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julia-pushkina [17]
3 years ago
12

14. Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure P of the gas is inversely

proportional to the volume V of the gas. Suppose that at a certain temperature the volume is 728 cm!, the pressure is 182 kPa, and the pressure is decreasing at a rate of 25 kPa/min. At what rate is the volume increasing at this instant?
Mathematics
1 answer:
Ostrovityanka [42]3 years ago
5 0

Answer:

dV/dt = 100 cm³/min

Step-by-step explanation:

Given

V = 728 cm³

P = 182 kPa

dP/dt = - 25 kPa/min

dV/dt = ?

If we apply the ideal gas equation

P*V = n*R*T

where n*R*T is constant

we have

d(P*V)/dt = d(n*R*T)/dt

⇒ d(P*V)/dt = 0

⇒ V*(dP/dt) + P*(dV/dt) = 0

⇒ dV/dt = - (V/P)*(dP/dt)

Plugging the known values we obtain

⇒ dV/dt = - (728 cm³/182 kPa)*(- 25 kPa/min)

⇒ dV/dt = 100 cm³/min

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Charli bought 2 3/4 pounds of pears for 0.76 per pound and 2 3/4 pounds of grapes for 1.40 per pound. how much money in dollars
MArishka [77]

Answer:

Total = \$5.94 ---- in dollars

Total = 594\ cents ---- in cents

5 dollars 94 cents

Step-by-step explanation:

Given

Pears

Weight = 2\frac{3}{4}\ lb

Amount = \$0.76 per pound

Grapes

Weight = 2\frac{3}{4}\ lb

Amount = \$1.40 per pound

Required

Determine the amount paid for the fruit in dollar and cents

First, we need to calculate the amount paid for each fruit.

This is calculated by multiplying the amount per pound by the number of pounds bought.

For Pears:

Total_{Pears} = 2\frac{3}{4} * \$0.76

Convert fraction to decimal

Total_{Pears} = 2.75 * \$0.76

Total_{Pears} = \$2.09

For Grapes

Total_{Grapes} = 2\frac{3}{4} * \$1.40

Convert fraction to decimal

Total_{Grapes} = 2.75 * \$1.40

Total_{Grapes} = \$3.85

Next, we add both amounts together to get the total amount spent in dollars.

Total = Total_{Pears} + Total_{Grapes}

Total = \$2.09 + \$3.85

Total = \$5.94

Multiply by 100 to convert this amount to cents

Total = 5.94 * 100\ cents

Total = 594\ cents

And it can be represented as dollars and cents as:

5 dollars 94 cents

8 0
2 years ago
Write the equation of a line passing through (6,-2) and perpendicular to -2x + 3y= -6
____ [38]
Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.


-2x+3y=-6                 Add 2x in both sides
3y=2x-6                    Divide by 3 in both sides to isolate y
y=2/3x-6/3


The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.

y=mx+b                 Substitute the given point and the previous slope found
-2=(-3/2)(6)+b       Combine like terms
-2=-9+b                 Add 9 in both sides to isolate b
7=b

The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.


4 0
3 years ago
Please help meeeeeeeeeeeew
Paladinen [302]

Answer:

  • 40 sq. units

Step-by-step explanation:

<h3>Solution 1</h3>

The figure (kite) is symmetric and covers half of the area of rectangle with sides 8 units aby 10 units

<u>The area of the rectangle:</u>

  • A = 8*10 = 80 sq. units

<u>The area of the kite:</u>

  • A = 1/2*80 = 40 sq. units
<h3>Solution 2</h3>

Split the kite into two triangles and calculate their area and add up

<u>Triangle DCB has b = 8, h = 2 and has area:</u>

  • A = 1/2*8*2 = 8 sq. units

<u>Triangle DAB has b = 8, h = 8 and has area:</u>

  • A = 1/2*8*8 = 32 sq. units

<u>Total area:</u>

  • 8 + 32 = 40 sq. units
6 0
2 years ago
Read 2 more answers
Please help me i cant get this i. honestly just need someone to give the answers for this lesson
Likurg_2 [28]
Area of the triangle = (1/2)*base* height = (1/2)*3*6 = 9 sm²
We have 4 triangles like this one ,
so area of 4 triangles  = 9*4 = 36 cm².
Area of the square = 3*3 = 9 cm²

Surface area here means area all triangles  + area of the square =36 +9 =
= 45 cm ²

Answer is 45 cm².

7 0
2 years ago
If Mike has 96 muffins that needs to be boxed up into dozens and 6 of them are blueberry. How many boxes does he need?
ella [17]

Answer:

8 boxes

Step-by-step explanation:

x*12=96

x*12/12=96/12

x=8

7 0
3 years ago
Read 2 more answers
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