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Mrac [35]
2 years ago
6

The variable z is directly proportional to x. When x is 11, z has the value 44. What is the value of z when x = 21?

Mathematics
1 answer:
dimulka [17.4K]2 years ago
4 0

Directly proportional, both increase/decrease, Multiple k(constant you needed to solve for)..

Inversely --one increases as the other decreases, increase the denominator & fraction gets smaller.... So

Problem:

Dirextly to X (× by X)

Inversely to Y, (÷ by Y)

Z= k X/Y

Solve, working backwards: Z =5 becomes

5 = k (X) ÷ (Y). And

X=15 and Y =9 becomes

5= k(15)/(9). Undo ÷9, ×9 both sides

45= k(15). Now undo ×15 by ÷15 both sides

45/15 = 3. So k=3, (also called your constant of variation)....and your Equation/Proportion becomes...

Z = 3X/Y

Use the new #s.... X=23, Y=14

Z= 3×23÷14 = 69/14. If they want spirochete answer divide and round to corresponding # if decimals

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horrorfan [7]

Answer:

12

Step-by-step explanation:

10 - 1/2 x = 12-4/3x

60 - 3x = 72-2x

-12 = - x

3 0
2 years ago
A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t
11Alexandr11 [23.1K]

Answer:

  • <u>Question 1:</u>      dm/dt=0.2m<u />

<u />

  • <u>Question 2:</u>     m=Ae^{(0.2t)}<u />

<u />

  • <u>Question 3:</u>      m=10e^{(0.2t)}<u />

<u />

  • <u>Question 4:</u>      m=10g<u />

Explanation:

<u>Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m</u>

<u></u>

a) By definition:  m'=dm/dt

b)  Given:  rate=0.2m

c) By substitution:  dm/dt=0.2m

<u>Question 2: Find the general solution of this equation. Use A as a constant of integration.</u>

a) <u>Separate variables</u>

     dm/m=0.2dt

b)<u> Integrate</u>

           \int dm/m=\int 0.2dt

            ln(m)=0.2t+C

c) <u>Antilogarithm</u>

       m=e^{0.2t+C}

       m=e^{0.2t}\cdot e^C

         e^C=A\\\\m=Ae^{(0.2t)}

<u>Question 3. Which particular solution matches the additional information?</u>

<u></u>

Use the measured rate of 4 grams per hour after 3 hours

            t=3hours,dm/dt=4g/h

First, find the mass at t = 3 hours

            dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g

Now substitute in the general solution of the differential equation, to find A:

          m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976

Round A to 1 significant figure:

  • A = 10.

<u>Particular solution:</u>

           

             m=10e^{(0.2t)}

<u>Question 4. What was the mass of the bacteria at time =0?</u>

Substitute t = 0 in the equation of the particular solution:

         m=10e^{0}\\\\m=10g

3 0
3 years ago
if your bag of M&amp;M’s has 8 yellow out of 24 , how many of them will be yellow i’d the bag has a total of 96?
Lera25 [3.4K]

Answer: 32

Step-by-step explanation:

96 divided by 24 is 4

8x4=32

7 0
3 years ago
What is the equation of the line that passes through the point (5,-2) and has a
tresset_1 [31]

Answer:

y = 6/5x - 2

Step-by-step explanation:

use y = mx+ c

m = slope

c = y intercept

y = 6/5x - 2

3 0
3 years ago
Read 2 more answers
The cake store is having a 30% percent off sale on all of its cakes. If the cake you want regularly costs $10, how much would yo
Akimi4 [234]
30% of £10 = £3
30% discount = £10 - £3 = £7
Cake costs £7
6 0
2 years ago
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