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Paul [167]
3 years ago
10

Marty cuts 2.05 ounces of cheese from a 4.6 ounce block of cheddar cheese. How many ounces of cheddar cheese are left in the blo

ck
Mathematics
1 answer:
melamori03 [73]3 years ago
8 0

Answer:Amount of cheese  left=2.55ounce

Step-by-step explanation:

Total amount of cheddar cheese =4.6ounce

Amount of cheese cut out =2.05 ounces

Amount left =Total amount of cheddar cheese-Amount of cheese cut out

=4.6ounce-2.05 ounces=2.55ounce

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(1,1)(2,4)(3,9)(4,16)

Step-by-step explanation:

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Suppose a certain population satisfies the logistic equation given by dP
Ksenya-84 [330]

Answer:

The population when t = 3 is 10.

Step-by-step explanation:

Suppose a certain population satisfies the logistic equation given by

\frac{dP}{dt}=10P-P^2

with P(0)=1. We need to find the population when t=3.

Using variable separable method we get

\frac{dP}{10P-P^2}=dt

Integrate both sides.

\int \frac{dP}{10P-P^2}=\int dt             .... (1)

Using partial fraction

\frac{1}{P(10-P)}=\frac{A}{P}+\frac{B}{(10-P)}

A=\frac{1}{10},B=\frac{1}{10}

Using these values the equation (1) can be written as

\int (\frac{1}{10P}+\frac{1}{10(10-P)})dP=\int dt

\int \frac{dP}{10P}+\int \frac{dP}{10(10-P)}=\int dt

On simplification we get

\frac{1}{10}\ln P-\frac{1}{10}\ln (10-P)=t+C

\frac{1}{10}(\ln \frac{P}{10-P})=t+C

We have P(0)=1

Substitute t=0 and P=1 in above equation.

\frac{1}{10}(\ln \frac{1}{10-1})=0+C

\frac{1}{10}(\ln \frac{1}{9})=C

The required equation is

\frac{1}{10}(\ln \frac{P}{10-P})=t+\frac{1}{10}(\ln \frac{1}{9})

Multiply both sides by 10.

\ln \frac{P}{10-P}=10t+\ln \frac{1}{9}

e^{\ln \frac{P}{10-P}}=e^{10t+\ln \frac{1}{9}}

\frac{P}{10-P}=\frac{1}{9}e^{10t}

Reciprocal it

\dfrac{10-P}{P}=9e^{-10t}

P(t)=\dfrac{10}{1+9e^{-10t}}

The population when t = 3 is

P(3)=\dfrac{10}{1+9e^{-10\cdot 3}}

Using calculator,

P=9.999\approx 10

Therefore, the population when t = 3 is 10.

8 0
3 years ago
Find the volume of the solid obtained by rotating the region bounded by y=4x and y=2sqrt(x) about the line x=6.
Pie

Check the picture below.

so by graphing those two, we get that little section in gray as you see there, now, x = 6  is a vertical line, so we'll have to put the equations in y-terms and this is a washer, so we'll use the washer method.

y=4x\implies \cfrac{y}{4}=x\qquad \qquad y=2\sqrt{x}\implies \cfrac{y^2}{4}=x~\hfill \begin{cases} \cfrac{y}{4}=x\\\\ \cfrac{y^2}{4}=x \end{cases}

the way I get the radii is by using the "area under the curve" way, namely, I use it to get R² once and again to get r² and using each time the axis of rotation as one of my functions, in this case the axis of rotation will be f(x), and to get R² will use the "farthest from the axis of rotation" radius, and for r² the "closest to the axis of rotation".

\stackrel{R}{\stackrel{f(x)}{6}-\stackrel{g(x)}{\cfrac{y^2}{4}}}\qquad \qquad \stackrel{r}{\stackrel{f(x)}{6}-\stackrel{g(x)}{\cfrac{y}{4}}}~\hfill \stackrel{R^2}{\left( 6-\cfrac{y^2}{4} \right)^2}-\stackrel{r^2}{\left( 6-\cfrac{y}{4} \right)^2} \\\\\\ \stackrel{\textit{doing a binomial expansion and simplification}}{3y-3y^2-\cfrac{y^2}{16}+\cfrac{y^4}{16}}

now, both lines if do an equation on where they meet or where one equals the other, we'd get the values for y = 0 and y = 1, not surprisingly in the picture.

\displaystyle\pi \int_0^1\left( 3y-3y^2-\cfrac{y^2}{16}+\cfrac{y^4}{16} \right)dy\implies \pi \left( \left. \cfrac{3y^2}{2} \right]_0^1-\left. y^3\cfrac{}{} \right]_0^1-\left. \cfrac{y^3}{48}\right]_0^1+\left. \cfrac{y^5}{80} \right]_0^1 \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{59\pi }{120}~\hfill

7 0
2 years ago
The lock of a safe has a wheel of 8 letters. A unique combination of 3 letters opens the safe. what is the probability that a bu
LiRa [457]

Answer:

1/512

Step-by-step explanation:

The robber has a 1/8 probability of getting each letter right. There are three letters, so you would multiply 1/8x1/8x1/8.

5 0
4 years ago
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