To answer this item, we let x be the speed of the boat in still water. The speed of the current, we represent as y.
When the boat travels upstream or against the current, the speed is equal to x – y and x + y if it travels downstream or along with the current.
The time it takes for the an object to travel a certain distance is calculated by dividing the distance by the speed.
First Travel: 35 / (x – y) + 55 / (x + y) = 12
Second travel: 30 / (x – y) + 44 / (x + y) = 10
Let us multiply the two equations with the (x-y)(x+y)
This will give us,
35(x + y) + 55(x – y) = 12(x-y)(x+y)
30(x + y) + 44(x – y) = 10(x-y)(x+y)
Using dummy variables:
Let a = x + y and b be x – y
35a + 55b = 12ab
30a + 44b = 10ab
From the first equation,
b = 35a/(12a – 55)
Substituting to the second equation,
30a + 44(35a/(12a – 55)) = 10a(35a/(12a-55))
The value of a is 11.
b = 35(11)/(12(11) – 55))
b = 5
Putting back the equations,
x + y = 11
x – y = 5
Adding up the equations give us,
2x = 16
x = 8 km/hr
The value of x, the speed of the boat in still water, is 8 km/hr.
speed of the stream = 3 km/hr
and speed of boat in still water= 8 km/hr
Step-by-step explanation:Let s be the speed of the boat upstream
and s' be the speed of the boat downstream.
We know that:
[tex]Time=\dfrac{distance}{speed}[/tex]
Hence, we get:
[tex]\dfrac{35}{s}+\dfrac{55}{s'}=12[/tex]
and
[tex]\dfrac{30}{s}+\dfrac{44}{s'}=10[/tex]
Now, let
[tex]\dfrac{1}{s}=a\ and\ \dfrac{1}{s'}=b[/tex]
Hence, we have:
[tex]35a+55b=12--------------(1)\\\\\\and\\\\\\30a+44b=10--------------(2)[/tex]
on multiplying equation (1) by 4 and equation (2) by 5 and subtract equation (1) from (2) we get:
[tex]a=\dfrac{1}{5}[/tex]
and by putting value of a in (2) we get:
[tex]b=\dfrac{1}{11}[/tex]
Hence, speed of boat in upstream= 5 km/hr
and speed of boat in downstream= 11 km/hr
and we know that:
speed of boat in upstream=speed of boat in still water(x)-speed of stream(y)
and speed of boat in downstream=speed of boat in still water(x)+speed of stream(y)
Hence, we get:
[tex]x-y=5\\\\\\and\\\\\\x+y=11[/tex]
Hence, on solving the equation we get:
[tex]x=8[/tex]
and y=3
Hence, we get:
speed of the stream = 3 km/hr
and speed of boat in still water= 8 km/hr
Sara must plant 340 trees. In the past 6 days Sara planted 204 trees. If she continues at this rate, how many more days will it take her to plant all the trees?
What is the volume of an oblique cone with radius 9 cm and height 12 cm?
972π cm3
486π cm3
648π cm3
324π cm3
The sales tax in Bill's state is 6%. Bill bought a Scion having a sales tax of $820. What was the cost of the car, rounded to the nearest dollar.
richerd works at an ice cream shop. regular cones get two scopes of ice cream and large cones get three scoops. One hot saturday richard scooped 234 regular cones and 156 large cones one scoop of ice cream is 3 ounces a tub of ice cream is 10 pounds how many tubs of ice cream did richerd use to make the cones?
234 x 2 = 468 scoops
156 x 3 = 468 scoops
468 + 468 = 936 total scoops
936 x 3 = 2808 ounces
16 ounces = 1 pound
2808/16 = 175.5 pounds
175.5/10 = 17.55 tubs
round answer as needed
which number produces a rational number when added to 0.5
Answer:
Any rational number.
Step-by-step explanation:
∴ [tex]x+0.5[/tex] is rational if and only if x is rational.
To proveL: we proceed as follows:
Suppose that [tex]x+0.5[/tex] is rational.
Then there are some integers p , q with [tex]q\neq 0[/tex] such that
[tex]x+\frac{1}{2}=\frac{p}{q}[/tex]
Subtract both sides by [tex]\frac{1}{2}[/tex], we get
[tex]x=\frac{p}{q}-\frac{1}{2}=\frac{2p-q}{2q}[/tex] which is rational.
