Differentiating both sides of PV = C with respect to t gives us ...
... P'V +PV' = 0
Filling in the given numbers gives us ...
... (40 kPa/min)(900 cm³) + V'(150 kPa) = 0
Solving for V' gives ...
... V' = -(40 kPa/min)(900 cm³)/(150 kPa)
.. V' = -240 cm³/min
The volume is decreasing at the rate of 240 cm³/min.
Final answer:
In Physics, Boyle's Law relates the pressure and volume of a gas at constant temperature. To find the rate at which volume is decreasing as pressure increases, we differentiate the equation PV = C with respect to time and solve for [tex]\frac{dV}{dt}[/tex] , given the pressure, volume, and rate of change of pressure which comes out to be 240 cm³/min.
Explanation:
The subject of this question is Physics, specifically relating to Boyle's Law, which is part of gas laws studied in chemistry and physics. The level of this question is appropriate for High School students. We know from Boyle's Law that for a given amount of gas at constant temperature, the pressure P is inversely proportional to the volume V, meaning that PV = C or k, where C is a constant.
To solve the problem stated, we differentiate both sides of PV = C with respect to time t. This will give us P[tex]\frac{dV}{dt}[/tex] + V[tex]\frac{dP}{dt}[/tex] = 0. With the known values of P, V, and[tex]\frac{dP}{dt}[/tex] , we can solve for [tex]\frac{dV}{dt}[/tex], which will give us the rate at which the volume is decreasing as the pressure increases.
By substituting the given values into the differentiated equation: 150 kPa x [tex]\frac{dV}{dt}[/tex]+ 900 cm³ x 40 kPa/min = 0, we solve for [tex]\frac{dV}{dt}[/tex] to find the rate at which the volume is changing.
[tex]\frac{dV}{dt}[/tex] = - [tex]\frac{900}{150}[/tex] x 40
[tex]\frac{dV}{dt}[/tex] = -6 x 40
[tex]\frac{dV}{dt}[/tex] = -240 cm³/min
Following this method, we find that the volume is decreasing at a rate of 240 cm³/min.
SHOW WORK
1) copper has density of 8.92 g/cm^3. How many milliliters of water would be displaced if 46kg of copper granules were poured into a barrel filled with water?
2) If the density of water is 1.00 g/mL, will the substances above float or sink in the water??
Answer:
1) Volume of water displaced = 5.16 L
2) Copper sinks in water.
Explanation:
1) Density of copper = 8.92[tex]g/cm^3[/tex]
Mass of copper = 46 kg = 46000 g
We know that, Density = Mass / volume
So, Volume = Mass/ density
Volume of copper = 46000/8.92 = 5156.95 [tex]cm^3[/tex]
Since the density of copper 8.92[tex]g/cm^3[/tex] is greater than density of water 1[tex]g/cm^3[/tex], the copper immerses in water. Since it immerses it will displace a volume of water which is equal to the volume of copper.
So volume of water displaced = volume of copper = 5156.95 [tex]cm^3[/tex] =5.16 L of water
2) Since the density of copper 8.92[tex]g/cm^3[/tex] is greater than density of water 1[tex]g/cm^3[/tex], the copper immerses in water. So copper sink in water.
I WILL GIVE BRAINLYYYY PLS HELPPPPPPPPPPPPPPPPPP
Two planes left the same airport traveling in opposite directions. The first plane left at 9:00 a.m. and 2.25 hours later, the two planes were 1825 miles apart. The second plane left at 10:00 a.m. and its average rate was 108 miles per hour slower than the first plane's average rate. Let x represent the first plane's average rate. What was the first plane's average rate? Enter an equation that can be used to solve this problem in the first box. Solve for x and enter the first plane's average rate in the second box.
WHAT IS THE EQUATION AND WHAT IS THE ANSWERRR???
