Answer:
The volume increases at 35.71cm^3/min
Step-by-step explanation:
Given
[tex]PV^{1.4} = C[/tex]
[tex]V = 400cm^3[/tex]
[tex]P =80kPa[/tex]
[tex]\frac{dP}{dt} =-10kPa/min[/tex]
Required
Rate at which volume increases
[tex]PV^{1.4} = C[/tex] [tex]V = 400cm^3[/tex] [tex]P =80kPa[/tex]
Differentiate: [tex]PV^{1.4} = C[/tex]
[tex]P*\frac{dV^{1.4}}{dt} +V^{1.4}*\frac{dP}{dt} = \frac{d}{dt}C[/tex]
By differentiating C, we have:
[tex]P*\frac{dV^{1.4}}{dt} +V^{1.4}*\frac{dP}{dt} = 0[/tex]
Rewrite as:
[tex]P*(1.4)*V^{0.4}* \frac{dV}{dt} + V^{1.4}*\frac{dP}{dt} = 0[/tex]
Solve for [tex]\frac{dV}{dt}[/tex]
[tex]P*(1.4)*V^{0.4}* \frac{dV}{dt} =- V^{1.4}*\frac{dP}{dt}[/tex]
[tex]\frac{dV}{dt} =- \frac{V^{1.4}*\frac{dP}{dt} }{P*(1.4)*V^{0.4}}[/tex]
Substitute values
[tex]\frac{dV}{dt} =- \frac{400^{1.4}*-10 }{80*(1.4)*400^{0.4}}[/tex]
[tex]\frac{dV}{dt} =\frac{400*10 }{80*1.4}[/tex]
[tex]\frac{dV}{dt} =\frac{4000 }{112}[/tex]
[tex]\frac{dV}{dt} =35.71cm^3/min[/tex]
What is the slope of the line shown below?
10
O A. 2
5
(3,6)
OB. 4
O c. -4
-5
10
15
5
(1,-2)
-5
O D. 2
-10
Answer:
B
Step-by-step explanation:
Slope Formula
6 - (-2) / 3 - 1
8 / 2 = 4
The slope of the graph is 4.
Option B is the correct answer.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The coordinates from the graph are:
(1, -2), and (3, 6)
Now,
Slope.
= (6 -(-2)) / (3 - 1)
= (6 + 2) / 2
= 8/2
= 4
Thus,
The slope of the graph is 4.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ5
PLEASE HELP!!!
WILL MARK BRAINLIEST!!!
Solve for X and Y in the rectangle.
Thank you!m
Y = 20
X = 70
We know Y is 20 because both triangles are the same size. 20 is in the opposite corner to Y. The right corner is 90 degrees. There are 180 degrees in a triangle. To get your answer you are going to add 20 and 90 to get 110 then you will subtract 110 from 180.
Answer this guys please
[tex]\longrightarrow{\green{A.\:-8}}[/tex] ✔
Step-by-step explanation:
[tex]f(x )= - {x}^{2} + 1[/tex]
Plugging in the value "[tex]x\:=\:-3[/tex]" in the above expression, we have
[tex]f( - 3) = - ({ - 3})^{2} + 1 \\ \\ = - ( - 3 \times - 3) + 1 \\ \\ = - (9) + 1 \\ \\ = - 9 + 1 \\ \\ = - 8[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
[tex] \quad \quad \quad \quad \tt{f(x) = { - x}^{2} + 1} \: \: when \: \: x = - 3[/tex]
Let's try![tex] \quad \quad \quad \quad \tt{ ⟶f(x) = { - x}^{2} + 1}[/tex]
[tex] \quad \quad \quad \quad \tt{⟶f(-3) = {- (-3)}^{2} + 1}[/tex]
[tex] \quad \quad \quad \quad \tt{⟶ f( - 3) = { - (9) + 1}}[/tex]
[tex]\quad \quad \quad \quad \tt{⟶ f( - 3) = { - 9 + 1}}[/tex]
[tex]\quad \quad \quad \quad \tt{ ⟶f( - 3) = { -8}}[/tex]
Hence, The answer is:[tex]\quad \quad \quad \quad \boxed{\tt{ \color{green}f( - 3) = { - 8}}}[/tex]
_________
#LetsStudy
Plz help me solve this
Any help to solve this one?
