A boat travels 20 miles downstream and then 40 miles upstream at a constant speed
of 30 miles per hour. The time the boat travels upstream is 1.5 hours longer than the
time it travels downstream. What is the average speed of the current? Write and solve a
rational equation to answer the question.
Answers
The speed can be determined by taking the ratio of distance over time.
Speed= Distance / Time
If any of the two of these are known we can find the third one by solving the equation.
The speed of water current c is found to be 45 miles per hour.
Solution:
The speed of the water current is required which can be found out by downstream and upstream speeds.
When the boat travels in the same direction as that of the current it is traveling downstream.
When the boat travels in the opposite direction to that of the current it is traveling upstream.
Suppose the speed of the boat downstream is d given by
Downstream speed= d = b + c
where b is the speed of boat and c is the speed of current .
Then the speed of the boat upstream is u given by
Upstream speed= u = b - c
The time the boat travels upstream is 1.5 hours longer than the
time it travels downstream.
Time upstream = 1.5 hours + time downstream
or
Distance upstream/ speed upstream =
1.5 + Distance downstream/ speed downstream
Putting the values:
40/30= 1.5 + 20/d
4/3- 1.5= 20/d
4- 4.5/3= 20/d
-0.5/3= 20/d
-0.5/60= 1/d
d= 60/-0.5
d= -120 miles per hour
The negative sign indicates that it is opposite to that of the given direction.
d= b+c ---------eq.1
u= b-c---------eq.2
Subtracting equation2 from eq.1
d-u= 2c
or
c= (d-u)/2
c= (120-30)/2
c= 90/2
c= 45 miles per hour
The speed of water current c is 45 miles per hour.
The boat speed can also be understood from the following.
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Related Questions
If the public debt in 2006 was 6,783,231,062,743.62 and the budget for 2007 was in deficit by 595,821,633,586.70 what was the public debt in 2007?
Answers
Answer: The public debt in 2007 would be 6,783,231,062,743.62 + 595,821,633,586.70 = 7,379,052,696,330.32
Step-by-step explanation:
Ms. jones wants to take her students for all of her classes on a field trip to see a Broadway production. There are three shows to choose from. She wants to determine which show students would like to see. which sample would be the most appropriate for this survey?
A: Every fifth student that enters her classroom
B: Her Honors class
C: 5 boys in each of her class
D: At the end of the day, ask teachers what they think student will like
Answers
Answer:
A
Step-by-step explanation:
Because it is a random sample
suppose that a and b are diagonalizable matrices of the same size, i.e.\ there exist invertible matrices u and v such that uau^{-1} and vbv^{-1} are diagonal. show that ab =
Answers
ab is diagonalizable and can be written as a product of invertible matrices.
Since a and b are both diagonalizable, there exist invertible matrices u and v such that \(uau^{-1} and vbv^{-1}\) are both diagonal matrices. Thus, we can rewrite ab as \(uau^{-1}vbv^{-1}\). Since matrix multiplication is associative, the order of multiplication does not matter and thus \(ab = u(au^{-1}vb)v^{-1}\). Since the \(au^{-1}vb\) is also diagonalizable, it can be written as c, where c is a diagonal matrix. Thus, \(ab = ucv^{-1}\), which is also a diagonal matrix. Therefore, ab is diagonalizable and can be written as a product of invertible matrices.
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Complete questiom:
Suppose that A and B are diagonalizable matrices of the same size, i.e.\ there exist invertible matrices U and V such that \(UAU^{-1} and VBV^{-1}\)are diagonal. Show that AB = UDEV, where UDEV is also a diagonal matrix.
Please see attached photo for problem from my homework set.
Answers
Answer:
y = (1/3)x - (1/3)
(1/3)
Step-by-step explanation:
We can find the slope by subtracting Q points by P points.
(2 - (-1)) / (7 - (-2))
3 / 9
1/3 = slope
To find y intercept we can use the slope and find the difference left
y = (1/3)x
-1 = (1/3)(-2)
-1 = -(2/3)
This is not true
To make it true we must subtract -(1/3)
This means our equation is
y = (1/3)x - (1/3)
if you times a 3 digit number by a 2 digit number what is the highest number you can get
Answers
Answer:
a 5 digit number
Step-by-step explanation:
Pick the largest three digit number (999) and the largest two digit number (99) and multiply them to get 999*99 = 98901
The result is a five digit number.
Answer: 5 digit number
Find two square numbers that total 45
Answers
x^2+^2=45
if ×=3 and y=6
then 9+36=45
how do you find the probability of a sample space
Answers
Answer:
Use the formula P = Specific Event / Sample Space to find the sample space.
2. Claire is painting some windows that are all the same size. She used gallon of paint to paint 2 windows. How many gallons of paint are needed to paint 1 window?
Answers
Answer:3
Step-by-step explanation:
since 7 is a number and b is to u should just put 3 windows cause u need to add them all up i think, not sure but just do that, why not,
You are preparing to buy a house. Your monthly gross income is $3,200. a. What is the maximum amount you can finance (mortgage)? (4 points)
Answers
The maximum amount you can finance is $896.
