters that can be used in our computation:
Reese is taller than Gage.
Also, we have
Reeses's height = r
Gage's height = g
Since Reese is taller than Gage, then it means that
The value of r is greater than the value of g
So, we have the following inequality expression;
r > g
Also, we have;
g < r
Hence, the inequality is g < r
Read more about inequality at
brainly.com/question/25275758
#SPJ1
The 7% sale tax on the new $32,000 car
Answer:
7/100x32000
cancel the two zeros in 100 and 32000
7x320=2240
Now, you do the math: Tell us if you can afford the apartment using the details below. . Your gross paycheck is $2100 per month. . You're looking at a very small one-bedroom apartment that rents for only $650 per month . The electric bill runs about $60 per month for power. . You'll pay about $10 per month for gas. . An Internet line will cost you $20 per month. . You have to rent a parking space for your old buggy at $20 per month. Can you afford to get this apartment? O Yes. O No. If no, how much can you afford to pay in rent plus housing expenses? $ Submit
Answer:
the answer it clearly no I use foolproof and i try and put yes but it wont let me pass but i dont understand why no
Step-by-step explanation:
No, the amount should be $700.
What is Gross Pay?Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, that amount is known as their gross pay. Net pay, often known as take-home pay, is the amount that is left after all withholdings have been taken into account.
Given:
Gross Pay = $2100 per month.
Maximum amount that can be spend on rent and housing expenses is
= 1 by 3 × $2100
= $700
Now, Total Expenses per month
= Rent + Electricity bill + Gas + Internet line + Parking space
= $650 + $60 + $10 + $20 + $20
= $760
No, I am unable to purchase this property since my monthly expenses exceed the maximum budget for rent and housing costs, which is $700.
According to the monthly amount authorised for the same, we can only pay a maximum of $700.
Learn more about taxes here:
brainly.com/question/16911495
#SPJ2
Someone help with this please
Answer:
1/2
Step-by-step explanation:
hridnrle9hsveienrorbroronrjr
Answer: d
Step-by-step explanation:
Hope you have a good day can I please get branlyist
Find the approximate number of grams of milk fat in a 200-gram serving of whole milk.
The answer is :6.5g
32. Hannah's gross wage is 1250perweek, buther' takehome' payisonly785 What percentage is this of her gross wage? Give your answer correct to the nearest whole percentage.
Therefore , the solution of gross pay problem is 62% is this of her gross wage.
What percentage is this of her gross wage?Hannah's take home pay of percentage 785 is 62.8% of her gross wage of 1250. This can be calculated by dividing 785 by 1250 and multiplying the answer by 100.
Here,
62.8% is the same as 0.628.
This can be calculated by dividing 785 by 1250.
To get the answer to the nearest whole percentage, we round up 0.628 to 0.63 which is 63%.
This means that Hannah's take home pay of 785 is 63% of her gross wage of 1250.
63% is the answer to the question: what percentage is Hannah's take home pay of her gross wage? This is correct to the nearest whole percentage.
To summarise, Hannah's take home pay of 785 is 63% of her gross wage of 1250, correct to the nearest whole percentage.
Hannah's take-home pay is 62.8% of her gross wage. This percentage is the result of taxes and other deductions taken by her employer.
Knowing this percentage can help Hannah better understand how much money she is taking home each week and how much money is being withheld from her paychecks.
To learn more about gross pay refer to:
brainly.com/question/4356180
#SPJ1
What is the formula of polynomial?
The general formula of a polynomial is:
P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0
A polynomial is a mathematical expression consisting of variables (such as x), coefficients, and exponents. The general formula of a polynomial is P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0. Here, a_n, a_(n-1), ... , a_2, a_1, and a_0 are coefficients, and n is the degree of the polynomial. The highest exponent in the polynomial is the degree of the polynomial. For example, in the polynomial 3x^2 + 5x – 8, x^2 is the highest exponent, so the degree of the polynomial is 2. The coefficient of the highest exponent is known as the leading coefficient. In the example above, 3 is the leading coefficient. Polynomials can be used to represent a variety of functions, from simple linear equations to complex curves.
Learn more about polynomial here
https://brainly.com/question/11536910
#SPJ4