Answer:
Step-by-step explanation:
[tex]81^{1/2}[/tex]
[tex]3^4*{1/2}[/tex]
[tex]3^{4/2}[/tex]
[tex]3^{2}[/tex]
9
[tex]-16^{3/4}[/tex]
[tex](-2)^{4 *3/4}[/tex]
[tex](-2)^{12/4}[/tex]
[tex](-2)^{3}[/tex]
-8
There are 6 chef assistants and 2 servers. How many staff are working there?
Answer: 8
Step-by-step explanation:
are you in elementary school
Answer:
8 staff
Step-by-step explanation:
6 +2 = 8 There are 8 staff working there.
If this is done a different way explain or lmk? Hope you are having a wonderful day!! Of not it'll get better I promisee! <33 :))
What addition statement does this show? A. 5.2 + 6.4 = –11.6 B. –5.2 + 6.4 = –11.6 C. 5.2 + (–6.4) = –11.6 D. –5.2 + (–6.4) = –11.6
Answer:
A
Step-by-step explanation:
I don’t know how to explain on why the student was incorrect
Answer:
the constant proportionality means the ratio between two directly proportional quantities.
so the constant proportionality will be 7.5÷6=1.25 or 10÷8=1.25 or 12.5÷10=1.25
constant proportionality should be same all through because it's a constant
What is the degree of 1
Answer:
28
Step-by-step explanation:
As one can see, the given diagram has two perpendicular lines. This means that two lines intersect each other at a right angle, therefore all of the resulting angles are (90) degree angles. This is indicated by one of the boxes around the angle. Moreover, this means that the angle that measures (62) degrees, plus angle (1) forms a (90) degree angle. Using this information, make an equation and solve for the measure of angle (1);
62 + (m<1) = 90
Inverse operations
62 + (m<1) = 90
m<1 = 28
What angle corresponds to 1/6 of a circle
4) A piece of hematite contains 70%
iron. If the hematite weighed 60g,
how much iron would there be?
6) A survey of 250 trees in a small
Answer:
42g
Step-by-step explanation:
70% of 60 = 42
GIVING OUT BRAINLIEST HELP ME PLSS !!
Answer:
C) 5.66
Step-by-step explanation:
For a 45-45-90 triangle, the length of each leg length (not including the hypotenuse) is congruent to each other. If 8=y√2, then y=8/√2=4√2=5.66
Answer:
5.66
Step-by-step explanation:
take 45 degree as reference angle
using cos rule
cos 45 =adjacent /hypotenuse
[tex]\frac{1}{\sqrt{2} }[/tex] =y/8
[tex]\frac{1}{\sqrt{2} } *8=y[/tex]
[tex]\frac{8}{\sqrt{2} }=y[/tex]
[tex]4\sqrt{2} =y[/tex]
5.66=y
What is the solution to the equation blow?
x + 6 = 24
Two letters from the word HAPPY are randomly chosen with replacement. What is the probability of choosing an H or P on either selection?
answer in decimal
Answer:
0.5 I believe
Step-by-step explanation:
The following data are monthly rents (in dollars) of studio and one-bedroom apartments in Harrisburg, Pennsylvania, in 2007, obtained from a random sample of such apartments advertised at rent.com in July 2007:
500, 549, 569, 575, 585, 600, 630, 680, 705, 790, 845
The mean of these eleven rent prices is $638.91 ,and the standard deviation is $105.93 .
1. Determine the standard error of the sample mean.
2. Describe what the population mean µmeans in this context.
3. Determine a 95% confidence interval for µ.
4. Write a sentence interpreting what this interval means.
5. Would you expect about 95% of the studio and one-bedroom apartments in Harrisburg in July 2007 to have a rent price within this interval? Explain.
Answer:
Part 1
SE= 31.94
Part2;
The population mean tells us that what would be the mean of all the monthly rents (in dollars) of studio and one-bedroom apartments in Harrisburg, Pennsylvania, in 2007.
Part 3:
576.31, 701.51
Part4:
This means that the 95%of the interval 576.31, 701.51 will have contain the value of the population parameter mean u.
Part 5:
Yes. out of 100 , 95 of the intervals will contain the true value of population mean u .
Step-by-step explanation:
Part 1
The standard error is calculated using the formula
SE = S/√n
where s is the standard deviation of the sample = $ 105.93
and n is the sample size= 11
Putting the values we get
SE= $ 105.93/ √11= 31.939
Part2;
The population mean tells us that what would be the mean of all the monthly rents (in dollars) of studio and one-bedroom apartments in Harrisburg, Pennsylvania, in 2007.
