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3 years ago

The width of a rectangle is 1 less than one-half its length, and the perimeter is 46. Find the dimensions.

Mathematics

1 answer:

ch4aika [34]3 years ago

6 0

Answer:

Length is 26, width is 7

Step-by-step explanation:

Supposing y= width and x= length

We know from the question that

y= 1/2x -1

And the perimeter of any rectangle is 2y + 2x

Substitute y for 1/2x-1

2(1/2x-1) + 2x = 46

x - 2 + 2x = 46

3x = 48

x= 16

y= (1/2*16)-1

y=7

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Simply<br> 7p2 x 3p<br> 14p4

vivado [14]

Answer:

${ \tt{ = \frac{7 {p}^{2} \times 3p}{14 {p}^{4} } }} \\ = { \tt{ \frac{21 {p}^{3} }{14 {p}^{4} } }} \\ = { \tt{1.5 {p}^{ - 1} }}$

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2 years ago

Question content area top

Mumz [18]

Answer:

(-6,-4)

Step-by-step explanation:

So there actually is really easy way to solve this problem(that many people will never teach you for some weird reason).

Find difference between two points first in x and y direction.

X difference = (-3 - (-8)) = 5

Y difference = (-1 - (-6)) = 5

Multiply 2/5 to each difference

X difference 5 * 2/5 = 2

y difference 5* 2/5 = 2

just add the two number to First point(point A)

-8 + 2 = -6

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(-6,-4)

7 0

2 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

What is the exact area of a circle with a diameter of 10 cm? a. 5πcm^2 b. 10πm^2 c. 25πcm^2 d. 100πcm^2

dalvyx [7]

Answer:

Step-by-step explanation:

a= $\pi$ r^2

To find the radius, divide the diameter by 2

r=d/2

r=10/2

r=5

a= $\pi$ r^2

a= $\pi$ 5^2

a=25 $\pi$

So, choice C is correct

Hope this helps! :)

4 0

3 years ago

How do you solve 13+4x=1-x

mel-nik [20]

13+4x=1-x
4x=-12-x (minus 13 from each side)
5x=-12 (add x to each side)
You divide -12 by 5x
-12÷5x=2 $\frac{2}{5}$ ⇒2.4
x=2.4

6 0

3 years ago

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