Please help with c d and e

It takes 3 hours to paddle a kayak 12 miles downstream and 4 hours for the return trip upstream. Find the rate of the kayak in s

Furkat [3]

The rate of the kayak in still water is 3.5 mph

<h3>Solution:</h3>

Given that It takes 3 hours to paddle a kayak 12 miles downstream

Distance covered in downstream = 12 miles

Time taken to cover downstream = 3 hours

Also given that it takes 4 hours for the return trip upstream

Distance covered in upstream = 12 miles

Time taken to cover upstream = 4 hours

Formula to remember:

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then: Speed downstream = (u + v) km/hr and Speed upstream = (u - v) km/hr

Let the speed of Kayak in still water = x mph

And The speed of current = y mph

For downstream:

Speed downstream = x + y

We know that $speed = \frac{distance}{time}$

$\frac{distance}{time} = x + y$

$x + y = \frac{12}{3}$

x + y = 4 ------ eqn 1

For upstream:

Speed upstream = x - y

$\frac{12}{4} = x - y$

x - y = 3 -------- eqn 2

Now let us eqn 1 and eqn 2

Add eqn 1 and eqn 2

x + y + x - y = 4 + 3

2x = 7

x = 3.5

speed of Kayak in still water = x mph = 3.5 mph

6 0

3 years ago

CHOOSE THE CORRECT ANSWER FROM THE BRACKET 1. The sum of 2 integers is zero. If one of them is -5, then the other is------------

Mandarinka [93]

Answer:

c) +5

Step-by-step explanation:

x + y = 0

-5 + (5) = 0

7 0

3 years ago

Read 2 more answers

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

bija089 [108]

Answer: $\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}$

b) 5314

c) ln 2.7

d) 4.6 hrs

Step-by-step explanation:

$P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}$

$10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}$

4 0

3 years ago

At the beginning of spring, Arianna planted a small sunflower in her backyard. When

zhannawk [14.2K]

Answer:

3 weeks: 21.5 inches

w weeks: 20+0.5w inches

Step-by-step explanation:

Equation: 20+0.5w.

20 was when it was first planted and 0.5 is the amount it grows per week.

6 0

3 years ago

How would you translate this situation below into an algebraic expression?

Natasha2012 [34]

Dime value: $0.10
Nickel value: $0.05

For this word problem, you are asked to create an algebraic expression (an equation) for the unknown variables.

Now, we know that a dime is worth $0.10 or 10 cents and a nickel is worth $0.05 or 5 cents. So, all you would have to do is create an equation that takes those values into account.
5n + 10d

Your algebraic expression would be B. 5n + 10d

I hope this helps!

5 0

3 years ago