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3 years ago

The temperature fell from 0 degrees to 6 3/5 degrees below 0 in 2 1/5 hours. what was the temperature change per hour?

Mathematics

1 answer:

sattari [20]3 years ago

7 0

divide 6 3/5 by 2 1/5

6 3/5 = 33/5

2 1/5 = 11/5

33/5 / 11/5 = 3

the temperature dropped 3 degrees per hour

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Kindlyy solve this question..

Bas_tet [7]

Answer:

Volume = 21688.37 in.³

Step-by-step explanation:

Volume of a sphere : V=4/3πr³

4/3π17.3³ ≈ 21688.37025

hope this helps :D

3 0

3 years ago

Three consecutive integers are such that three times the smallest is 26 more than the largest. Find the integers.

Sidana [21]

Answer: 14, 15 and 16

Step-by-step explanation:

Let the numbers be a, a+1 and a+2

We are told that the three consecutive integers are such that three times the smallest is 26 more than the largest. This can be formed into an equation as:

(3 × a) = (a+2 + 26)

3a = a + 28

3a - a = 28

2a = 28

a = 28/2

a = 14

The numbers are 14, 15 and 16

7 0

3 years ago

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) Plot the Solution to see the ultimate behavior of the graph

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

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4 0

3 years ago

Solve a-c. Please show all steps!

ziro4ka [17]

Answer:

The problem is stupidly written but the intercepts are:

(0 ,+/-625.02)

(+/-625.02, 0)

Radius is 625.02

Area 1,227,263.17 square miles

Step-by-step explanation:

7 0

3 years ago

You are the manager of a donut shop. Presently, you sell your donuts for $1.00 each and everyday you sell 500 donuts. However, y

never [62]

Answer: $1.75

Solve for:

What price would result in the most revenue?

Step-by-step explanation:

Let the price of one donut = 1 + 0.05x

Let the # of donuts he can sell = 500 - 10x

Revenue,

$R(x) = (1 + 0.05x)(500 - 10x)$

$R(x) = 500 - 10x + 25x - 0.5x^2$

$R(x) = -10 + 25-0.5(2x)$

$= 15-x\\x=15$

Revenue is maxed when x = 15

When the revenue is maxed,

$Price = 1 + 0.05(15)\\=1 + 0.75\\=1.75$

Therefore the best price for this scenario is $1.75

3 0

2 years ago