Answer:
The streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h
Step-by-step explanation:
Let v = streamer's speed in still water and v' = stream's speed. His speed upstream is V = v + v' and his speed downstream is V' = v - v'.
Since he travels 36 km upstream, the time taken is t = 36/V = 36/(v + v').
he travels 32 km downstream, the time taken is t' = 32/V' = 32/(v - v')
The total time is thus t + t' = 36/(v + v') + 32/(v - v')
Since the whole trip takes 6,5 hours,
36/(v + v') + 32/(v - v') = 6.5 (1)
Multiplying each term by (v + v')(v - v'), we have
(v + v')(v - v')36/(v + v') + (v + v')(v - v')32/(v - v') = 6.5(v + v')(v - v') (1)
(v - v')36 + (v + v')32 = 6.5(v + v')(v - v') (1)
36v - 36v' + 32v + 32v' = 6.5(v² + v'²)
68v - 4v' = 6.5(v² + v'²) (2)
Also he travels 4 km upstream, the time taken is t" = 4/V = 4/(v + v').
he travels 40 km downstream, the time taken is t'" = 40/V' = 40/(v - v')
The total time is thus t" + t'" = 4/(v + v') + 40/(v - v')
Since the whole trip takes 180 minutes = 3 hours,
4/(v + v') + 40/(v - v') = 3 (3)
Multiplying each term by (v + v')(v - v'), we have
(v + v')(v - v')4/(v + v') + (v + v')(v - v')40/(v - v') = 3(v + v')(v - v') (1)
(v - v')4 + (v + v')40 = 3(v + v')(v - v') (1)
4v - 4v' + 40v + 40v' = 3(v² + v'²)
44v - 36v' = 3(v² + v'²) (4)
Dividing (2) by (4), we have
(68v - 4v')/(44v - 36v') = 6.5(v² + v'²)/3(v² + v'²)
(68v - 4v')/(44v - 36v') = 6.5/3
3(68v - 4v') = 6.5(44v - 36v')
204v - 12v' = 286v - 234v'
204v - 286v = 12v' - 234v'
-82v = -222v'
v = -222v'/82
v = 111v'/41
Substituting v into (2), we have
68v - 4v' = 6.5(v² + v'²)
68(111v'/41) - 4v' = 6.5[(111v'/41)² + v'²]
[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²
[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²
[7548/41 - 4]v' = 6.5[12321/1681 + 1]v'²
[(7548 - 164)/41]v' = 6.5[(12321 + 1681)/1681]v'²
[7384/41]v' = 6.5[14002/1681]v'²
[7384/41]v' = [91013/1681]v'²
[91013/1681]v'² - [7384/41]v' = 0
([91013/1681]v' - [7384/41])v' = 0
⇒ v' = 0 or ([91013/1681]v' - 7384/41) = 0
⇒ v' = 0 or [91013/1681]v' - 7384/41) = 0
⇒ v' = 0 or v' = 7384/41 × 16841/91013
⇒ v' = 0 or v' = 180.097 × 0.185
⇒ v' = 0 or v' = 33.33 km/h
Since v' ≠ 0, v' = 33.33 km/h
Substituting v' into v = 111v'/41 = 111(33.33 km/h)/41 = 3699.63 km/h ÷ 41 = 90.23 km/h
So, the streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h
2.5kg of potatoes cost $1.40 work out the cost of 4.25 kg of potatoes
Answer:
Cost of 4.25 kilogram potato = $2.38 (Approx.)
Step-by-step explanation:
Given:
Cost of 2.5 kilogram potato = $1.40
Find:
Cost of 4.25 kilogram potato
Computation:
Cost potato = Amount of potato need[Price of y potato / Amount of y potato]
Cost of 4.25 kilogram potato = [4.25][1.40 / 2.5]
Cost of 4.25 kilogram potato = [4.25][0.56]
Cost of 4.25 kilogram potato = 2.38
Cost of 4.25 kilogram potato = $2.38 (Approx.)
