The speed 120 km/h is about<br><br><br><br> 25 m/s<br><br> 33 m/s<br><br> 42 m/s<br><br> 50 m/s

a gym consists of a rectangular region with a semi-circle on each end. if the perimeter of the room is to be a 200 m running tra

Nikolay [14]

The dimensions of the rectangle are:

l = 50 m

b = $100/\pi$ m

<h3>What is a perimeter in math?</h3>

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides.

<h3>How do we find a perimeter of a rectangle?</h3>

The perimeter of a rectangle,denoted by P is given by the formula, P=2l+2b, where l is the length and b is the breadth of the rectangle.

<h3>Given:</h3>

As per the question:

Perimeter of the room is given as P = 200 m

The region is rectangular having a semicircle at each end.

Now,

Let 'l' be the length of the rectangle, 'b' be its breadth and 'r' be the radius of the semi-circle at each end.

Then, Area of the given rectangle, A = lb

Perimeter of the room, P is = $\pi r+l+\pi r+l=2\pi r+2l=\pi b+2l$

Therefore, $\pi b+2l=200$

$b=(200-2l)/\pi$

Now,

Area, A = $l(200-2l)/\pi=(200l-2l^{2} )/\pi$

Now, differentiate A w.r.t l:

Again differentiating w.r.t 'l', we get:

$d^{2} A/dl^{2} =-4l/\pi$ < 0

Thus we get maximum are when $dA/dl=0$

Therefore,

$(200-4l)/\pi=0$

l = 50 m

Now, from

$\pi b+2l=200$

$\pi b=200-2*50$

$b=100/\pi$

$r=b/2=50/\pi$

To know more about area of a recatangle, visit the link

brainly.com/question/20693059

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4 0

1 year ago

Two vectors A and B are added to give a resultant R. The components of A are Ax = -8.0 units and Ay = 6.0 units and the componen

Georgia [21]

Answer:

<em>10.09 units</em>

Explanation:

For the A

Ax = -8.0 units

Ay = 6.0 units

The resultant vector = Ra = $\sqrt{A^2_{x} + A^2_{y} }$

Ra = $\sqrt{(-8)^2 + 6^2 }$ = 10 units

For B

Bx = 1.0 units

By = -1.0 units

The resultant vector = Rb = $\sqrt{B^2_{x} + B^2_{y} }$

Rb = $\sqrt{1^2 + (-1)^2 }$ = $\sqrt{2}$ units

Adding these two vectors A and B together, magnitude of vector R is

R = $\sqrt{R^2_{a} + R^2_{b} }$

R = $\sqrt{10^2 + (\sqrt{2} ) ^2}$ = <em>10.09 units</em>

5 0

4 years ago

A block is at rest on a incline plane as shown in the diagram.As angle is increased, the componet of the blocks weight parallel

Elodia [21]

Answer:

The component of block weight parallel to the plane, Wₓ = W cosθ

Explanation:

Let the weight of the block due to gravitation is W

The direction of the weight is vertically down

Let θ be the angle formed with the vertical weight of the block and the incline.

Taking two components of weight one along the vertical weight and another component perpendicular to it.

Then the component `of weight long the parallel of the plane is

Wₓ = W cosθ

6 0

3 years ago

A massless string connects a 1.00 kg mass to a 3.00 kg cart which is resting on a frictionless horizontal surface. The mass hang

Romashka-Z-Leto [24]

Both masses will have the same acceleration. The cart accelerates to the right with a magnitude of 4.9 m/ $s^{2}$ . The correct answer is 4.90 m/ $s^{2}$

Given that a massless string connects a 1.00 kg mass to a 3.00 kg cart which is resting on a frictionless horizontal surface.

Let M = 1kg and m = 3 kg

Since the horizontal surface is frictionless, the tension in the string will be the same. when the mass is hanged over a frictionless pulley, the tension will also be the same.

When the mass is released, the cart accelerates to the right can be calculated from Newton' second law of motion. That is,

M( g + a) = m(g - a)

1(9.8 + a) = 3( 9.8 - a)

9.8 +a = 29.4 - 3a

collect the like terms

4a = 19.6

a = 19.6/4

a = 4.9 m/ $s^{2}$

Therefore, the cart accelerates to the right with a magnitude of 4.9 m/ $s^{2}$ . The correct answer is 4.90 m/ $s^{2}$

Learn more about dynamics here: brainly.com/question/24994188

5 0

3 years ago

Ikg of a fluid is compressed reversibly to

Katen [24]

Answer:

I'm learning physics too, mabye we can learn together. by the way, the are 2 very good apps with physics : "khan academy" and "crash course"

4 0

3 years ago

The speed 120 km/h is about 25 m/s 33 m/s 42 m/s 50 m/s