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3 years ago

12

A curve along a highway is to be designed for cars moving at 100 kilometers per hour. Find the angle of banking if the radius of

the curve is 200 m.

1 answer:

statuscvo [17]3 years ago

5 0

Answer:

hope this will help you

Step-by-step explanation:

.........

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The problem is in the picture.

Semmy [17]

Answer:

an = 5 + 10(n -1)
a7 = 65

Step-by-step explanation:

The explicit formula for the n-th term of an arithmetic sequence is ...

an = a1 + d(n -1)

where a1 is the first term and d is the common difference.

The sequence of seat counts has a1=5 and d=10, so the explicit formula is ...

an = 5 +10(n -1)

___

The 7th term is ...

a7 = 5 +10(7 -1) = 65

5 0

3 years ago

What is the volume of the following rectangular prism below?

Yakvenalex [24]

28 units cubed I believe to be the right answer

4 0

3 years ago

A gardener grows sunflowers and records the heights, y , in centimeters, each day, x . The table shows the gardener’s data.

PolarNik [594]

Answer:

Explanation is in a file

Step-by-step explanation:

5 0

2 years ago

A shark swims at a rate of 18 feet per second while chasing his prey and then slows down to a rate of 7 feet per second. The sha

solong [7]

The answer would be, B

7 0

3 years ago

Water is leaking out of a large barrel at a rate proportional to the square rooot of the depth of the water at that time. If the

sdas [7]

Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let $y(t)$ be the depth of water in the barrel at time $t$ , where $y$ is measured in inches and $t$ in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

$\frac{dy}{dt}=-k\sqrt{y}$

where $k$ is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by $\frac{1}{\sqrt{y}}$

$\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k$

Multiply by $dt$

$\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt$

Take integral

$\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt$

Integrate

$2\sqrt{y}=-kt+C$

Isolate $y$

$y(t)=(\frac{C}{2} -\frac{k}{2}t)^2$

We know that the water level starts at 36, this means $y(0)=36$ . We use this information to find the value of $C$ .

$36=(\frac{C}{2} -\frac{k}{2}(0))^2\\C=12$

$y(t)=(\frac{12}{2} -\frac{k}{2}t)^2\\\\y(t)=(6 -\frac{k}{2}t)^2$

At t = 1, y = 34

$34=(6 -\frac{k}{2}(1))^2\\k=12-2\sqrt{34}$

So our formula for the depth of water in the barrel is

$y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\$

To find the time, $t$ , at which all the water leaks out of the barrel, we solve the equation

$\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49$

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

5 0

3 years ago