We are given that;
The monthly gross income = $3,200
Now,
28% of your gross monthly income on your mortgage, including taxes and insurance
The percentage = 28%
3200* 28/100
=32*28
=896
Therefore, by percentage the answer will be $896.
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Which of the following consists of discrete data?
A. Number of suitcases on a plane.
B. Amount of rainfall.
C. Hair color.
D. Tree height.
Answers
Answer:
A
Step-by-step explanation:
Number of suitcases on a plane is discrete because you can only have an integer amount. You can't have a fraction of a suitcase on a plane.
Genevieve has $9000 to invest. She invests some at 6% annual interest and the rest at 4% annual interest. After one year, her total interest from both accounts is $444. How much did she invest in each account? (Clearly label which amount is for which account in your answer. Hint: Over a one year period, annual interest is the same as simple interest.)
Answers
Answer:
The first account, she invested = $4200 and in the second = $4800
Step-by-step explanation:
Let us assume that Genevieve invests $x at 6% ,
Hence, she invests ($9000 - $x ) at 4% ,
It's given that the combined interest from both of the above accounts is $444,
So,
0.06x + 0.04 (9000 - x) = 444
=> 0.06x + 360 - 0.04x = 444
=> (0.06x - 0.04x) + 360 = 444
=> 0.02x = 444 - 360
=> 0.02x = 84
=> x = 84/0.02
=> x = 8400/2 (By multiplying the denominator and numerator)
=> x = 4200
Therefore, 9000 - x = 9000 - 4200 = 4800
$4200 at 6% and $4800 at 4%
Therefore, the first account, she invested = $4200 and in the second = $4800
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
AB - BC
3x - 31
А
Find x:
O 22
0 -25
O 16
0 43
None of the other answers are correct
Answers
Answer:
43
Step-by-step explanation:
\( AB = x + 6 \)
\( AC = 3x - 31 \)
Since AB = BC, therefore, \( BC = \frac{1}{2}3x - 31 \).
Thus,
\( x + 6 = \frac{1}{2}3x - 31 \)
Solve for x
\( 2(x + 6) = (\frac{1}{2}3x - 31)2 \) (multiplying both sides by 2)
\( 2x + 12 = 3x - 31 \)
Collect like terms
\( 2x - 3x = - 12 - 31 \)
\( -x = -43\)
Divide both sides by -1
\( x = 43\)
suppose a porch is thought of as a region in the plane and suppose the roof covering this porch can bemodeled as a portion of the plane below. if the area of the porch is square units, find the surface area of the roof.
Answers
On solving the provided question, we can say that - Surface area of the following will be 20 sq unit sq.
What is prime surface area ?A three-dimensional shape's surface area is the total amount of space that surrounds it. Additional distinctions between interface types include: The area that includes the base and curving section is referred to as the gross area. The curved area is the section of the curved portion that is devoid of a base. A plane is a two-dimensional object that occupies space. square units of measurement. The surface area of a three-dimensional object refers to the space it takes up on its outside surface.
Given plane:
\(-\sqrt{20} + 2y + z = 82\\ z = 82 + \sqrt{20} -2y\\\frac{dx}{dy} = \frac{d}{dy}(82 + \sqrt{20} -2y) \\= -2\)
Surface area =
\(\sqrt{1 + (\sqrt{20} )^2 + (-2)^2}\\ \sqrt{(1 + 20 + 2} \\5\)
5 X Area of the Porth
5 X 6
30 unit sq
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the ratio of red marbles to blue marbles in a bag is 2 to 3 .which of the following could be the number of red and blue marbles in the bag
Answers
ABC~A'B'C'. Their scale factor is 7:9. If the perimeter of smaller ABC is 42, then the
perimeter of A'B'C' is.
Pls hurry!!
Answers
Answer:
54
Step-by-step explanation:
ratio is 7:9
7=42
9=?
9×42÷7
PLS HELP 20 PONTS! which expression is equivalent to -2.5(1-2n) - 1.5n. select all that apply
Answers
Answer:
B
Step-by-step explanation:
Answer:
-2.5 + 3.5 n
Taylor buys candy at the store that costs $1.50 per candy bar.
Create a table that could represent Taylor’s cost per candy bar.
Candy
Cost
0 /0
1 /1.50
? ?
? ?
? ?
Answers
Answer:
2/ 3.00
3/4.50
4/6.00
Step-by-step explanation:
A nine-month old baby drank an average of 7 1/4 oz during each of four feedings. If the baby drank 7 1/2oz, 7 3/8oz, & 6 3/8oz in the first three feedings, how many ounces were taken during the fourth feeding?
A) 7 3/8
B) 6 3/8
C) 6 3/4
D) 7 3/4
Show work please
Answers
Answer: D) 7 3/4
Step-by-step explanation:
With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.