Answer:
The Average rate of the first plane is 560 mph
Step-by-step explanation:
x = first plane's average rate (in mph)
x−108 = second plane's average rate (in mph)
First planes total distance = 2.25x
Second planes total distance = 1.25(x−108)
2.25x + 1.25(x−108) = 1825
x = 560
Subtract the following polynomials
subtracting term by term
(3.1x - 4.3x ) + (2.8z - (- 1.2z ) )
= - 1.2x + (2.8z + 1.2z ) = - 1.2x + 5z
rearrange 2y=x into y=mx+b
You want to get y by itself
y=1/2 x
y=mx+b
m=1/2 b=0
y = [tex]\frac{1}{2}[/tex] x + 0
given 2y = x ( divide both sides by 2 )
y = [tex]\frac{1}{2}[/tex] x + 0
The longest side of an acute triangle measures 30inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded out the nearest hundredth
The two short sides must be longer than those required in an isosceles right triangle. The ratio of side length to hypotenuse length in a 45°-45°-90° triangle is 1 : √2. So, such a triangle requires side lengths of 30/√2 ≈ 21.213 inches. Its perimeter will be about
... (30 +21.213 +21.213) in = 72.426 in
Since the perimeter needs to be slightly longer than that for the triangle to be acute, the smallest possible perimeter is ...
... 72.43 in
Balls numbered from 1 to 38 are placed in a contianer and stirred. If one is drawn at random what is the probability that the number is a prime number?
The primes in the range 1–38 are ...
... 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
There are 12 of them, so the probability of drawing a prime is
... 12/38 = 6/19
Answer:
[tex]\text{Probability}=\frac{6}{19}[/tex]
Step-by-step explanation:
Given : Balls numbered from 1 to 38 are placed in a container and stirred. If one is drawn at random.
To find : The probability that the number is a prime number
Solution :
Probability is defined by,
[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]
Favorable outcomes - To get the number is prime number from 1 to 38
Prime numbers are those which were not divisble by any number except 1 and itself.
From 1 to 38 - 2,3,5,7,11,13,17,19,23,29,31,37
Favorable outcome = 12
Total number of outcome is 1 to 38 = 38
[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}[/tex]
[tex]\text{Probability}=\frac{12}{38}[/tex]
[tex]\text{Probability}=\frac{6}{19}[/tex]
Q#16 I need help please
For this case we have the following expressions:
[tex]x = -4y + 4\\\\2x + 8y = 8\\[/tex]
Rewriting the second equation we have:
[tex]2x = -8y + 8\\[/tex]
It is observed that by multiplying the first equation by 2, the second equation is obtained.
Thus, the equations are linearly dependent and since the lines are equal then they are intercepted in infinite points. Therefore, the system has endless solutions.
Answer:
Option D
Divide. (5 1/4)÷(−2 1/2) Enter your answer as a mixed number, in simplified form, in the box.
Answer:
2 1/10
Step-by-step explanation:
(5 1/4)/(2 1/2)
Change mixed fraction to improper fractions
(21/4)/(2 1/2)
(21/4)/(5/2) =21/10
=2 1/10
Answer:
2 1/10
Step-by-step explanation:
What is the slope of a line that is perpendicular to line m
the slope of a perpendicular line = - [tex]\frac{3}{5}[/tex]
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange 5x - 3y = 2 into this form
subtract 5x from both sides
- 3y = - 5x + 2 ( divide all terms by - 3 )
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex]
with slope m = [tex]\frac{5}{3}[/tex]
the slope of a line perpendicular = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{3}{5}[/tex]
What is the value of –2x2 + 4y if x = –2 and y = 3?
You would first substitute x and y into the equation so: -2(-2)^2+4(3)
Then you solve:
-2(-2)^2+4(3)
8+12
so your answer will be 20
help me with this problem
- 9 ≤ x ≤ 7
the domain is the values of x on the x- axis that define y = f(x)
y is defined for all values of x in the stated domain
The temperature outside is 12 Celsius, overnight the temperature drops 15 degrees. What is the temperature now?
1. Evaluate a/b + c^2d for a = 6,b=3,c=4,and d=5
A. 42
B. 18
C. 82
D. 360
2.What is the product? 6(-3)
A. -18
B. -3
C. 18
D. 9
3. Simplify the expression (4/7)^3
A. 343/64
B. 12/21
C. 12/49
D. 64/343
Will mark brainliest for correct answers :D
Answer:
1) C
2) A
3) D
Step-by-step explanation:
A) We substitute the values for a ,b , c and d in the given equation.[tex]\frac{6}{3} +4^2 (5) \\= 2+80\\=82[/tex]
Hence option c. 82 is the answer.
2) The product 6(-3)
Since positive x negative gives negative
we get -(6x3) = -18
Option A is the answer.
