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2 years ago

Beth is using triangular shaped pieces to cover the front of a pillow. The base of each triangle is 9 inches and the height of

Mathematics

2 answers:

Anarel [89]2 years ago

8 0

The answer is 27 square inches

dezoksy [38]2 years ago

8 0

The answer is 27 square inches

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A sailboat is sitting at rest near its dock. A rope attached to the bow of the boat is drawn in over a pulley that stands on a p

irina [24]

Answer:

The boat is approaching the dock at rate of 2.14 ft/s

Step-by-step explanation:

The situation given in the question can be modeled as a triangle, please refer to the attached diagram.

A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.

The length of rope from bow to pulley is 13 feet that means y = 13 ft.

We know that Pythagorean theorem is given by

$x^{2} + y^{2} = z^{2}$

Differentiating the above equation with respect to time yields,

$2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}$

$x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}$

dx/dt = 0 since dock height doesn't change

$y\frac{dy}{dt} = z\frac{dz}{dt}$

$\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}$

The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s

First we need to find z

z² = (5)² + (13)²

z² = 194

z = √194

z = 13.93 ft

So,

$\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}$

$\frac{dy}{dt} = \frac{13.93}{13}(2)$

$\frac{dy}{dt} = 2.14$ $ft/s$

Therefore, the boat is approaching the dock at rate of 2.14 ft/s

8 0

1 year ago

R=2s-6t+5 / 2 , solve for s

cestrela7 [59]

S = R + 3t - 5/2

multiply the r by the 2 and transfer -6t and 5 over to the left side which makes them +6t and -5, then divide the whole left side by 2 which gives you s

5 0

1 year ago

Tobias gold sells computers at the office Center he's guaranteed a minimum salary of $1,959 per month plus 6.3% commission on to

ICE Princess25 [194]

Answer:2269.95

Step-by-step explanation:

You would take 1,959 and divide it by 6.3. The answer of that will be added to 1,959. And that's how I got the answer good luck! And I hope that this helps.

Also quick note 2269.95 is how much is made in a month! :)

6 0

1 year ago

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Mr. Singh needed to understand the trend of his students’ latest test scores. Find the mean and median for each set of data, and

marishachu [46]

Answer:

The Median should be 89.5

And the mean should be 69.75

I hope that helped

9 0

2 years ago

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Eric is studying people's typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a per

hichkok12 [17]

Answer:

The confidence interval is (0.81, 0.87).

Step-by-step explanation:

There's 90% confidence that population proportion is within the interval obtained from the following formula:

$\hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}*(1-\hat{p})}{n}}$

Knowing that the sample size, $n=525$ we obtain the proportion of people from the sample who leave one space after a period as $\hat{p}=\frac{440}{525}=0.8381\approx 0.84$ .

We then look for the critical value:

$z_{\alpha/2}=1.645$

Now we can replace in the formula to obtain the confidence interval:

$0.84\pm 1.645\sqrt{\frac{0.84*(1-0.84)}{525}}= (0.8137; 0.8663)$

Therefore we can say that there's 90% probability that the population proportion of people who leave one space after a period lies between the values (0.8137; 0.8663).

3 0

1 year ago

Read 2 more answers