HELP ME PLS- math question
Answer:
x+2x+90 =180
3x =180
x =60
x=2y
2y=60
y=30
2y +z =180
z =180-60
. z =120
A scientist uses a submarine to study ocean life.
*She begins at sea level, which is an elevation of 0 feet.
*She descends for 91 seconds at a speed of 2.2 feet per second.
*She then ascends for 32 seconds at a speed of 0.7 feet per second.
At this point, what is her elevation, in feet?
if you anserw corectly ill give you crown and more points
Answer:
-177.8 feet below sea level.
Step-by-step explanation:
First, we know that decend means to lower. Anything lower than 0 has to be negative. It says that she decends for 91 seconds at a speed of 2.2 feet per second. So first to find out how many feet she descended in those 91 seconds, you need to multiply 91*-2.2= -200.2. Then, it says that she ascends for 32 seconds at the speed of 0.7 feet per second. It's the same thing, but ascend means to go up. So, we multiply 32*0.7=22.4. Now we add the two numbers together to get -177.8.
Hope this helps!
For a function g(x), the difference quotient is StartFraction 6 Superscript x + h minus 3 Baseline minus 6 Superscript x + 3 Baseline Over h EndFraction. What is the average rate of change of g(x) on the interval from x = –2 to x = 1?
Answer:
The average rate of change in that interval is 1.99
Step-by-step explanation:
Here we have that the difference quotient for g(x) is:
[tex]\frac{6^{x + h} - 3 - 6^x + 3}{h}[/tex]
Remember that for a general function f(x), the difference quotient is:
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
So if we look at the difference quotient for g(x), we can conclude that:
[tex]g(x) = 6^x - 3[/tex]
Also remember that the average rate of change in an interval (a, b) is just:
[tex]\frac{g(b) - g(a)}{b - a}[/tex]
So here we want the average rate of change of g(x) in the interval from x = -2 to x = 1, this is:
[tex]R = \frac{(6^1 - 3) - (6^{-2} - 3)}{1 - (-2)} = \frac{6 - 6^{-2}}{3} = 1.99[/tex]
The average rate of change in that interval is 1.99
8/-5. + -1/2 how do you do it because I really don't know
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{ - 21}{10} \:(or) \: - 2 \frac{1}{10} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{8}{ - 5} + ( \frac{ - 1}{2} )[/tex]
[tex] \\= \frac{ - 8}{5} - \frac{1}{2} [/tex]
Since the denominators are unequal, we find the L.C.M (lowest common multiple) for both denominators.
The L. C. M for 5 and 2 is 10.
Now, multiply the L.C.M. with both numerator & denominator.
[tex]\\ = \frac{ - 8 \times 2}{5 \times 2} - \frac{1 \times 5}{2 \times 5} [/tex]
[tex] \\= \frac{ - 16}{10} - \frac{5}{10} [/tex]
Now that the denominators are equal, we can subtract the numerators.
[tex] \\= \frac{ - 16 - 5}{10} [/tex]
[tex] \\= \frac{ - 21}{10} [/tex]
[tex] \\= - 2 \frac{1}{10} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♨}}}}}[/tex]
Answer:
-21/10
Step-by-step explanation:
-8/5. + -1/2
2(-8/5) + (-1/2)5
-16/10 - 5/10
-21/10
(Find m∠IGH) m∠IGH=
Answer:
angle IGH = 50 degree
Step-by-step explanation:
triangle GHI is an isosceles triangle because it's two sides are equal.
if angle I is 50 degree then angle G is also 50 degree becasue in isosceles triangle the base angles are equal.
The length of a rectangle is 18 cm and the width is 6 cm. A similar rectangle has a width of 2 cm.What is the length of the second rectangle? pls help im solving hw ._.
Given:
Two rectangles are similar.
Length of first rectangle = 18 cm
Width of first rectangle = 6 cm
Width of second rectangle = 2 cm
To find:
The length of the second rectangle.
