Which of the following does the situation below best describe?

Jackson and Jonah are both swimming. Jackson swims at 1350 meters per hour. Jonah swims at a speed of 1250 millimeters per secon

Vladimir [108]

For this question we will use the following relations.

100 centimeters=1 meter (or 1 centimeter= 0.01 meter)

10 millimeter=1 centimeter (or 1 mm=0.1 cm)

60 minutes = 1 hour (or 1 min= $\frac{1}{60}$ hour)

Now, Jackson's speed is 1350 meters per hour. This can be converted to cm per minute as follows:

$\frac{1350 m}{1 h}=\frac{1350\times 100 cm}{60 min}=2250 cm/min$ ...Equation 1

Likewise, Jonah's swim speed in cm/min can be calculated as:

$\frac{1250 mm}{1 s}=\frac{1250\times 0.1 cm}{\frac{1}{60}min } =\frac{125\times 60 cm}{1 min}=7500cm/min$ ...Equation 2

As we can see clearly after comparing Equation 1 and Equation 2, Jonah's swim speed of 7500 cm/min is faster than that of Jackson.

Thus, option B is correct.

7 0

2 years ago

Rectangle $ABCD$ is the base of pyramid $PABCD$. If $AB = 8$, $BC = 4$, $\overline{PA}\perp \overline{AD}$, $\overline{PA}\perp

11Alexandr11 [23.1K]

Answer:

Step-by-step explanation:

Since the base of the pyramid PABCD is a rectangle, the shape in question is a rectangular based pyramid. Volume of a rectangular based pyramid is expressed as V = 1/3 * Base Area * Height of the pyramid.

Given a rectangle ABCD with AB = 8 and BC = 4, the area of the rectangle will be equivalent to the base area of the pyramid.

Base Area = Length * Breadth

Base Area = AB * BC

Base Area = 8*4 = 32

If $\overline{PA}\perp \overline{AD}\ and \ \overline{PA}\perp \overline{AB}$ , and PB = 17, then the height of the pyramid is PB = 17.

Volume of the pyramid = 1/3 * 32 * 17

Volume of the pyramid = 1/3 * 544

Volume of the rectangular based pyramid = 181.33

8 0

3 years ago

Need by TONIGHT please help

igor_vitrenko [27]

Slope = 1/2 :)
rise over run (rise/run)
so... 2/4 = 1/2
hope this helps!

7 0

3 years ago

An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn

Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43 inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24, this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative value ( -49.7) so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0

2 years ago

Frank had hip replacement surgery and was given a prescription with instructions to take a 200 milligram (mg) tablet three times

IgorC [24]

Answer:

12,600mg per 21 days

Step-by-step explanation:

200mg three times a day → (200mg)(3) = 600mg per a day

21 days → (21)(600mg) = 12,600mg per 21 days

5 0

3 years ago