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1 year ago

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Write an equation that expresses the following relationship. p varies directly with d and inversely with the square root of u In

your equation, use k as the constant of proportionality.

1 answer:

NARA [144]1 year ago

3 0

<span>The equation given as p varies directly with d and inversely with the square root of u is written as:
</span>
p = k1d
k1 is the proportionality constant.
and p = k2 $\frac{1}{ \sqrt{u} }$
here k2 is the proportionality constant.

Thus,
combining both equations we get, p = C $\frac{d}{ \sqrt{u} }$
where K = K1*K2, K is the proportionality constant.

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The picture shows the footprints of a man walking. The pace length P is the distance between the rear of two consecutive footpri

Rina8888 [55]

Bernard’s walking speed is 140 meters per minute

Bernard’s walking speed is 8.4 kilometers per hour

Step-by-step explanation:

The pace length P is the distance between the rear of two consecutive footprints

The formula, n P = 140, gives an approximate relationship between n and P where,

n = number of steps per minute
P = pace length in meters
Bernard knows his pace length is 0.80 meters
The formula applies to Bernard’s walking

We need to calculate Bernard’s walking speed in meters per minute and in kilometers per hour

∵ n = number of steps per minute

∴ n unit is number / minute

∵ P = pace length in meters

∴ P unit is meter

- That means n P unit is meters/minute

∴ n P represents the speed in meters per second

∵ The formula applies to Bernard’s walking

∵ His pace length is 0.80 meters

∵ n P = 140

∴ n(0.8) = 140

- Divide both sides by 0.8

∴ n = 175

- That means he moves 175 steps per minute

∵ The distance he walks in minute = 175 × 0.8 = 140 meters/minute

∴ His speed is 140 meters per minute

Bernard’s walking speed is 140 meters per minute

∵ 1 km = 1000 m

∵ 1 hour = 60 minutes

- Divide the meters by 1000 and the minute by 60 to change

from meters per minute to kilometers per hour

∴ His walking speed = $\frac{140}{1000}$ ÷ $\frac{1}{60}$

- Change ÷ to × and reciprocal the fraction after the division sign

∴ His walking speed = $\frac{140}{1000}$ × $\frac{60}{1}$ = 8.4 km/h

Bernard’s walking speed is 8.4 kilometers per hour

Learn more:

You can learn more about the speed in brainly.com/question/5461619

#LearnwithBrainly

7 0

2 years ago

Triangles ABC, EDC, and EFG are similar triangles. The measures of the three interior angles of triangle EFG are °, °, and °.

Misha Larkins [42]

Because of the vertical angles theorem, BAC becomes 50°. And angle B is 180-(50+30)=100.

If all 3 triangles are similar, the angles of triangle EFG are 30°, 50°, 100°

4 0

2 years ago

Read 2 more answers

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

3 0

1 year ago

If DE = 4x + 10, EF = 2x-1, and DF = 9x-15, find DF

Dmitrij [34]

Hello,
<span>We have that:
(4x+10)+(2x-1)=9x-15

</span>We solve the equation:
4x+10+2x-1=9x-15;
6x+9=9x-15;
6x-9x=-15-9;
-3x=-24;
3x=24;

<span>from which
</span>x=24:3=8

<span>Then:
DF=9x-15=(9</span>×8)-15=72-15=57

bye :-)

5 0

2 years ago

Read 2 more answers

PLEASE HELP A pizza parlor sells 320 pizzas per night when they charge $9.00 per pizza. The owner believes increasing the price

Sonja [21]

1. $9.00+$0.15=$9.15
2. 320-4=316

6 0

2 years ago