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Elodia [21]
3 years ago
12

a paddle boat can move at a speed of 6km/h in still water. the boat is paddeled 16km downstream in a river in the same time it t

akes to go 8km upstream what is the speed of the river?
Mathematics
1 answer:
kaheart [24]3 years ago
5 0
v-the\ speed\ of\ the\ river\\\\16:(6+v)=8:(6-v)\\\\\frac{16}{6+v}=\frac{8}{6-v}\\-------------\\multiply\ on\ the\ cross\\-------------\\8(6+v)=16(6-v)\\\\48+8v=96-16v\\\\8v+16v=96-48\\\\24v=48\ \ \ /:24\\\\v=2\ (km/h)\leftarrow Answer
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I need help pretty please!
Naddika [18.5K]

Answer:

cos(z) = .3846153846 and angle z = 67.38°

Step-by-step explanation:

Side UV is corresponding to side YX.  Side VW is corresponding to side YZ.  Side UW is corresponding to side XZ.

Starting with the first corresponding pair, we are told that side UV is 36, and that side YX is 3/5 of that.  So side YX is

\frac{3}{5}*36=21.6

We are next told that side VW is 39, so side YZ is

\frac{3}{5}*39=23.4

In order to find the cos of angle z, we need the adjacent side, which is side XZ.  Side XZ is 3/5 of side UW.  Right now we don't know the length of side UW, so we find it using Pythagorean's Theorem:

39^2-36^2=UW^2 and

UW^2=225 so

UW = 15

Now we can say that side XZ is

\frac{3}{5}*15=9

The cos of an angle is the side adjacent to the angle (9) over the hypotenuse of the triangle (23.4) so our ratio is:

cos(z)=\frac{9}{23.4}

which divides to

cos(z) = .3846153846

If you need the value of the angle, use the inverse cosine function on your calculator in degree mode to find that

angle z = 67.38°

3 0
2 years ago
Match the parabolas represented by the equations with their foci.
Elenna [48]

Function 1 f(x)=- x^{2} +4x+8


First step: Finding when f(x) is minimum/maximum
The function has a negative value x^{2} hence the f(x) has a maximum value which happens when x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2. The foci of this parabola lies on x=2.

Second step: Find the value of y-coordinate by substituting x=2 into f(x) which give y=- (2)^{2} +4(2)+8=12

Third step: Find the distance of the foci from the y-coordinate
y=- x^{2} +4x+8 - Multiply all term by -1 to get a positive x^{2}
-y= x^{2} -4x-8 - then manipulate the constant of y to get a multiply of 4
4(- \frac{1}{4})y= x^{2} -4x-8
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is 12- \frac{1}{4}=11.75

Hence the coordinate of the foci is (2, 11.75)

Function 2: f(x)= 2x^{2}+16x+18

The function has a positive x^{2} so it has a minimum

First step - x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4
Second step - y=2(-4)^{2}+16(-4)+18=-14
Third step - Manipulating f(x) to leave x^{2} with constant of 1
y=2 x^{2} +16x+18 - Divide all terms by 2
\frac{1}{2}y= x^{2} +8x+9 - Manipulate the constant of y to get a multiply of 4
4( \frac{1}{8}y= x^{2} +8x+9

So the distance of focus from y-coordinate is \frac{1}{8} to the north of y=-14
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: f(x)=-2 x^{2} +5x+14

First step: the function's maximum value happens when x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25
Second step: y=-2(1.25)^{2}+5(1.25)+14=17.125
Third step: Manipulating f(x)
y=-2 x^{2} +5x+14 - Divide all terms by -2
-2y= x^{2} -2.5x-7 - Manipulate coefficient of y to get a multiply of 4
4(- \frac{1}{8})y= x^{2} -2.5x-7
So the distance of the foci from the y-coordinate is -\frac{1}{8} south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when x=8.5 and y=79.25. The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when x=-2.75 and y=-10.125. Manipulating coefficient of y, the distance of foci from y-coordinate is \frac{1}{8} to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when x=1.5 and y=9.5. The distance of the foci from the y-coordinate is \frac{1}{8} to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

8 0
3 years ago
A car rental agency rents cars for $26.20 per day plus $0.35 per mile driven. Your travel budget is $200. Write an inequality th
laila [671]

For this case we have to:

x: Represents the number of miles that can be traveled in a day

We have that the cost of daily car rental is given by the following expression:

26.20 + 0.35x

If the person has a budget of $200 then we have to:

26.20+0.35x\leq200\\0.35x\leq200-26.20\\0.35x\leq173.8\\x\leq\frac{173.8}{0.35}\\x\leq496.57

Thus, you can travel 496 miles in one day.

Answer:

26.20 + 0.35x \leq200

6 0
3 years ago
Problem PageQuestion A Web music store offers two versions of a popular song. The size of the standard version is 2.6 megabytes
dalvyx [7]

Answer:

There were 210 downloads of the standard version.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of downloads of the standard version.

y is the number of downloads of the high-quality version.

The size of the standard version is 2.6 megabytes (MB). The size of the high-quality version is 4.2 MB. The total size downloaded for the two versions was 4074 MB.

This means that:

2.6x + 4.2y = 4074

Yesterday, the high-quality version was downloaded four times as often as the standard version.

This means that y = 4x

How many downloads of the standard version were there?

This is x.

2.6x + 4.2y = 4074

Since y = 4x

2.6x + 4.2*4x = 4074

19.4x = 4074

x = \frac{4074}{19.4}

x = 210

There were 210 downloads of the standard version.

8 0
3 years ago
How many meters is a 10 by 3 foot flag?
DENIUS [597]

Answer: 30

Step-by-step explanation:

3 0
3 years ago
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