Solution:
We know that the corresponding sides of similar triangles are proportional. So,
[tex]\dfrac{\text{Length of first rectangle}}{\text{Width of first rectangle}}=\dfrac{\text{Length of second rectangle}}{\text{Width of second rectangle}}[/tex]
Let x be the length of the second rectangle. Then,
[tex]\dfrac{18}{6}=\dfrac{x}{2}[/tex]
[tex]3=\dfrac{x}{2}[/tex]
[tex]3\times 2=x[/tex]
[tex]6=x[/tex]
Therefore, the length of the second rectangle is 6 cm.
Help
Will
Give
BRIANLIST
Answer
The system of inequalities below describes the relationship between Cori's age C and Livy's age L. C + L ≥ 43 C - 4L ≤ 3 Livy could be 13 years old and Cori could be 35 years old.
Answer:
Cori could be 35 years old.
Livy could be 8 years old
Step-by-step explanation:
Given
[tex]C + L \ge 43[/tex]
[tex]C - 4L \ge 3[/tex]
Required
Possible values of C and L
Make C the subject in: [tex]C - 4L \ge 3[/tex]
[tex]C \ge 3 + 4L[/tex]
Substitute for C in [tex]C + L \ge 43[/tex]
[tex]3 + 4L + L \ge 43[/tex]
[tex]3 + 5L \ge 43[/tex]
Collect like terms
[tex]5L \ge 43-3[/tex]
[tex]5L \ge 40[/tex]
Solve for L
[tex]L \ge 8[/tex]
Solve for C
[tex]C \ge 3 + 4L[/tex]
[tex]C \ge 3 + 4 * 8[/tex]
[tex]C \ge 35[/tex]
Select the correct answer. The elevations of five points below sea level are given here. Which elevation is closest to sea level? A. -50 feet B. -68 feet C. -77 feet D. -86 feet E. -97 feet
Answer:
the answer is B i think
Step-by-step explanation:
In the circle below, segment AB is a diameter. If the length of arc ACB is 6pi what is the length of the radius of the circle?
Answer:
12
Step-by-step explanation:
Length of the radius of the circle is equals to 6units.
What is length of the arc?" Length of the arc is defined as the distance between two point as a part of the circumference of the given curve."
Formula used
Length of the arc = rθ
r = radius of the circle
θ = central angle
Radius = [tex]\frac{diameter}{2}[/tex]
According to the question,
Given,
Diameter = AB
Length of the arc = 6pi
Here central angle formed with diameter 'θ' = 180°
= [tex]\pi[/tex]
Substitute the value in the length of the arc formula we get,
[tex]6\pi = r \pi[/tex]
⇒ [tex]r = 6units[/tex]
Hence, length of the radius of the circle is equals to 6units.
Learn more about length of the arc here
https://brainly.com/question/16403495
#SPJ2
Find f(-3) PLEASE HELP
Answer:
2
Step-by-step explanation:
When the point on the x-axis is on -3, the point on the y-axis is 2. Therefore, f(-3) is equal to 2.
If this helps please mark as brainliest
Name the ordered pair for point H.
25 points if answered.
Answer:
H=(1,3)
This because the x-axis position is 1, and the y-axis position is 3.
what is the common difference for this arthimitic sequence? -8, -13, -18, -23
a. 5
b. -5
c. -28
d. -21
you have five dollar bills and ten dollars bills for a total amount of $325. you have a total of 37 bills. A) write a system of linear equations that models the situation. B) how many of each type of bill do you have?
Answer:
nine $5 bills and twenty-eight $10 bills
Step-by-step explanation:
f = # of five dollar bills
t = # of ten dollar bills
system of equations:
t + f = 37
10t + 5f = 325
solve the first equation for 't' to get:
t = 37-f
substitute '37-f' to 't' in second equation to get:
10(37-f) + 5f = 325
370 - 10f + 5f = 325
-5f = -45
f = 9
t + 9 = 37
t = 28
pls help in this
7.6x5.2
Answer:
39.52
Step-by-step explanation:
Answer:
Table multiplication:
7.6 times
5.2 =
15.2
38.0
—-
39.52
angle2 cong angle5 so A|| B
Answer:
False
Step-by-step explanation:
If angle 2 and angle 5 are equal in length, then what we have is that the two lines are not parallel
For the two lines to be parallel, these two angles should be supplementary
what this mean is that these two angles should add up to give 180 degrees
Someone help me with this please!
