Ask question

Ask question

All categories

Studentka2010 [4]

2 years ago

9

You need to stabilize a flagpole by string in a guy-wire from the top of a flagpole to the ground. The pole is 15 feet tall and

angle of elevation is 70 degrees. Using trig ratios calculate how much wire is needed

2 answers:

Mandarinka [93]2 years ago

7 0

Sinα=h/w

w=h/sinα, we are told that h=15 ft and α=70° so

w=15/sin70° ft

w≈15.96 ft (to nearest hundredth of a foot)

Leto [7]2 years ago

6 0

<h2>Answer:</h2>

The length of the wire needed is:

15.9625 feet

<h2>Step-by-step explanation:</h2>

We will model this problem with the help of a right angled triangle such that the side opposite to the angle 70 degree is: 15 feet.

Now, we are asked to find the amount of wire used i.e. we are asked to find the hypotenuse of the right angled triangle.

We will use the sine trignometric ratio as follows:

$\sin 70=\dfrac{15}{x}\\\\i.e.\\\\x=\dfrac{15}{\sin 70}\\\\i.e.\\\\x=\dfrac{15}{0.9397}\\\\i.e.\\\\x=15.9625\ feet$

You might be interested in

g Assume that the distribution of time spent on leisure activities by adults living in household with no young children is norma

OLga [1]

Answer:

"<em>The probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day</em>" is about 0.8749.

Step-by-step explanation:

We have here a <em>random variable</em> that is <em>normally distributed</em>, namely, <em>the</em> <em>time spent on leisure activities by adults living in a household with no young children</em>.

The normal distribution is determined by <em>two parameters</em>: <em>the population mean,</em> $\\ \mu$ , and <em>the population standard deviation,</em> $\\ \sigma$ . In this case, the variable follows a normal distribution with parameters $\\ \mu = 4.5$ hours per day and $\\ \sigma = 1.3$ hours per day.

We can solve this question following the next strategy:

Use the <em>cumulative</em> <em>standard normal distribution</em> to find the probability.
Find the <em>z-score</em> for the <em>raw score</em> given in the question, that is, <em>x</em> = 6 hours per day.
With the <em>z-score </em>at hand, we can find this probability using a table with the values for the <em>cumulative standard normal distribution</em>. This table is called the <em>standard normal table</em>, and it is available on the Internet or in any Statistics books. Of course, we can also find these probabilities using statistics software or spreadsheets.

We use the <em>standard normal distribution </em>because we can "transform" any raw score into <em>standardized values</em>, which represent distances from the population mean in standard deviations units, where a <em>positive value</em> indicates that the value is <em>above</em> the mean and a <em>negative value</em> that the value is <em>below</em> it. A <em>standard normal distribution</em> has $\\ \mu = 0$ and $\\ \sigma = 1$ .

The formula for the <em>z-scores</em> is as follows

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Solving the question

Using all the previous information and using formula [1], we have

<em>x</em> = 6 hours per day (the raw score).

$\\ \mu = 4.5$ hours per day.

$\\ \sigma = 1.3$ hours per day.

Then (without using units)

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{6 - 4.5}{1.3}$

$\\ z = \frac{1.5}{1.3}$

$\\ z = 1.15384 \approx 1.15$

We round the value of <em>z</em> to two decimals since most standard normal tables only have two decimals for z.

We can observe that z = 1.15, and it tells us that the value is 1.15 standard deviations units above the mean.

With this value for <em>z</em>, we can consult the <em>cumulative standard normal table</em>, and for this z = 1.15, we have a cumulative probability of 0.8749. That is, this table gives us P(z<1.15).

We can describe the procedure of finding this probability in the next way: At the left of the table, we have z = 1.1; we can follow the first line on the table until we find 0.05. With these two values, we can determine the probability obtained above, P(z<1.15) = 0.8749.

Notice that the probability for the z-score, P(z<1.15), of the raw score, P(x<6) are practically the same, $\\ P(z$ . For an exact probability, we have to use a z-score = 1.15384 (without rounding), that is, $\\ P(z$ . However, the probability is approximated since we have to round z = 1.15384 to z = 1.15 because of the use of the table.

Therefore, "<em>the probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day</em>" is about 0.8749.

We can see this result in the graphs below. First, for P(x<6) in $\\ N(4.5, 1.3)$ (red area), and second, using the standard normal distribution ( $\\ N(0, 1)$ ), for P(z<1.15), which corresponds with the blue shaded area.

5 0

2 years ago

The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillat

Greeley [361]

Answer:

1) $L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

2) $T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

3) $T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

Step-by-step explanation:

Part 1

For this case we know the following info: The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillation), T seconds.

$L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

Part 2

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

Part 3

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

Replacing we got:

$T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

8 0

2 years ago

Joy makes 6.5 litres of soup, correct to the nearest 0.5 litre. She serves the soup in 280 ml portions, correct to the nearest 1

Levart [38]

Answer:

Joy definitely does have enough soup for 22 people.

Step-by-step explanation:

Upper Bound: 285ml turn it to 0.285 L 10÷2=5

280ml :

Lower Bound: 275ml turn it to 0.275 L

Upper Bound: 6.75 L 0.5÷2=0.25

6.5 Litters :

Lower Bound:6.25 L

6.75÷0.275=24.54 or 25

6.25÷0.285=21.92 or 22

7 0

2 years ago

Read 2 more answers

Please help! Tim and Jane both work at a company that sells boxes of breakfast cereal. The boxes of cereal cost £3.00 and the am

patriot [66]

Answer: Jane needs to reduce the price by 20%

Step-by-step explanation: The first thing to note is the original price of the cereal and that is given as £3 for every 160 grams.

The change proposed by Tim is as follows;

Put 25% more cereal in the box (and do not change the price). That means 160 g plus 25%. Mathematically, this can be expressed as;

New weight = 160 + (160 * 25%)

New weight = 160 + (160 * 0.25)

New weight = 160 + 40

New weight = 200

Hence, Tim's idea would result in a cereal box with 200 grams that still cost £3. At this rate, each gram would cost

1 gram = Price / Total grams

1 gram = 3/200

1 gram = 0.015

However, Jane has proposed that the amount of cereal in the box should not be changed, which means the box of cereals should remain 160 grams. The price should be reduced to give the same value as Tim's idea. This means 160 g of cereals should now sell for £0.015 per gram. That would bring the price of 160 g to,

1 gram = 0.015

160 grams = 0.015 * 160

160 grams = 2.4

With Jane's proposal, a 160 g box of cereal should now be sold at £2.4 each. That is a reduction of £0.6

Therefore, the percentage reduction can be calculated as follows;

% decrease = (0.6/3) * 100

% decrease = (1/5) * 100

% decrease = 20

From the results above, Jane should reduce the price (£3 per 160 g) by 20%.

7 0

3 years ago

The mayor of Brookmarsh is running a campaign to revitalize his city. Currently, the population of Brookmarsh is 10,000 and is i

lisabon 2012 [21]

The equation correctly modeled would be

1000+.02t = 15000

8 0

2 years ago