Are all proportional relationships functions?

A submarine elevation is -14 feet relative to sea level. A shark is swimming at elevation of -56 feet what is the difference in

likoan [24]

In order to solve this kind of problem, we must find the difference between two negative numbers describing elevation. Although when you have 2 negative numbers in a subtraction-elevation problem, the elevation difference won't be negative... It would be positive. -56 - (-14) would usually equal -42 feet but that would just describe a regular negative subtraction problem, so it becomes 42 feet. This answer is positive since it describe the distance between these integers.

4 0

3 years ago

The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the bridge is 1210 m long and

brilliants [131]

Answer:

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

The equation of the parabola is:

$y=0.00035x^{2}$

Compute the first order derivative of y as follows:

$y=0.00035x^{2}$

$\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}]$

$=2\cdot 0.00035x\\\\=0.0007x$

Now, it is provided that |x | ≤ 605.

⇒ -605 ≤ x ≤ 605

Compute the arc length as follows:

$\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx$

$=\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\$

Now, let

$x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u$

$\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u$

$={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}$

Plug in the solved integrals in Arc Length and solve as follows:

$\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\$

$=1245.253707795227\\\\\approx 1245.25$

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

7 0

3 years ago

Dakota and Christine went shopping. Dakota bought two scarves and one hat for $13 Christine bought one scarves and two hats for

White raven [17]

One scarf=s
One hat=h

2s+h=13
s+2h=14

h=13-2s
(plug that into the other equation)

s+2(13-2s)=14
s+26-4s=14
26-3s=14
-3s=-12
s=4

One hat=$5
One scarf=$4
5+4=9
Price of one hat AND one scarf is $9

5 0

3 years ago

The table represents the average daily price of a two-bedroom beachfront condo each month, with January represented as month 1,

ruslelena [56]

Answer:

y = - 9.1768x2 + 122.2567x + 14.9091

Step-by-step explanation:

Given the following :

Month (x) Daily Rental Price (y) 1 $154 2 $205 3 $266 4 $358 5 $403 6 $425 7 $437 8 $430 9 $381 10 $285 11 $211 12 $195

Using the online regression equation graphing tool ; The quadratic model obtained in the form,

y = Ax^2 + Bx + C is :

y = - 9.1768x2 + 122.2567x + 14.9091

Attached below is a picture of the quadratic regression curve.

7 0

3 years ago

Tell whether the ordered pair is a solution of the system of equations.

katovenus [111]

Answer:

2x + y = 5

y = 4x – 1

Substitute (2, 1) into system, then:

2x + y = 5 => 2 x 2 + 1 = 5 => 5 = 5 (satisfied)

y = 4x– 1 => 4 x 2 - 1 = 1 => -7 = 1 (not satisfied)

=> Option 3 is correct.

Hope this helps!

:)

8 0

3 years ago