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3 years ago

A plant grows 3 centimeters in 10 days. How much does it grow per day? Write your answer as a fraction in simplest form

2 answers:

5 0

It grew 3/10, which equals 0.3 centimeters every day, and as a fraction, 3/10 would be the answer.

3/10 is the answer.

Hope this helps, and have a nice day!

skelet666 [1.2K]3 years ago

5 0

Answer:

The plant grows 3/10 centimeters per day

Step-by-step explanation:

This question can be solved using a simple rule of three.

In 10 days, it grows 3 centimeters. In 1 day, it grows x centimeters. We have to find x. So

10 days - 3 centimeters

1 day - x centimeters.

$10x = 3$

$x = \frac{3}{10}$

The plant grows 3/10 centimeters per day

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A tank contains 100 gal of water and 50 oz of salt. Water containing a salt concentration of ¼ (1 + ½ sin t) oz/gal flows ito th

Likurg_2 [28]

Answer:

Part a)

$y\left(t\right)=\frac{-1250cost+25sint}{5002}+25+\frac{63150}{2501}\frac{1}{e^{\frac{t}{50}}}$

Part b)

Check the attached figure to see the ultimate behavior of the graph.

Part c)

The level = 25, Amplitude = 0.2499

Step-by-step Solution:

Part a)

Given:

$Q(0)=50$

Rate in:

$\frac{1}{4}\left(1+\frac{1}{2}sint\right)\cdot 2\:=\:\frac{1}{2}\left(1+\frac{1}{2}sint\right)$

Rate out:

$\frac{Q}{100}\cdot 2=\frac{Q}{50}$

So, the differential equation would become:

$\frac{dQ}{dt}=\frac{1}{2}\left(1+\frac{1}{2}sint\right)-\frac{Q}{50}$

Rewriting the equation:

$\frac{dQ}{dt}+\frac{Q}{50}=\frac{1}{2}\left(1+\frac{1}{2}sint\right)$

As $p(x)$ is the coefficient of $y$ , while $q(x)$ is the constant term in the right side of the equation:

$p\left(x\right)=\frac{1}{50}$

$q\left(x\right)=\frac{1}{2}\left(1+\frac{1}{2}sint\right)$

First it is important to determine the function $\mu$ :

$\mu \left(t\right)=e^{\int \:p\left(t\right)dt}$

$=e^{\int \:\left(\frac{1}{50}\right)dt}$

$=e^{\frac{t}{50}}$

The general solution then would become:

$y\left(t\right)=\frac{1}{\mu \left(t\right)}\left(\int \mu \left(t\right)q\left(t\right)dt+c\:\right)$

$=\frac{1}{e^{\frac{t}{50}}}\int e^{\frac{t}{50}}\:\frac{1}{2}\left(1+\frac{1}{2}sint\right)dt+\frac{1}{e^{\frac{t}{50}}}c$

$=\frac{1}{e^{\frac{t}{50}}}\left(\frac{-25e^{\frac{t}{50}}\left(50cost-sint\right)}{5002}+25e^{\frac{t}{50}}\right)+\frac{1}{e^{\frac{t}{50}}}c$

$=\frac{\left-1250cost+25sint\right}{5002}+25+\frac{1}{e^{\frac{t}{50}}}c$

Evaluate at $t=0$

$50=y\left(0\right)=\frac{\left(-1250cos0+25sin0\right)}{5002}+25+\frac{1}{e^{\frac{0}{50}}}c$

Solve to c:

$c=25+\frac{1250}{5002}$

$\mathrm{Cancel\:}\frac{1250}{5002}:\quad \frac{625}{2501}$

$c=25+\frac{625}{2501}$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:25=\frac{25\cdot \:2501}{2501}$

$c=\frac{25\cdot \:2501}{2501}+\frac{625}{2501}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$c=\frac{25\cdot \:2501+625}{2501}$

$c=\frac{63150}{2501}$

$c\approx 25.25$

Therefore, the general solution then would become:

$y\left(t\right)=\frac{-1250cost+25sint}{5002}+25+\frac{63150}{2501}\frac{1}{e^{\frac{t}{50}}}$

Part b) <em>Plot the Solution to see the ultimate behavior of the graph</em>

The graph appears to level off at about the value of $Q=25$ .

The graph is attached below.

Part c)

In the graph we note that the level is $Q=25$ .

Therefore, the level = 25

The amplitude is the (absolute value of the) coefficient of $cost\:t$ in the general solution (as the coefficient of the sine part is a lot smaller):

Therefore,

$A=\frac{1250}{5002}\:\approx 2.499$

Keywords: differential equation, word problem

Learn more about differential equation word problem from brainly.com/question/14614696

#learnwithBrainly

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3 years ago

A shape is made of 12 right triangles of equal size each right triangle has a base of 4 centimeters and a height a 5-cm what is

mart [117]

Answer:

$120\ cm^2$

Step-by-step explanation:

The area $(A_t)$ of a triangle is equal to half the product of its length (L) because of its height (h).

$A_t = 0.5h*L$

The base of the triangles is $L = 4\ cm$

The height of the triangles is $h = 5\ cm$

Then the area of one of the triangles is:

$A_t = 0.5(4)(5)\\A_t = 10\ cm^2$

The figure is formed by 12 equal triangles, then the area of the figure $(A_f)$ is:

$A_f = 12(A_t)\\A_f = 12(10)\\A_f = 120\ cm^2$

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3 years ago

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Which expression represents "3 more than twice a number"? Choices: 2n−3 3−2n 2n+3 2+n+3

Alekssandra [29.7K]

2n+3

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4 years ago

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Joe jumps into the water, and it takes him 5 seconds to reach the bottom of a pool 8 feet deep.

Soloha48 [4]

Answer:

hm looks like the equation is 5/8

Step-by-step explanation:

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3 years ago

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PLZ SHOW YOUR WORK!!

cestrela7 [59]

Tony walks 116.7 m diagonally across the lot.

Solution:

Length of the rectangle = 80 m

Width of the rectangle = 85 m

<u>To find the diagonal of the rectangle:</u>

Diagonal of the rectangle = $\sqrt{l^2+w^2}$

$=\sqrt{80^2+85^2}$

$=\sqrt{6400+7225}$

$=\sqrt{13625}$

$=5\sqrt{545}$

Diagonal of the rectangle = 116.7 m

Hence Tony walks 116.7 m diagonally across the lot.

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3 years ago