3) For this we have to find cube of a fraction with numerator 4 and denominator 7
We find cube of numerator first = 4x4x4 =64
Cube of denominator = 7x7x7 = 343
Hence cube of fraction = 64/343
Option D
A book store has twice as many history books as science books. The store has 81 history and science books altogether how many of wach kind does the bookstore have? Write equation too....
let h= history books
science books = s
h=2s there are 2 times as many history as science so to get them equal we double the science
h+s=81 there are 81 total history and science books
2s+s=81 substitute 2s for h in the above equation
3s = 81 combine like terms
s = 27
There are 27 science books
h=2s
h=2(27)
h=54
there are 54 history books
find an equation of the circle whose diameter has endpoints (-2,-5) and (6,-1)
The equation of the circle in standard form with a center at (2, -3) and a radius [tex]\(4\sqrt{5}\)[/tex] is [tex]\( (x - 2)^2 + (y + 3)^2 = 80 \)[/tex].
To find the equation of the circle with the diameter endpoints given,
The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
Midpoint [tex]\((M_x, M_y)[/tex] = [tex]\left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)\)[/tex]
For the endpoints A (-2,-5) and B (6,-1), we calculate:
[tex]\(M_x = \frac{-2 + 6}{2} = \frac{4}{2} = 2\)[/tex]
[tex]\(M_y = \frac{-5 + (-1)}{2} = \frac{-6}{2} = -3\)[/tex]
So, the midpoint, which is the center of the circle, is C (2, -3).
The radius is half the length of the diameter, and the length of the diameter is the distance between the endpoints A and B using the distance formula:
Distance d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2} \)[/tex]
r = [tex]\frac{d}{2} = \frac{\sqrt{(6 - (-2))^2 + (-1 - (-5))^2}}{2} \)[/tex]
Calculating the expressions:
r = [tex]\frac{\sqrt{(6 + 2)^2 + (-1 + 5)^2}}{2} \)[/tex]
= [tex]\frac{\sqrt{8^2 + 4^2}}{2} \)[/tex]
= [tex]\frac{\sqrt{64 + 16}}{2} \)[/tex]
= [tex]\frac{\sqrt{80}}{2} \)[/tex]
= [tex]\frac{8\sqrt{5}}{2} \)[/tex]
r = [tex]4\sqrt{5} \)[/tex]
The equation of a circle with center (h, k) and radius r can be represented as:
[tex]\( (x - h)^2 + (y - k)^2 = r^2 \)[/tex]
Plugging our midpoint as the center and our radius into the equation:
[tex]\( (x - 2)^2 + (y + 3)^2 = (4\sqrt{5})^2 \)[/tex]
Simplifying,
[tex]\( (x - 2)^2 + (y + 3)^2 = 16 \cdot 5 \)[/tex]
[tex]\( (x - 2)^2 + (y + 3)^2 = 80 \)[/tex]
Thus, the required equation is [tex]\( (x - 2)^2 + (y + 3)^2 = 80[/tex].
Rameen’s heating bill is $5.42 per month plus $1.08 per therm. How many therms can Rameen use if he wants his heating bill to be a maximum of $87.50? Write the solution in interval notation.
Write and solve an inequality:
Total(t) = $5.42 + ($1.08/therm)(t) ≤ $87.50.
First, subtract $5.42 from $87.50: then ($1.08/therm)(t) ≤ $82.08
Next, divide both sides by $1.08 per therm:
t ≤ ($82.08) / ($1.08/therm) = 76 therms (maximum). Thus, Rameen's usage could be [0,76] (therms).
Answer:
[0,76]
Step-by-step explanation:
Step 1. Read the problem.
Step 2. Identify what you are looking for.
the number of therms Rameen can buy
Step 3. Name what you are looking for. Choose a variable to represent that quantity.
Let t= the number of therms.
Step 4. Translate. Write a sentence that gives the information to find it. Translate into an inequality.
$5.42 plus $1.08 times the number of therms is less than or equal to $87.50.
5.42+1.08t≤87.50
Step 5. Solve the inequality.
1.08tt≤82.08≤76
Step 6. Check the answer in the problem and make sure it makes sense.
Yes, 5.42+1.08(76)=87.50.
Step 7. Answer the question with a complete sentence.
Rameen can buy no more than 76 therms if he wants his heating bill to be a maximum of $87.50.
Since it is not possible to buy a negative number of therms, the lest number of therms Rameen can buy is 0.