7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4
Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses
29 = 21 1/4 + x
Now we can isolate x by subtracting 29-21 1/4
so
x = 7 3/4 thus the answer is D
Answer:
D) 7 3/4
Step-by-step explanation:
Let x = amount of last feeding.
7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4
4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x
28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x
29 = 20 10/8 + x
(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)
29 = 21 2/8 + x
29 = 21 1/4 + x
x = 29 - 21 1/4
x = 28 4/4 - 21 1/4
x = 7 3/4
Answer: 7 3/4
simplify 2(3x²y)² x 3x
Answers
Answer:
54 x^5 y²
Step-by-step explanation:
2 (3x² y)² X 3x
square bracket:
2 ((3)² (x²)² y²) X 3x
= 2 ((9) x^4 y²) X 3x
multiply 2 and 3x:
(6x) (9 x^4 y²)
multiply 6 and 9. add powers for x (ie x^(1+4))
54 x^5 y²
can someone please help
Answers
Answer:
The measure of CD is 46
Step-by-step explanation:
From the midpoint theorem, we have,
FG = (1/2)CD
so,
\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)
Now,
\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)
three sides of triangle is x cm y cm z cm its perimeter and semi perimeter
Answers
Answer:
Step-by-step explanation:
Perimeter:
\(P=(x+y+z) \ cm\)
Semi-perimeter:
\(SP=\frac{1}{2} (x+y+z) \ cm\)
To find 10% of a number all you need to do is move the decimal to the left once. Explain why this is true
Answers
When dividing by 10, 100, 1000 and so on, move the decimal point to the left as many places as there are 0s. So when dividing by 10, move the decimal point one place, by 100 two places, by 1000 three places and so on. If there is no decimal point in the original number, then imagine it at the end of the number.
Just help don’t ask please
Answers
Step-by-step explanation:
change graphic into alohabet so it is easier to see
solve easy equation with only a type of unknown first..
once you found the value of the unknownm , substitute it in any equation so you can find the value of other unknown.
What is F(-x)?
F(x)=x^3+1
Answers
Answer:
F(-x) = 0
Step-by-step explanation:
What is F(-x)?
F(-x) = F(-1)
F(x) = x³ + 1 F(-1)
F(-1) = -1³ + 1
F(-1) = -1 + 1
F(-1) = 0
So, F(-x) = 0
Answer:
f(-1) = 0
Step-by-step explanation:
Evaluating a function for f(-x) is the same as evaluating it for f(-1).
So we plug in -1 instead.
f(-1) = x³ + 1
= (-1)³ + 1 (here we cube -1)
= -1 + 1 (here we subtract)
= 0 (and, this is the answer)
\(\therefore\) The answer is f(-1) = 0
Examine the rotation. Which best describes point D?
angle of rotation
center of rotation
image
pre-image
Answers
Answer:
The answer is the "center of rotation."
Step-by-step explanation:
The center of rotation is the point at which an image is rotated to create a second image. That is what has occurred here at point D, therefore it is the center of rotation.
I hope this helps! ☺
When a shape is rotated, it must be rotated through a point.
Point D is the center of rotation
From the diagram, we have:
Triangle ABCTriangle A'B'C'Point DNotice that the triangles are located at either sides of point D
A general rule of rotation is that
The image and the pre-image of the shape that is being rotated will be at the either sides of the center of rotation.
Hence. point D represents the center of rotation.
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The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years?
Answers
Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15
How to find the value of the car in 4 yearsThe value of the car is solved by using the formula for depreciation which is y = A(1 – r)t
definition of variables
where
y = current value, = ?
A = original cost, = $24,000
r = rate of depreciation, = 15% and
t = time, in years. = 4 years
substituting the variables
current value, y = A(1 – r)t
current value, y = 24000 * (1 - 0.15)⁴
current value, y = 12528.15
the depreciation is $12528.15
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what is the median of numbers 20,35,28,15,22,36,26
Answers
The median of the given data set is 26.
What is the median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
Given the data set, we need to find the median.
So, let's arrange the numbers from smallest to largest in order to find the median.
\(\sf 15,20,22,26,28,35,36.\)
\(\text{Median}=\sf 26\)
Therefore, the median of the data set is 26.
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Which term can be added to the list so that the greatest common factor of the three terms is 12h3?
36h3, 12h6, __________
Answers
The term that can be added to the list so that the greatest common factor of the three terms 12h3 36h3, 12h6, is 48h5
How can the term be known?A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.
The term that can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12 without any fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.
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An elevator started at the third floor and went up 17 floors, then down 11 floors, and up again 9 floors. Which floor is the elevator on now?
(Be sure to include your number sentence and answer.)
Answers
Answer:
18
Step-by-step explanation:
it is at 18th floor buddy
Answer:18rd floor
Step-by-step explanation:
3 + 17- 11 + 9 = 18
Matthew bought flowers for his mother. Exactly 1/4 of the roses were white. How many roses were white?
Answers
Answer:
1/4
Step-by-step explanation:
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