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2 years ago

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A small boat traveled 29.5 miles upstream in 2 hours. The same boat took 3 hours to travel 59.25 miles downstream. If the speed

and direction of the water was the same in both directions, find the speed of the boat in still water and the speed of the current.

1 answer:

mel-nik [20]2 years ago

5 0

Answer:

boat speed: 17.25 mph
current: 2.5 mph

Step-by-step explanation:

Upstream, the speed of the current (c) subtracts from the speed of the boat (b) to give the net speed. Downstream, the speed of the current adds. We can make use of the relation ...

speed = distance/time

b-c = 29.5/2 = 14.75 . . . . . miles/hour

b+c = 59.25/3 = 19.75 . . . .miles/hour

Subtracting the first equation from the second, we get ...

(b+c) -(b-c) = 19.75 -14.75

2c = 5

c = 2.5

Then either equation can be used to find b:

b = 14.75 +c = 17.25

The speed of the boat in still water is 17.25 miles per hour; the speed of the current is 2.5 miles per hour.

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If the farmer has 234 feet of fencing, what are the dimensions of the region which enclose the maximal area?

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Answer: 58 ft × 58 ft

Step-by-step explanation:

Let the length of the region = x feet

And, the width of the region = y feet

Since, the perimeter of the region = 234 feet ( Given )

⇒ $2(x+y) = 234$

⇒ $x+y = 117$

⇒ $y = 117 - x$

Again the area of the region, A = xy

⇒ $A(x) = x(117-x)$

⇒ $A(x) = 117x - x^2$

By differentiating the above equation with respect to x,

⇒ $A'(x) = 117 - 2x$

For maxima or minima,

$A'(x) = 0$

$\implies 117 - 2x = 0$

$\implies -2x = -117$

$\implies x = 58.5$

Again differentiating equation A'(x) with respect to x,

We get, A''(x) = -2

Hence, For x = 58.5 A''(x) = negative

⇒ For x = 58.5 feet the area A(x) is maximum,

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2 years ago

Read 2 more answers

A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports

hichkok12 [17]

Answer:

1

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

2

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

3

$t = 3.054$

4

The p-value is $p-value = P(Z > 3.054) = 0.0011291$

5

The conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 51$

The first sample mean is $\mu_1 = 36$

The second sample size is $n_2 = 41$

The second sample size is $\mu_2 = 25$

The first standard deviation is $\sigma _1 = 21.4 \ g$

The second standard deviation is $\sigma _2 = 12.8 \ g$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 = \mu_ 2$

The alternative hypothesis is $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }$

=> $t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }$

=> $t = 3.054$

The p-value is mathematically represented as

$p-value = P(Z > 3.054)$

Generally from the z table

$P(Z > 3.054) = 0.0011291$

=> $p-value = P(Z > 3.054) = 0.0011291$

From the values obtained we see that $p-value < \alpha$ so the null hypothesis is rejected

Thus the conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

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