In interval notation, the amount of therms Rameen can buy is [0,76].
Mrs. Riley is teaching her class to sew pillows. Each pillow requires yards of fabric. The fabric she purchased cost $2.40 per yard.
How many pillows will her class be able to make if she purchased $405 of fabric?
A.
75 pillows
B.
78 pillows
C.
85 pillows
D.
98 pillows
Mrs. Riley can make 168 pillows because she bought 168.75 yards of fabric and each pillow requires 1 yard of fabric.
Explanation:First, we need to determine how many yards of fabric Mrs. Riley purchased. We do this by dividing the total cost of the fabric ($405) by the cost per yard ($2.40). So, 405 ÷ 2.4 = 168.75 yards. Each pillow requires 1 yard of fabric, therefore she can sew 168 pillows with no leftover fabric.
Here is the calculation in more detail:
Divide the total money Mrs. Riley spent on fabric by the cost of fabric per yard. That is, 405 ÷ 2.4 = 168.75.Since each pillow requires 1 yard of fabric, the number of pillows that can be made is the same as the number of yards of fabric purchased. Therefore, Mrs. Riley can make 168 pillows (rounding down to the nearest whole pillow).Learn more about Math Calculation here:https://brainly.com/question/31573607
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Which of the following is the equation of a line that passes through the point (3,2) and is parallel to the y-axis? A. x = 2 B. y = 3 C. x = 3 D. y = 2
Answer:
Option C is right answer
Step-by-step explanation:
We have in coordinate geometry a straight line in slope intercept form as
y = mx+c
where m is the slope and c is the y intercept
There are special lines when m=0 and m = infinity.
When a line is parallel to y axis, it has slope = tan90 = infinity.
Hence line will have equation of the form x = a for some a.
Since the line passes through (3,2) we can find a using this.
Substitute x value to get 3 = x
Hence equation of the line is x =3
Answer:
X=3
Step-by-step explanation:
Use the identity a^3+b^3=(a+b)^3−3ab(a+b) to determine the sum of the cubes of two numbers if the sum of the two numbers is 4 and the product of the two numbers is 1.
Your identity says ...
... sum of cubes = (sum)³ -3(product)(sum)
... = 4³ -3·1·4
... = 64 -12 = 52
_____
The two numbers are 2±√3, and the sum of their cubes is indeed 52.
A bag contains 5 blue marbles, 3 red marbles and 4 yellow marbles.
What is the probability of choosing one yellow marble and then a red marble with replacement?
[tex]|\Omega|=12^2=144\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{144}=\dfrac{1}{12}[/tex]
Answer:
Step-by-step explanation:
Find the quotient 4/15÷1/6
Answer:
1 3/5
Step-by-step explanation:
4/15÷1/6
Copy dot flip
4/15 * 6/1
24/15
Divide the top and bottom by 3
8/5
Change the improper fraction to a mixed number
5 goes into 8 1 time with 3 left over
1 3/5
. The dimensions of a large broken window are 122⁄3 feet wide and 81⁄3 feet tall. How many square feet of glass are required to replace the window?
Answer:
[tex]1098[/tex] square feet of glass is needed to replace the window.
Step-by-step explanation:
Square feet is the unit of measure of Area. How many square feet of glass are required to replace the window can be found by calculating the area of the window.
Area of the window = Width * Length
=[tex]\frac{122}{3}*\frac{81}{3}[/tex]
=[tex]\frac{122*81}{3*3}[/tex]
=[tex]\frac{9882}{9}[/tex]
=[tex]1098[/tex] square feet.
∴ we need [tex]1098[/tex] square feet of glass.
1098 ft²
Area = width × height
= [tex]\frac{122}{3}[/tex] × [tex]\frac{81}{3}[/tex]
= [tex]\frac{122(81)}{3(3)}[/tex] = [tex]\frac{9882}{9}[/tex]= 1098 ft²
Q # 4 if anybody can help me
Solution:
Given equation of line [tex]-4x+2y=24[/tex]
To find the x-intercept of the equation, substitute [tex]y=0[/tex] in the equation,
[tex]\Rightarrow -4x+2(0)=24\\\Rightarrow -4x=24\\\Rightarrow x=-\frac{24}{4} =-6[/tex]
Hence, x-intercept of the equation is [tex](-6,0)[/tex].
