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WITCHER [35]
3 years ago
11

I can't seem to figure out this problem -4q + 9 = 7q - 31 ​

Mathematics
2 answers:
Nikolay [14]3 years ago
6 0

Answer:

\large\boxed{q=\dfrac{40}{11}}

Step-by-step explanation:

-4q+9=7q-31\qquad\text{subtract 9 from both sides}\\\\-4q+9-9=7q-31-9\\\\-4q=7q-40\qquad\text{subtract }\ 7q\ \text{from both sides}\\\\-4q-7q=7q-7q-40\\\\-11q=-40\qquad\text{divide both sides by -11}\\\\\dfrac{-11q}{-11}=\dfrac{-40}{-11}\\\\q=\dfrac{40}{11}

Kipish [7]3 years ago
3 0

Answer:

q = 3.636363636 repeating

Step-by-step explanation:

  - 4q + 9 = 7q - 31

   + 4q      + 4q

     9 = 11q - 31

  + 31         + 31

      40 = 11q

      \frac{40}{11} = \frac{11q}{11}

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Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3
Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

\frac{dV}{dt} = -kA

Using Euler's method

\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i}    \\

Where initial droplet volume is:

V(0) = \frac{4pi}{3} * r(0)^3 =  \frac{4pi}{3} * 2.5^3 = 65.45 mm^3

Hence, the iterative solution will be as next:

  • i = 1, ti = 0, Vi = 65.45

V'_{i}  = -k *4pi*(\frac{3*65.45}{4pi})^(2/3)  = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88

  • i = 2, ti = 0.5, Vi = 63.88

V'_{i}  = -k *4pi*(\frac{3*63.88}{4pi})^(2/3)  = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33

  • i = 3, ti = 1, Vi = 62.33

V'_{i}  = -k *4pi*(\frac{3*62.33}{4pi})^(2/3)  = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\

The average change of droplet radius with time is:

Δr/Δt = \frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0
3 years ago
Answer if you know
Arlecino [84]
I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set y=1.25 for this example.)

The length of each cross section (the side lying in the base) has length determined by the horizontal distance x between the y-axis x=0 and the curve y=\sqrt x. In terms of y, this distance is x=y^2. The height of each cross section is twice the value of y, so the area of each rectangular cross section should be 2y^3.

This means the volume would be given by the integral

\displaystyle\int_0^22y^3\,\mathrm dy
8 0
3 years ago
Una caja de fideos de 7.2 onzas a 0.67 o una caja de fideos de 13 onzas a 1.28 cual tiene el mejor precio
uysha [10]

Answer:

The first one. Brainly is also in spanish

4 0
3 years ago
Six yards of rope costs $5.50 while four yards costs $4.75
Amiraneli [1.4K]

The best option is the first one (Six yards of rope costs $5.50). It is the lowest unit cost.

<u>Step-by-step explanation:</u>

For the given question case, first we should compare the unit costs of the choices provided and evaluate the best option.

Choice 1:

Six yards of rope costs $ 5.50

            \frac{5.50 \text { dollar}}{6 \text { yard }}=0.9167\ dollar/yard

Choice 2:

Four yards costs $ 4.75

           \frac{4.75 \text { dollar}}{4 \text { yard }}=1.1875\ dollar/yard

Thus, the best choice is the first one. Because it is the lowest unit cost.

3 0
3 years ago
What is 18.5% of 500?
denis-greek [22]

Answer:

92.5

Step-by-step explanation:

18.5% = 0.185

0.185 x 500 = 92.5

Hope that helps!

4 0
3 years ago
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