1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zloy xaker [14]
3 years ago
8

Solve and show steps. will award brainliest.

Mathematics
1 answer:
a_sh-v [17]3 years ago
8 0

For the first question please find the attached diagram.

As per the diagram, P is the upstream point and Q is the downstream point. The distance between P and Q is 22.5 miles.

Let the speed of the boat in the still waters of the lake be represented by S.

Then, when the boat travels upstream, the net speed of the boat will be (S-6) miles per hour because the river flows downstream and thus the speed of the boat will have to be subtracted from the speed of the river.

Now, we know that the relationship between the net speed, distance and time of travel is give as:

Distance = Net Speed x Time of travel

For the upstream ride of the board we know that Distance is 22.5 miles and Net Speed is (S-6). Therefore, the above equation will become:

22.5=(S-6)\times T_{1} where T_{1} represents the time taken to travel upstream.

We can rearrange the above equation to be:

T_{1}=\frac{22.5 }{S-6}......................(Equation 1)

By similar arguments we know that the downstream speed of the boat is S+6 and the distance travelled is the same and so the time taken to travel downstream (represented by T_{2}) will be:

T_{2}=\frac{22.5}{S+6}................(Equation 2)

Now, we know that the total time of travel should be 9 hours.

This means that: T_{1}+T_{2}=9............(Equation 3)

Plugging in the values of T_{1} and T_{2} from (Equation 1) and (Equation 2) into (Equation 3), we get:

\frac{22.5 }{S-6} +\frac{22.5 }{S+6}=9

Simplifying the above we will get a quadratic equation:

9S^2-45S-54=0

The roots of this quadratic equation are:

S=-1 and S=6

Since, speed cannot be negative, S=-1 is out of consideration.

The speed of the boat in the lake is thus S=6 miles per hour.

But we have a problem with S=6 too. The problem is that if S=6, then the boat will not be able to move upstream.

Let us solve problem 2

We are given that: \frac{x-2}{x+3}+\frac{10x}{x^2-9}

We can rewrite it as:

\frac{x-2}{x+3}+\frac{10x}{(x-3)(x+3)}

\frac{(x-3)(x-2)+10x}{(x-3)(x+3)} =\frac{x^2-5x+6+10x}{(x-3)(x+3)}

Now, the numerator can be simplified as:

\frac{x^2+10x+6}{(x-3)(x+3)} =\frac{(x+3)(x+2)}{(x-3)(x+3)} =\frac{x+2}{x-3}

Thus, our final simplified answer is:

\frac{x+2}{x-3}

The restriction on the variable x is that it cannot be equal to either +3 or -3 as that would make the denominator of the original question equal to zero.

Thus, the restriction is x\neq \pm 3

You might be interested in
A rectangular jewelry box costs $125 to gold plate. Calculate the cost of gold plating a box which is similar in shape and that
Alja [10]
To determine the amount of gold plating necessary for the similar box, you will use the fact that it is 8 times larger in volume to determine how many times larger the area is.  This would be what you will multiply $125 by.

Volume is a three dimensional measurement, so the fact that it is 8 times larger tells us each dimension was 2 times larger (2 x 2 x 2=8).  

Area is a two dimensional measurement, so the area would have been 2 x 2 or 4 times larger.  This means the price would be 4 times as much.
$125 x 4 = $500.

It will cost $500 to gold plate the similar jewelry box.
7 0
3 years ago
Which expression is equivalent to (3x - 4)(4x - 3)?
Ulleksa [173]

Answer:

1\/48 (24 x - 25)^2 - 49\/48

x (12 x - 25) + 12

Step-by-step explanation:

7 0
3 years ago
25⋅5⋅5⋅4<br><br> A.500<br><br> B.2000<br><br> C.2500<br><br> D.5000
kenny6666 [7]

Answer:

c

Step-by-step explanation:

25 x 5 = 125

125 x 5 = 625

625 x 4 = 2500

So, 25 x 5 x 5 x 4 is 2,500

Vote Brainliest, Thx :)

7 0
3 years ago
Read 2 more answers
Write an equation of the line through the given points<br><br><br>(0, 4), (3, 3)​
andre [41]

Hello! :)

Step-by-step explanation:

Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}

\frac{3-4}{3-0}=\frac{-1}{3}=-\frac{1}{3}

<u><em>Therefore, the slope is -1/3.</em></u>

<u><em>-1/3 is the final answer.</em></u>

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thank you!

4 0
3 years ago
Write the equation in standard form for the circle with center (-3,3) and radius 3
leva [86]

Answer:

(x+3)^2+(y−3)^2=9

Step-by-step explanation:

The equation for a circle is given by

(x−h)^2+(y−k)^2=r^2  where (h,k) is the center and r is the radius

(x− -3)^2+(y−3)^2=3^2

(x+3)^2+(y−3)^2=9

3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the standard form of a line with the x intercept of 4 and y intercept of -2?
    7·1 answer
  • May somebody please help me on this
    9·1 answer
  • Write the following mixed decimal as a mixed number and reduce to the lowest term 17.46 92.004
    5·1 answer
  • Help PLEASE im stucckkkk!!!
    9·1 answer
  • NEED HELP NOW 100 POINTS 2 PHOTOS WILL MARK BRAINLIEST ANSWER!!! HURRY!!!!!!
    7·2 answers
  • 2(4x+9)=8x+18 solve for x
    14·2 answers
  • Look at this angle TUV what are the sides
    14·1 answer
  • 5. Write 8% as a decimal
    10·1 answer
  • A stereo normally priced at $399 is on sale for 15% off. Find the discount and the sale price.
    11·1 answer
  • . 5, 10, 20, 40.....​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!