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3 years ago

Is this true? 2.5 meters > 220 cm

Mathematics

2 answers:

andreev551 [17]3 years ago

8 0

1 Metre is 100 cm

2.5 X 100 = 250.

250 is bigger than 220. Therefore, it is true.

dalvyx [7]3 years ago

7 0

Yes it is true that 2.5 m = 220 cm

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A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th

Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

of sugar. Let $S(t)$ be the amount of sugar in the tank at time $t$ . Then $S(0)=25$ .

Sugar is added to the tank at a rate of P lb/min, and removed at a rate of

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and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

$\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}$

Separate variables, integrate, and solve for S.

$\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt$

$\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt$

$-100\ln\left|P-\dfrac S{100}\right|=t+C$

$\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t$

$P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}$

$\dfrac S{100}=P-Ce^{-100t}$

$S(t)=100P-100Ce^{-100t}=100P-Ce^{-100t}$

Use the initial value to solve for C :

$S(0)=25\implies 25=100P-C\implies C=100P-25$

$\implies S(t)=100P-(100P-25)e^{-100t}$

The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

$1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}$

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

of sugar, so we pick P such that

$S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}$

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2 years ago

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2 years ago

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Answer:

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Step-by-step explanation:

Isolate the variable by dividing each side by factors that do not contain the variable. Hope this helps.

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An investment firm invested in two companies last year. They invested $40,000 in company A and made a profit of 15%. They invest

alexira [117]

Answer:

A) $8200.

B) 16.4%

Step-by-step explanation:

Here is the complete question: An investment firm invested in two companies last year. They invested $40,000 in company A and made a profit of 15%. They invested $10,000 in company B and made a profit of 22%.

A) What is the investment firms total profit?

B) What is the percent profit of the total investment?

Given: Company A invested $40000 and made profit of 15%

Company B invested $10000 and made profit of 22%

A) First lets find the profit of company A and B.

Company A= $\frac{15}{100} \times \$ 40000= \$ 6000.$

∴ Profit of company A is $6000.

Company B= $\frac{22}{100} \times \$ 10000= \$ 2200$

∴ Profit of company B is $2200.

Total profit= profit of company A+ profit of company B

⇒ $Total\ profit= \$ 6000+\$ 2200$

∴ Total Profit= $\$ 8200$

Hence, the total profit of investment firm is $8200.

B) Now finding the percentage of total profit made by firm.

Total investment by the firm= $\$ 40000+\$ 10000= \$ 50000$

∴ Total investment done by the firm is $50000.

Percent of profit= $\frac{Total\ profit}{Total\ investment} \times 100$

⇒ Percent of profit= $\frac{8200}{50000} \times 100$

⇒ Percent of profit= $\frac{82}{5} = 16.4\%$

Hence, 16.4% is the percent profit of the total investment.

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2 years ago