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3 years ago

A quantity with an initial value of 600 decays exponentially at a rate of

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

8 0

Answer:

The value of the quantity after 87 months will be of 599.64.

Step-by-step explanation:

A quantity with an initial value of 600 decays exponentially at a rate of 0.05% every 6 years.

This means that the quantity, after t periods of 6 years, is given by:

$Q(t) = 600(1 - 0.0005)^{t}$

What is the value of the quantity after 87 months, to the nearest hundredth?

6 years = 6*12 = 72 months

So 87 months is 87/72 = 1.2083 periods of 6 years. So we have to find Q(1.2083).

$Q(t) = 600(1 - 0.0005)^{t}$

$Q(1.2083) = 600(1 - 0.0005)^{1.2083} = 599.64$

The value of the quantity after 87 months will be of 599.64.

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Stock Market At the beginning of the day the stock market goes down 50 3/4 points and stays at this level for most of the day. A

yarga [219]

Answer:

69 3/4

Step-by-step explanation:

The stock market goes down to 50 3/4 at the beginning of the day

At the end of the day it goes up to 120 1/2

Therefore total change in the stock market from the beginning to the end of the day can be calculated as follows

= 120 1/2 - 50 3/4

= 241/2 - 203/4

= 279/4

= 69 3/4

Hence the total change in the stock market from the beginning to the end of the day is

69 3/4

7 0

3 years ago

the surface areas of two similar solids are 1008cm^2 and 1372ccm^2. the volume of the larger solid is 1801cm^3 find the volume o

adoni [48]

This can be treated as a proportion problem.

Larger solid:
Surface area = 1,372 cm²
Volume = 1,801 cm³

Smaller solid:
Surface area = 1,008cm²
Volume = ?

1,372 / 1,801 = 1008 / x
1,372 * x = 1,801 * 1008
1,372x = 1,815,408
x = 1,815,408 / 1,372
x = 1,323.18

The volume of the smaller solid is 1,323.18 cm³

4 0

3 years ago

4t+3c=$81.00 10t+3c=$135.00

muminat

$\left \{ {{4t+3c=81.00\:(I)} \atop {10t+3c=135.00\:(II)}} \right.$
Simplify the first equation by (-1)
 $\left \{ {{4t+3c=81.00\:*(-1)} \atop {10t+3c=135.00\:\:\:\:\:}} \right.$
Once simplified, cancel the opposing terms.
 $\left \{ {{-4t-\diagup\!\!\!\!3c=-81.00} \atop {10t+\diagup\!\!\!\!3c=135.00}} \right.$
Now find the value of "t".
$\left \{ {{-4t=-81.00} \atop {10t=135.00}} \right.$
-------------------------------
$6t = 54.00$
$t = \frac{54.00}{6}$
$\boxed{\boxed{t = 9.00}}\end{array}}\qquad\quad\checkmark$

Now find the value of "c", replace the found value of "t" in the first equation:
$4t+3c=81.00\:(I)$
$4*9+3c=81.00$
$36 + 3c = 81.00$
$3c = 81.00 - 36$
$3c = 45.00$
$c = \frac{45.00}{3}$
$\boxed{\boxed{c = 15.00}}\end{array}}\qquad\quad\checkmark$

Answer:
The values of "t" and "c" satisfying the linear system are successively: $ 9.00 and $ 15.00

3 0

3 years ago

Show that the points A(2,-2), B(14, 10), C(11, 13) and

Vedmedyk [2.9K]

Answer:

is not a rectangle

Step-by-step explanation:

The midpoints of the diagonals are ...

AC midpoint = ((2, -2) +(11, 13))/2 = (13/2, 11/2)

BD midpoint = ((14, 10) +(-2, 1))/2 = (6, 11/2)

The midpoints of the diagonals are different, so this is not a rectangle or any sort of parallelogram.