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grandymaker [24]
3 years ago
8

Find the distance BF for the points B(1, –1) and F(–3, 5).

Mathematics
1 answer:
Levart [38]3 years ago
8 0
They are 8units apart
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Calculate the gradient of the straight line which joins A(2,-3) and B(6,9)<br>​
Pie

Answer:

Gradient: m = 3

Step-by-step explanation:

m = change in y/change in x

m = \frac{Y2-Y1}{X2-X1}

m = \frac{9-(-3)}{6-(2)}

m = 12/4

m = 3

5 0
3 years ago
What is the volume, in cubic centimeters, of a right rectangular prism that has a lenght of 4 centimeters, a width of 9 centimet
Temka [501]

Answer:

The volume of the prism is 360 cm^3.

Step-by-step explanation:

The rectangular prism is a three dimensional figure formed by six rectangular faces. It's volume is given by the product of it's three dimensions. The calculation for the volume of this prism is shown bellow:

volume = width*height*length

volume = 9*10*4

volume = 360 cm^3

The volume of the prism is 360 cm^3.

7 0
3 years ago
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Which equation applies the associative property of multiplication?
ohaa [14]

Answer:

<u>C) −12/5⋅(7/12⋅1/9)⋅8/5=(−12/5⋅7/12)⋅(1/9⋅8/5)</u>

5 0
2 years ago
In a flower garden, there are 3 tulips for every 8 daisies. If there are 18 tulips, how many daisies are there?
LenaWriter [7]
18/3 = 6
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6 0
3 years ago
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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
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