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3 years ago

Use logarithm tables to evaluatethe following 723.7 X 0.0667

Mathematics

1 answer:

jok3333 [9.3K]3 years ago

4 0

Answer:

1.68

Step-by-step explanation:

log723.7=2.86

multiplication in log is addition so 2.86+

log0.0667=-1.18

so 2.86+-1.18=1.68

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What is the Simplified form of √46/192

Lorico [155]

Answer:

(√138)/24

Step-by-step explanation:

$\displaystyle\sqrt{\frac{46}{192}}=\sqrt{\frac{46\cdot 3}{192\cdot 3}}=\sqrt{\frac{138}{24^2}}=\frac{\sqrt{138}}{24}$

8 0

3 years ago

Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per g

AysviL [449]

Answer:

The quantity of salt at time t is $m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$ , where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

$\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}$

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

$(0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}$

Where:

$c$ - The salt concentration in the tank, as well at the exit of the tank, measured in $\frac{pd}{gal}$ .

$\frac{dc}{dt}$ - Concentration rate of change in the tank, measured in $\frac{pd}{min}$ .

$V$ - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

$V \cdot \frac{dc}{dt} + 6\cdot c = 3$

$60\cdot \frac{dc}{dt} + 6\cdot c = 3$

$\frac{dc}{dt} + \frac{1}{10}\cdot c = 3$

This equation is solved as follows:

$e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }$

$\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }$

$e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt$

$e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C$

$c = 30 + C\cdot e^{-\frac{t}{10} }$

The initial concentration in the tank is:

$c_{o} = \frac{10\,pd}{60\,gal}$

$c_{o} = 0.167\,\frac{pd}{gal}$

Now, the integration constant is:

$0.167 = 30 + C$

$C = -29.833$

The solution of the differential equation is:

$c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }$

Now, the quantity of salt at time t is:

$m_{salt} = V_{tank}\cdot c(t)$

$m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$

Where t is measured in minutes.

7 0

3 years ago

Item 32 On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What per

stira [4]

97.2% on the final.
Find the total amount of points needed to get a 93%. 150+150+150+250 = 700 total points. 700*.93 = 651 total points needed to get 93%. find the points received from the other quizzes and subtract the sum from 651 to find how many points need to be scored on the final.
150*.88=132 (test 1)
150*.94=141 (test 2)
150*.90=135 (test 3)
132+141+135= 408

651-408 = 243 points to score on the final exam.
243/250 =.972 or 97.2%

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3 years ago

If he paints 1/2 of the wall blue, hoy many square feet will be blue?

Katen [24]

To determine how much of the wall is blue we first need to find its area. The wall is a rectangle, then its area is the product of its height and length:

$\begin{gathered} A=(8\frac{2}{5})(16\frac{2}{3}) \\ A=(\frac{42}{5})(\frac{50}{3}) \\ A=(14)(10) \\ A=140 \end{gathered}$

Hence, the area of the wall is 140 square ft. To determine how much of the wall is already painted we multiply this by 1/2, then:

$(140)(\frac{1}{2})=70$

Therefore, 70 square ft are blue.

6 0

1 year ago

Which is the vertex of x^2 + 10x = - 17?

Dafna11 [192]

Answer:

(-5, -8)

Step-by-step explanation:

Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k).

x^2 + 10x = - 17

x^2+10x+17=0

x^2+2*5x+25 - 8=0

(x+5)^2-8=0

h=-5, k= -8

vertex is (-5, -8)

3 0

3 years ago

Use logarithm tables to evaluatethe following 723.7 X 0.0667​

Use logarithm tables to evaluatethe following 723.7 X 0.0667