Conversely, if x is rational, then there are integers a,b with b>0 such that [tex]x=\frac{a}{b}[/tex] then we have,
[tex]x+\frac{1}{2}=\frac{a}{b}+\frac{1}{2}=\frac{2a+b}{2b}[/tex] which is also a rational.
5. Simplify (15x2 – 24x + 9) ÷ (3x – 3) = ?
Three counters are used for a board game.If the counters are tossed,how many ways can at least one counter with Side A occur?
What is the arc measure of an arc with length 4.189 cm and radius equal to 3 cm.'?
A bird feeder is in the shape of a cylinder. It has a volume of about 100 cubic inches. It has a radius of 2 inches. What is the approximate height of the bird feeder? Use 3.14 for pi
volume = pi x r^2x h
100 = 3.14 x 2^2 x h
100 =3.14 x 4 x h
100 = 12.56 x h
h = 100/12.56 = 7.9617
the height is approximately 8 inches tall
What's the average of 200 and 300
A chemist is using 353 millimeters of a solution of acid and water. If 16.5% of the solution is acid, how many millimeters of acid are there? Round your answer to the nearest tenth.
What is the slope of a line that passes through the following points (-3,8) and (2,1)
Hello!
Step-by-step explanation:
Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]
[tex]\frac{1-8=-7}{2-(-3)=2+3=5}=\frac{-7}{5}=-\frac{7}{5}[/tex]
Slope is -7/5
Answer is -7/5
Hope this helps!
Thanks!
-Charlie
:)
:D
Bill's Roast Beef sells 5 times as many sandwiches as Pete's Deli. The difference between their sales is 360 sandwiches. How Many did each sell ?
Answer:
5y-y =360
4y =360
y= 90 sandwiches by Pete's deli
x= 5(90) = 450 sandwiches by Bills Roast Beef
Step-by-step explanation:
Find an approximation of the area of the region R under the graph of the function f on the interval [-1, 2]. Use n = 6 subintervals. Choose the representative points to be the left endpoints of the subintervals. f(x) = 7 - x2
The approximation of the area of the region R under the graph of the function is 18.625 square units.
In this question we must calculate the approximate area ([tex]A[/tex]) below the curve by means of Riemann sums with left endpoints, whose expression is described below:
[tex]A = \Delta x \cdot \Sigma\limits^{n-1}_{i=0} f(a + i\cdot \Delta x)[/tex], for [tex]x \in [a,b][/tex] (1)
[tex]\Delta x = \frac{b-a}{n}[/tex] (2)
Where:
[tex]a[/tex] - Lower bound[tex]b[/tex] - Upper bound[tex]n[/tex] - Number of subintervals[tex]i[/tex] - IndexIf we know that [tex]a = -1[/tex], [tex]b = 2[/tex], [tex]n = 6[/tex] and [tex]f(x) = 7 - x^{2}[/tex], then the approximate area is:
[tex]\Delta x = \frac{2-(-1)}{6}[/tex]
[tex]\Delta x = 0.5[/tex]
[tex]A = 0.5\cdot [f(-1) + f(-0.5)+f(0)+f(0.5)+f(1)+f(1.5)][/tex]
[tex]A = 0.5\cdot (6+6.75+7+6.75+6+4.75)[/tex]
[tex]A = 18.625[/tex]
The approximation of the area of the region R under the graph of the function is 18.625 square units.
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A total of 504 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?
Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.
Explanation:Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.
Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.
Therefore, 225 adult tickets were sold.
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In how many different ways can you make exactly 0.75 using only nickles dimes and quarters if you have at least one of each coin?
In the middle of the page draw a equilateral triangle with 2 inch sides and the bottom parallel to the of the page
The sum of the angle of a triangle is 180 degrees. If you are to draw a pattern of equilateral triangles then you know that an equilateral triangle has three equal sides. Also, its angles are the same, having 60 degrees at each corner of the triangle. A triangle cannot qualify as an equilateral triangle if it is greater than 180 degrees or less than 180 degrees as a total angle. Also if a triangle that has no two right angles, then it is called a scalene triangle. If the triangle has two right angles, it is called isosceles triangle. A triangle with equal sides is called an equilateral triangle.
a patient requires 30% decrease in the dosage of the medication her current dosage is 340 MGS what will the dosage be after the decrease
Answer:
The dosage will be 238 MGS after decrease.
Step-by-step explanation:
The current dosage of the medication of the patient = 340 MGS
patient requires 30% decrease in the dosage of the medication.