Answer: y=40
Step-by-step explanation: 70-30=40
Jodi has two bank accounts. Her parents started Account A for her. It currently has $100 in it, and Jodi deposits $20 into it each month. Jodi's grandparents started Account B for her. It currently has $300 in it, and her grandparents deposit $40 into it each month.
Answer:
(f+g)(x) = 60x + 400
Step-by-step explanation:
Given :
Amount in account A:
f(x) = 20x + 100
Amount in account B :
g(x) = 40x + 300
Total amount in Account A and B:
f(x) + g(x) = (20x + 100) + (40x + 300)
(f+g)(x) = (20x + 40x) + (100 + 300)
(f+g)(x) = 60x + 400
Drag each tile to the correct box
Arrange the following pairs of coordinates in order from least to greatest based on the distances between the points.
(4.1) and (2, 2)
(-5. 2) and (-3, -2)
(3.-4) and (-2, 1)
(-1.-2) and (1-4)
(5.-2) and (-1, -1)
Answer:
Step-by-step explanation:
Use the formula of distance between two points (x₁, y₁) and (x₂, y₂),
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
1). Distance between (4, 1) and (2, 2) = [tex]\sqrt{(4-2)^2+(1-2)^2}[/tex]
= [tex]\sqrt{5}[/tex]
= 2.24
2). Distance between (-5, 2) and (-3, -2) = [tex]\sqrt{(-5+3)^2+(2+2)^2}[/tex]
= [tex]\sqrt{20}[/tex]
= 4.47
3). Distance between (3, -4) and (-2, 1) = [tex]\sqrt{(3+2)^2+(-4-1)^2}[/tex]
= [tex]\sqrt{50}[/tex]
= 7.07
4). Distance between (-1, -2) and (1, -4) = [tex]\sqrt{(1+1)^2+(-4+2)^2}[/tex]
= [tex]\sqrt{8}[/tex]
= 2.83
5). Distance between (5, -2) and (-1, -1) = [tex]\sqrt{(5+1)^2+(-2+1)^2}[/tex]
= [tex]\sqrt{37}[/tex]
= 6.08
Therefore, increasing order of the distance will be 2.24 > 2.83 > 4.47 > 6.08 > 7.07
Answer:
Use the formula of distance between two points (x₁, y₁) and (x₂, y₂),
Distance =
1). Distance between (4, 1) and (2, 2) =
=
= 2.24
2). Distance between (-5, 2) and (-3, -2) =
=
= 4.47
3). Distance between (3, -4) and (-2, 1) =
=
= 7.07
4). Distance between (-1, -2) and (1, -4) =
=
= 2.83
5). Distance between (5, -2) and (-1, -1) =
=
= 6.08
Therefore, increasing order of the distance will be 2.24 > 2.83 > 4.47 > 6.08 > 7.07
Step-by-step explanation:
Which number represents the probability of an event that is very likely to occur?
A. O 0.09
B. O 0.12
C. O 0.3
D. O 0.95
Answer:
D
Step-by-step explanation:
higher amount then the rest
In the diagram below of triangle PQS, S is the midpoint of PR and T is the midpoint of QR. If ST = 5x - 22, and PQ = 3x + 19, what is the measurement of PQ?
