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Shtirlitz [24]
2 years ago
6

Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 924 square milimetres an

d its perimeter is 122 milimetres.
Mathematics
1 answer:
BigorU [14]2 years ago
6 0

Length =l

Height = h

Area function = l * h = 924

Perimeter function = 2i + 2h = 122

Divide by 2

I + h = 61.

Plug in I or h for the other variable

I * (61 - I) = 924

61i - i^2 = 924

Factor the function

(-I + 28)(I - 33) = 0

l = 33 as l cannot be negative

61 - 33 = 28

h = 28

Difference between h and l is 33-28=5

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Modeling Radioactive Decay In Exercise, complete the table for each radioactive isotope.
Travka [436]

Answer :

The amount after 1000 years will be, 5.19 grams.

The amount after 10000 years will be, 0.105 grams.

Step-by-step explanation :

Half-life = 1599 years

First we have to calculate the rate constant, we use the formula :

k=\frac{0.693}{t_{1/2}}

k=\frac{0.693}{1599\text{ years}}

k=4.33\times 10^{-4}\text{ years}^{-1}

Now we have to calculate the amount after 1000 years.

Expression for rate law for first order kinetics is given by:

t=\frac{2.303}{k}\log\frac{a}{a-x}

where,

k = rate constant  = 4.33\times 10^{-4}\text{ years}^{-1}

t = time passed by the sample  = 1000 years

a = initial amount of the reactant  = 8 g

a - x = amount left after decay process = ?

Now put all the given values in above equation, we get

1000=\frac{2.303}{4.33\times 10^{-4}}\log\frac{8}{a-x}

a-x=5.19g

Thus, the amount after 1000 years will be, 5.19 grams.

Now we have to calculate the amount after 10000 years.

Expression for rate law for first order kinetics is given by:

t=\frac{2.303}{k}\log\frac{a}{a-x}

where,

k = rate constant  = 4.33\times 10^{-4}\text{ years}^{-1}

t = time passed by the sample  = 10000 years

a = initial amount of the reactant  = 8 g

a - x = amount left after decay process = ?

Now put all the given values in above equation, we get

10000=\frac{2.303}{4.33\times 10^{-4}}\log\frac{8}{a-x}

a-x=0.105g

Thus, the amount after 10000 years will be, 0.105 grams.

4 0
3 years ago
Is this true? if not what’s the answer asap!
tensa zangetsu [6.8K]

Answer:

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4 0
3 years ago
2 lines intersect and create VERTICAL angles. One of the angles measures (3n-28) degrees and the other angle measures 83 degrees
kykrilka [37]

Answer:

n=37

Step-by-step explanation:

Two lines intersect and create vertical angles.

The vertical angles are (3n-28)^\circ$ and 83^\circ.

We know that vertical angles (also called vertically opposite angles) are equal. Therefore:

(3n-28)^\circ$ = 83^\circ.\\3n=28+83\\3n=111\\$Divide both sides by 3\\n=37

8 0
3 years ago
Which graph does not represent a function
Marysya12 [62]

Answer:

Graph D

Step-by-step explanation:

it does not pass the linear test to qualify as a function

3 0
3 years ago
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What is the radius of a circle with an area of 50.24 square inches?
Vladimir [108]

Answer:

<h3>Area of a circle= πr²</h3><h2>50.24 = 3.14 *r²</h2><h2>r²= 50.24/3.14</h2><h2>r² =16</h2><h2>r= √16</h2><h2>r = 4</h2>

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2 years ago
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