Now her new dosage after decrease = 340 -(30% × 340)
= 340 -(0.30 × 340)
= 340 - 102
= 238 MGS
The dosage will be 238 MGS after decrease.
Tina wants to save money for school. Tina invests 400$ in an account that pays interest rate of 8%. How many years will it take if her goal is 5500$
222+203 is rounded up to what?
A company made 4 million in the second quarter this is 1/3 more then it made in the first quarter and 4/5 of what it made in the third quarter how much did the company make in all 3/4 combined
Find the arc length of the curve on the given interval. (round your answer to three decimal places.) parametric equations interval x = 6t + 5, y = 7 − 7t −1 ≤ t ≤ 3
The arc length of the curve on the given interval −1 ≤ t ≤ 3 with parametric equation x = 6t + 5 and y = 7 − 7t −1 is 4√85.
What is integration?It is the reverse of differentiation.
The arc length of the curve on the given interval.
Parametric equations interval
x = 6t + 5, −1 ≤ t ≤ 3
y = 7 − 7t, −1 ≤ t ≤ 3
We know that the parametric form of the arc length will be given as
[tex]\rm \int _{-1}^3 \sqrt{(\dfrac{dx}{dt})^2 + (\dfrac{dy}{dt})^2} \ dt[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = 6\\\\\dfrac{dy}{dt} = -7[/tex]
Then the arc length will be
[tex]\rightarrow \rm \int _{-1}^3 \sqrt{(3)^2 + (-7)^2} \ dt\\\\\rightarrow \sqrt{85} [t]_{-1}^3 \\\\\rightarrow 4 \sqrt{85}[/tex]
More about the integration link is given below.
https://brainly.com/question/18651211
Simplify the expression. 33 • 32 + 12 ÷ 4
The expression 33 • 32 + 12 ÷ 4 simplifies to 1059.
Explanation:To simplify the expression 33 • 32 + 12 ÷ 4, we follow the order of operations - performing multiplication and division before addition.
Multiply 33 and 32 to get 1056.Divide 12 by 4 to get 3.Now we can add the results: 1056 + 3 = 1059.
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A cold front moved in last weekend. In eight hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour ?
How Do You Sell More Walnuts In A Perfectly Competitive Market?
If the equilibrium price in a perfectly competitive market for walnuts
is $4.99 per pound,then an individual firm in this market can
A. Not sell additional walnuts unless the firm lowers its price.
B. Not sell additional walnuts at any price because the market is at equilibrium.
C. Sell an additional pound of walnuts at $4.99.
D. Sell more only by increasing its advertising budget.
the subject is Economics.
A total of 487 tickets were sold for the school play. They were either adult tickets or student tickets. There were 63 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Final answer:
To determine the number of adult tickets sold for the school play, a system of equations is set up and solved, revealing that 275 adult tickets were sold.
Explanation:
To find the number of adult tickets sold for the school play, we need to set up a system of equations based on the information given. Let x represent the number of adult tickets and y represent the number of student tickets. According to the problem, the following two statements are true:
The total number of tickets sold is 487: x + y = 487
There were 63 fewer student tickets sold than adult tickets: y = x - 63
We can substitute the second equation into the first to find the value of x:
x + (x - 63) = 487
2x - 63 = 487
2x = 487 + 63
2x = 550
x = 275
Therefore, 275 adult tickets were sold.
Mick and LaToya have some shirts. The ratio of the number of shirts Mick has to the number of shirts LaToya has is 3:8. If they have a total of "k" shirts, how many fewer shirts does Mick have than LaToya?
A company that creates model cars uses a 1.5 foot : 1 inch ration when creating the models. If a real car is 12 feet long, how long will the model car be?
A figure has a vertex at (5, 2). If the figure has line symmetry about the y-axis, what are the coordinates of another vertex of the figure?
Answer:
[tex](-5,2)[/tex]
Step-by-step explanation:
We have been given that a figure has a vertex at (5,2). The figure has line symmetry about the y-axis.
We know that if a figure is symmetric about y-axis, then its x-coordinate changes to opposite sign and y-coordinate remains same.
We can see that x-coordinate of our given point is 5, so x-coordinate of another vertex of the figure would be -5.
Therefore, the point [tex](-5,2)[/tex] is symmetric about y-axis for our given point.
Suppose Q and R are independent events. Find P(Q and R) if P(Q) =4/5 and P(R) =4/11