Answer:
PQ = 46
Step-by-step explanation:
The midsegment ST is half the length of the third side PQ , that is
ST = [tex]\frac{1}{2}[/tex] PQ , so
5x - 22 = [tex]\frac{1}{2}[/tex] (3x + 19) ← multiply both sides by 2 to clear the fraction
10x - 44 = 3x + 19 ( subtract 3x from both sides )
7x - 44 = 19 ( add 44 to both sides )
7x = 63 ( divide both sides by 7 )
x = 9
Then
PQ = 3x + 19 = 3(9) + 19 = 27 + 19 = 46
Brainiest will be given . Please help me
Answer:
If the shape of end face has n sides
Then, in total, there are n+2 faces
Using that formula
Faces in 20-sided polygon = n+2 = 20+2 = 22
Step-by-step explanation:
Pls vote as brainliest
2 to the negative 3 power times how much is 2 to the negative 1 power? Does the answer match your answer from question 3b? Why or why not?
Answer: 2^-3 = 1/8
2^-1 = 1/2
you have to multiply 2^-3 by 4 to get to 2^-1
Step-by-step explanation:
someone help!!!!!!!!
Answer:
Top right
Step-by-step explanation:
First, we have "h is increasing on the interval (3, +∞)." This means that h must be increasing for all values 3 and higher. This is shown on the top left, top right, and bottom right graphs because when x goes up on each of them, the function increases as well. However, for the bottom left graph, this is not shown because as x goes from 3 to 4, the function decreases.
Next, the statement given is "h(4)=2". This means that when the x value is 4, the y value is equal to 2. This is true for the top left and top right pictures. However, for the bottom right, as the x value is 4 on the x axis, the corresponding y value is 1, not 2.
This leaves us with the top left and top right. The final characteristic given is "The domain of h is [3, +∞). This means that the x values of said function only go from 3 to infinity. As the top left graph has values of x below 3, this leaves the top right graph as h
Which transformations could have occurred to map
AABC to AA"B"C?
O a rotation and a reflection
O a translation and a dilation
O a reflection and a dilation
O a dilation and a rotation
The transformations that could map ABC to A"B"C" are: (d) a dilation and a rotation
From the figure, we have the following highlights:
Triangle A"B"C is smaller than triangle ABCThe side lengths of both triangles are in equivalent ratioTriangle ABC is rotated about point C to form triangle A"B"CThe above highlights mean that:
The transformations that could map ABC to A"B"C" are dilation and rotation
Hence, option (d) is true
Read more about transformations at:
https://brainly.com/question/4289712
five fifth-grade teachers and six fourth-grade teachers ordered 2 large pizzas all together how much will each person need to pay.
Answer:
$5.50
Step-by-step explanation:
5+6= 11
11/2
can someone help me i dont understand
Answer:
8900000 * 10^-3
Step-by-step explanation:
(8.9*10^-3)/(10^-6)
(8.9*10^-3)/(1/1000000)
8.9*10^-3* 1000000
8900000 * 10^-3
" El ingreso mensual de una empresa está dado por la siguiente ecuación: (0,2) 10000(0,95) p I , dondep es la cantidad gastada en publicidad:a) ¿Cuál es el ingreso total, cuando no se tienen gastos publicitarios?b) ¿Cuál es el valor del ingreso total, si $ 15 es el gasto mensual en promoción?"
Respuesta:
Ingresos = 9500
Ingresos = 8573,75
Explicación paso a paso:
La ecuacion:
Yo = 10000 (0,95) ^ (0,2) p
p = monto gastado en publicidad
Los ingresos totales cuando no hay gastos:
p = 0
Yo = 10000 (0,95) ^ (0,2) * 0
Yo = 10000 (0,95) ^ 0
Yo = 10000 (0,95)
Yo = 9500
Si el gasto mensual de la promoción es de $ 15
p = $ 15
Yo = 10000 (0,95) ^ (0,2) * 15
Yo = 10000 (0,95) ^ 3
Yo = 10000 (0,857375)
Yo = 8573,75
and angle is 21 more than twice its complement find it
Answer:
angle = 67°
Step-by-step explanation:
let
a = angle in degrees
(90-a) = complement
given
a = 2(90-a)+21
Solve for a
a = 180 - 2a + 21
3a = 201
a = 67°