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ad-work [718]
3 years ago
8

In still water, a boat averages 12 miles per hour. It takes the same amount of time to travel 14 miles downstream, with the curr

ent, as it does 7 miles upstream, against the current. What is the rate of the waters current?
Mathematics
1 answer:
anyanavicka [17]3 years ago
8 0
T is equal in both situations ... d = r X t   so d/r = t
c is rate of waters current

\frac{14}{12+c} = \frac{7}{12-c}
14(12 - c) = 7(12 + c)
2(12 - c) = 12 + c
24 - 2c = 12 + c
12 = 3c
4 = c     The rate of the waters current is 4 miles per hour.
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What is the value of w?
sergeinik [125]

Answer:  Most likely, the value of w is 5 units.

Step-by-step explanation: P = 2L + 2w

If the perimeter is 28, the side lengths must be less than 14, otherwise there is no width, just two lines on top of one another.

If the width is 7, then all four sides would be 7 units, and <u>that would create a square</u>-- which is a type of rectangle-- but probably not what this question is about.

A width of 5 units makes sense, 2w would be 10, leaving 28-10 = 18 to be divided by 2 for lengths of 9

The rectangle would have a width of 5 units and a length of 9 units.

7 0
3 years ago
Find the degree of this polynomial. .<br><img src="https://tex.z-dn.net/?f=%20-%205%20%7Bu%7D%5E%7B4%7D%20" id="TexFormula1" tit
Firlakuza [10]

Answer:

4

Step-by-step explanation:

The degree of a polynomial is the highest of the degrees of the polynomial's monomials with non-zero coefficients

5 0
3 years ago
Louis has a rectangular piece of property with an area of 1/3 fourth square miles the length of the property is 2 1/3 miles what
riadik2000 [5.3K]

Answer: b

Step-by-step explanation:

3 0
2 years ago
For which value of a does the following system of equations have no solution? -x+6y=7 , -5x+10ay=32
dlinn [17]

Remark

If the lines are parallel, there are no solutions to the system of equations. Start with the equation you know the most about.

x + 6y = 7                Subtract x from both sides

x - x + 6y = 7 - x      Combine

6y =  - x + 7             Switch and divide by 6

y = -x / 6 + 7/6

The general equation for a line is y = mx + b where m is the slope of the line.

m = - 1/6

================

Now look at the second equation

10ay - 5x = 32               Add 5x to both sides

10ay = 5x + 32              Divide by 10a

y = (5/10a)x + 32/(10a)  

===============

Now you must make

5/10a = - 1/6                     Cross Multiply

5* 6 = - 10a * 1

30 = - 10a                        Divide by - 10

a = 30 / - 10

a = - 3

So these two equations will have no solution when a = - 3



8 0
3 years ago
The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours
ella [17]

Answer:

137

Step-by-step explanation:

Use the model A = Pe^(kt), where P is the initial number and k is the growth constant.  Then, in case 1,

300 = Pe^(k*3)

and in case 2,

4000 = Pe^(k*10).  We need to find P and e^k.

300 = Pe^(k*3) can be rewritten as (300/P) = [e^k]^3, which in turn may be solved for e^k:

∛(300/P) = e^k

Now we go back to 4000 = Pe^(k*10) and rewrite it as (4000/P) = [e^k]^10.  Substituting ∛(300/P) for e^k, we obtain:              

(4000/P) =  (300/P )^(10/3)

which must now be solved for P.  Raising both sides by the power of 3, we get:

(4000/P)^3 = (300/P)^10.  Therefore,

4000^3       300^10

------------- = -------------

   P^3             P^10

which reduces to:

4000^3       300^10

------------- = -------------

       1             P^7

or

        1         P^7

------------  =  -----------

4000^3       300^10

or:

           300^10

P^7 = ---------------- = 9.226*10^13  = 92.26*10^12

           4000^3

Taking the 7th root of both sides results in P = (92.26*10^12)^(1/7), or

                                                                        P = 137.26

The initial number of bacteria was 137.

7 0
2 years ago
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