To find the y-intercept of the equation, substitute [tex]x=0[/tex] in the equation,
[tex]\Rightarrow -4(0)+2y=24\\\Rightarrow 2y=24\\\Rightarrow y=\frac{24}{2} =12[/tex]
Hence, y-intercept of the equation is [tex](0,12)[/tex].
Which inequality is equivalent to -m ≥ 15?
A. m ≥ 15
B. m ≥ -15
C. m ≤ -15
D. m ≤ 15
Answer:
c
Step-by-step explanation:
The inequality equivalent to -m ≥ 15 is m ≤ -15, achieved by multiplying both sides of the inequality by -1, which reverses the inequality symbol. So the correct answer is C. m ≤ -15.
The question asks which inequality is equivalent to the inequality -m ">≥ 15. To find the equivalent inequality where m is positive, we need to multiply or divide both sides of the inequality by -1, remembering that doing so reverses the inequality symbol. Therefore, multiplying both sides by -1 gives m ≤ -15, which means that the inequality that is equivalent to -m ≥ 15 is m ≤ -15.
So the correct answer is C. m ≤ -15.
Find the value of {2/3}^3 Explain or show how you got your answer.
[tex]\frac{8}{27}[/tex]
(2/3)^3 = [tex]\frac{2^{3} }{3^{3} }[/tex] = (2 × 2 × 2 )/(3 × 3 × 3 ) = [tex]\frac{8}{27}[/tex]
Answer:
Step-by-step explanation:
Given: C∉ BD ,△ABC D∈ ray BC ,AB=AC=BC Prove: BD>DA>AB
Triangle ABC is equilateral, because AB=BC=AC=a. Then
m∠A=m∠B=m∠C=60°.
Let point D lie on the ray BC to the right from points B and C and let CD=x. Then BD=a+x, AB=a.
Consider triangle ACD. In this triangle, m∠ACD=180°-m∠ACB=180°-60°=120°.
By the cosine theorem,
[tex]AD^2=AC^2+CD^2-2\cdot AC\cdot CD\cdot \cos \angle ACD,\\\\AD^2=a^2+x^2-2\cdot a\cdot x\cdot \cos 120^{\circ},\\\\AD^2=a^2+x^2+ax,\\\\AD=\sqrt{a^2+x^2+ax}.[/tex]
Since [tex]a^2+x^2+ax=a^2+x^2+ax+ax-ax=(a+x)^2-ax,[/tex] then
[tex]AD^2=(a+x)^2-ax<(a+x)^2=BD^2\Rightarrow AD<BD[/tex]
and
[tex]AD^2=a^2+x^2+ax>a^2=AB^2\Rightarrow AD>AB.[/tex]
Therefore, you get double inequality
[tex]AB<AD<BD[/tex] or [tex]BD>AD>AB.[/tex]
Answer:
The proof is below
Step-by-step explanation:
Please look at the attachment below
Please let me know if this is wrong
Let me know if you have any questions
If right please give me brainiest
Thanks
Which statement about the graph of f(x)=e^x is true?Please Help
O It crosses the x-axis at e.
O It crosses the y-axis at e.
O It passes through the point (1,e).
O It passes through the point (e,1).
The function f(x) = e^x never crosses the x-axis and crosses the y-axis at point (0,1). It does not pass through the point (e,1), but it does pass through the point (1,e). Hence, the correct statement is 'It passes through the point (1,e)'.
Explanation:The function f(x) = e^x is an exponential function where 'e' is Euler's number, approximately equal to 2.71828. Its graph has distinctive traits which are related to the options provided.
The statements 'It crosses the x-axis at e' and 'It crosses the y-axis at e' are incorrect because the graph of f(x) = e^x never crosses the x-axis, and it crosses the y-axis at the point (0,1), not e.
The statement 'It passes through the point (e,1)' is also incorrect. This function, f(x) = e^x, will pass through the point (1,e), not (e,1). Hence, the option 'It passes through the point (1,e)' is the true statement about the graph of the function.
Learn more about exponential function here:https://brainly.com/question/15352175
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Simplify. 8√-76 Enter your answer, in simplest radical form, in the box.
Answer:
6i\sqrt{19}
Step-by-step explanation:
How can you write 0.326 in two other forms
144 divide by 12 - 18 + 3?
if im not mastaken the answer is -48