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2 years ago

14

Bob used identical cubes to build a rectangular tower that is 25 cubes tall, 5 cubes wide, and 6 cubes long. Beatrice used the s

ame type of cube to build a tower that is 12 cubes tall, 3 cubes wide, and 5 cubes long. Then Bob destroyed Beatrice's tower and used all of her cubes to make his tower even taller, while keeping its width and length the same. How many cubes tall is Bob's tower now?
HEELLLLLPPPP :(

1 answer:

Mazyrski [523]2 years ago

3 0

Answer:

ok so first we have to find out how meaning cubes are in each tower so

bob 25*5*6=750

beatrice 12*3*5=180

ok so we want to see how many extra layers bob can add on with beatrices blockes so from looking at bobs tower we can see that 5*6 each layer is 30 so

180/30=6

so bobs will be 31 blocks tall

Hope This Helps!!!

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3 years ago

A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical is given by the equatio

GaryK [48]

Answer:

a) $N=N_0e^{-0.069t}$

b) $N=696.9$ grams

c) $t=10$ days

Step-by-step explanation:

a)

We are going to use separation of variables to solve.

Get all your t's to one side and your N's to opposing side.

$\frac{dN}{dt}=-0.069N$

Multiply both sides by $dt$ :

$dN=-0.069N dt$

Divided both sides by $N$ :

$\frac{dN}{N}=-0.069 dt$

Integrate both sides:

$\ln|N|=-0.069t+C$

The equivalent exponential form is:

$e^{-0.069t+C}=N$

Using law of exponents you can write this as:

$e^{-0.069t}e^C=N$

$e^C$ is just a positive constant that I'm going to replace with K:

$e^{-0.069t}K=N$

Applying the symmetric property of equality:

$N=e^{-0.069t}K$

Applying the commutative property of multiplication:

$N=Ke^{-0.069t}$

K actually represents the initial amount of chemical substance since when plugging in 0 for t you get K for N, like so:

$N=Ke^{-0.069 \cdot 0}$

$N=Ke^{0}$

$N=K(1)$

$N=K$

We are given at time 0 the amount of chemical substance,N, is K. They want us to represent this value with $N_0$ instead. So the exponential equation is:

$N=N_0e^{-0.069t}$

b)

We are given $N_0=800$ at $t=0$ .

We are asked to find how much of the chemical substance, N, remains after 2 days. So we replace t with 2 in $N=800e^{-0.069t}$ :

$N=800e^{-0.069 \cdot 2}$

Put into calculator:

$N=696.9$ (this was rounded to the nearest tenths)

c)

The last part is asking for how many days will it take a initial 800 grams to go down to half of 800 grams.

We need to see the following equation:

$\frac{1}{2}(800)=800e^{-0.069t}$

$400=800e^{-0.069t}$

Divide both sides by 800:

$\frac{400}{800}=e^{-0.069t}$

Reduce the fraction:

$\frac{1}{2}=e^{-0.069t}$

Convert to logarithmic form:

$\ln(\frac{1}{2})=-0.069t$

Divide both sides by -0.069:

$\frac{\ln(\frac{1}{2})}{-0.069}=t$

Input into calculator:

$10.0=t$

$t=10.0$

$t=10$

6 0

3 years ago

Find the value of two numbers if their sum is 16 and their difference is 2.4

Verdich [7]

Lets x and y are the value of two numbers.

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If x + y = 16 then x = 16 - y

Substitute x = 16 - y into x - y = 2.4

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Answer:

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7 0

3 years ago

Please help me thanks

Savatey [412]

<span>x=6.6

If rounded it should be 6.7 or 7

Hope this helped. Good luck!</span>

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3 years ago

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