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
Contact [7]
3 years ago
7

Kellen's boat travels 12 mph. Find the rate of the

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
5 0

<u>Answer:</u>

Rate of  river current is = 3 mph

<u>Explanation: </u>

Given speed of boat in still water is equal to 12mph

We know speed = distance divided by time

Given distance travelled upstream = 6 miles and

that  distance travelled downstream = 10 miles

Let x = rate of river current

and t = time taken to travel 6miles upstream as well as to travel 10 miles downstream

We know, speed downstream = speed of current + speed of boat = x + 12

Speed upstream = speed of current - speed of boat = x - 12

speed downstream = 10 divided by t and speed upstream = 6 divided by t  

so the two equations are -  

\frac{10}{t}=\mathrm{x}+12

and \frac{6}{t}=x-12

dividing the two equations we get  \frac{10}{6}=\frac{(x+12)}{(x-12)}

10 \times(\mathrm{x}-12)=6 \times(\mathrm{x}+12)

solving for x we get x = 3mph  is the rate of river current.

You might be interested in
Find the slope of the line containing points (1,3) (-3,-8)
Dmitry_Shevchenko [17]
Y=mx+c 
1/-3=m3/8+c 
m= 11/4
4 0
3 years ago
A rectangle's length is twice its width. if the perimeter is 66 cm find the width of the rectangle
Lesechka [4]
Perimeter = 2L + 2W

Let x = width and let 2x = length 

Perimeter = 66

2x + 2(2x) = 66

2x + 4x = 66 --> 6x = 66 --> x = 66/6 --> x = 11

The width of the rectangle is 11 cm.

6 0
3 years ago
What is the value of h when the function is converted to vertex form?
Dmitrij [34]

Answer:  The value of 'h' is 3.

Step-by-step explanation:  Given that the vertex form of a function is given by

g(x)=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~~~~~~(i)

We are to find the value of 'h' when the following function is converted to the vertex form.

g(x)=x^2-6x+14~~~~~~~~~~~~~~~~~~~~~~(ii)

From equation (ii), we have

g(x)=x^2-6x+14\\\\\Rightarrow g(x)=x^2-2\times x\times 3+3^2-3^2+14\\\\\Rightarrow g(x)=(x-3)^2-9+14\\\\\Rightarrow G(x)=(x-3)^2+5.

Comparing it with the vertex form (i), we get

h=3.

Thus, the value of 'h' is 3.

4 0
3 years ago
Prove the following identity ​
Deffense [45]

Answer:

sec(x)/(tan xsin(x))=cot^2 x+1 = Ture

Step-by-step explanation:

Verify the following identity:

sec(x)/(tan(x) sin(x)) = cot(x)^2 + 1

Hint: | Eliminate the denominator on the left hand side.

Multiply both sides by sin(x) tan(x):

sec(x) = ^?sin(x) tan(x) (cot(x)^2 + 1)

Hint: | Express both sides in terms of sine and cosine.

Write cotangent as cosine/sine, secant as 1/cosine and tangent as sine/cosine:

1/cos(x) = ^?sin(x)/cos(x) sin(x) ((cos(x)/sin(x))^2 + 1)

Hint: | Simplify the right hand side.

((cos(x)/sin(x))^2 + 1) sin(x) (sin(x)/cos(x)) = (((cos(x)^2)/(sin(x)^2) + 1) sin(x)^2)/(cos(x)):

1/cos(x) = ^?(sin(x)^2 (cos(x)^2/sin(x)^2 + 1))/cos(x)

Hint: | Put the fractions in cos(x)^2/sin(x)^2 + 1 over a common denominator.

Put cos(x)^2/sin(x)^2 + 1 over the common denominator sin(x)^2: cos(x)^2/sin(x)^2 + 1 = (cos(x)^2 + sin(x)^2)/sin(x)^2:

1/cos(x) = ^?sin(x)^2/cos(x) (cos(x)^2 + sin(x)^2)/sin(x)^2

Hint: | Cancel down ((cos(x)^2 + sin(x)^2) sin(x)^2)/(sin(x)^2 cos(x)).

Cancel sin(x)^2 from the numerator and denominator. ((cos(x)^2 + sin(x)^2) sin(x)^2)/(sin(x)^2 cos(x)) = (sin(x)^2 (cos(x)^2 + sin(x)^2))/(sin(x)^2 cos(x)) = (cos(x)^2 + sin(x)^2)/cos(x):

1/cos(x) = ^?(cos(x)^2 + sin(x)^2)/cos(x)

Hint: | Eliminate the denominators on both sides.

Multiply both sides by cos(x):

1 = ^?cos(x)^2 + sin(x)^2

Hint: | Use the Pythagorean identity on cos(x)^2 + sin(x)^2.

Substitute cos(x)^2 + sin(x)^2 = 1:

1 = ^?1

Hint: | Come to a conclusion.

The left hand side and right hand side are identical:

Answer: (identity has been verified)

3 0
2 years ago
Multi-step equations solve the equation
S_A_V [24]
Can you be more specific please
4 0
3 years ago
Read 2 more answers
Other questions:
  • Brady wants to purchase a skateboard that costs $245. So far, he has saved $98 and plans to save
    5·1 answer
  • Solve this equation<br><br><br> -3(6 + 6b) + 4 = -104
    6·1 answer
  • How do I do this activity?
    6·1 answer
  • I need help showing work for 44756/167
    8·2 answers
  • (5.2x + 36.4x + 52)/ (2.6x +13)
    13·1 answer
  • Can i please get help with this geometry test?
    5·2 answers
  • Factor the following 3x + 66y
    8·1 answer
  • A landscaper plants 18 bushes in a 36-foot section of land along the side of a house. How many bushes does the landscaper plant
    12·1 answer
  • Im not good at percentages
    5·1 answer
  • At the average rate of 3.054 in/hr how much snow fell in 15 hours
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!