Part 3:
The z∝/2 value for 0.05 is ± 1.96
The 95 % confidence interval will be given by
x` ±z ∝/2 * s/√n
Putting the values
638.91 ± 1.96 * 31.94
638.91 ± 62.6006
576.31, 701.51
Part4:
This means that the 95%of the interval 576.31, 701.51 will have contain the value of the population parameter mean u.
Part 5:
Yes when the hypothesis testing is done and the sample mean is found to be equal to the population mean then it means that the population mean is to be found in this interval; 95% .
Or out of 100 , 95 of the intervals will contain the true value of population mean u.
The volume of a sphere is 904.32 mm3. What is the approximate volume of a cone that has the same height and a circular base with the same diameter? Use 3.14 for π and round to the nearest hundredth.
Answer:
[tex]V_c=452.16\ mm^3[/tex]
Step-by-step explanation:
Given that,
The volume of a sphere is 904.32 mm³.
The volume of a cone that has the same height and circular base with the same diameter is:
[tex]V_c=\dfrac{1}{3}\pi r^2 \times 2r=\dfrac{2}{3}\pi r^3[/tex]
The volume of a sphere with the same radius is:
[tex]V_s=\dfrac{4}{3}\pi r^3=2\times \dfrac{2}{3}\pi r^3[/tex]
So, the volume of sphere is :
[tex]V_c=\dfrac{V_s}{2}\\\\V_c=\dfrac{904.32 }{2}\\\\V_c=452.16\ mm^3[/tex]
So, the volume of the cone is [tex]452.16\ mm^3[/tex].
determine the missing angle.
The angle at the vertex of a rectangle is 90°
So, it means that,
= ? + 40 = 90
= ? = 90 - 40
= ? = 50
Answer:
50°
Step-by-step explanation:
x = ?°
x + 40° = 90°
x = 90° - 40°
x = 50°
what is 1 6/9 +5 9/7
[tex]\longrightarrow{\green{7 \frac{20}{21}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]1 \frac{6}{9} + 5 \frac{9}{7} \\ \\ = \frac{15}{9} + \frac{44}{7} \\ \\ = \frac{15 \times 7}{9 \times 7} + \frac{44 \times 9}{7 \times 9} \\ \\ = \frac{105 + 396}{63} \\ \\ = \frac{501}{63} \\ \\ = \frac{167}{21} \\ \\ = 7 \frac{20}{21} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
1. Name a decimal between 0.2222 and 0.2223.
2. if you laid 4 million bills end to end, how long (in miles) would that be? (use 6.14 inches for the length of a single bill. round your answer to one decimal place.)
2a. how long (in miles) would 4 billion dollars be? ( Round answer to one decimal place.)
3. what base is c in this statement?
695 base ten = 852 base x
4. order the numbers to smallest to largest.
3/11, 0.027, 0.27, -13
Step-by-step explanation:
You should be breaking this up
One
Decimal between 0.2222 and 0.2223 would be something like 0.22225
Two
1 mile = 5280 feet
1 mile = 5280 feet * 12 = 63360 inches
4 miles = 253440 inches
answered on my cell phone. I can't really do this.
How many quarts of pure antifreeze must be added to 8 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution
Let q be the number of quarts of pure antifreeze that needs to be added to get the desired solution.
8 quarts of 40% solution contains 0.40 × 8 = 3.2 quarts of antifreeze.
The new solution would have a total volume of 8 + q quarts, and it would contain a total amount of 3.2 + q quarts of antifreeze. You want to end up with a concentration of 60% antifreeze, which means
(3.2 + q) / (8 + q) = 0.60
Solve for q :
3.2 + q = 0.60 (8 + q)
3.2 + q = 4.8 + 0.6q
0.4q = 1.6
q = 4
Find mZ3 if mZ5 = 145º and mZ4 = 45°
9514 1404 393
Answer:
C. 100°
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles.
∠5 = ∠3 +∠4
145° = ∠3 +45° . . . . fill in the given values
100° = ∠3 . . . . . . subtract 45° from both sides
Whats the order of rotational symmetry for brainlest
Answer:
1Step-by-step explanation:
A circle has rotation symmetry around the center for every angle. A circle has an unlimited number of angles of symmetry and the order of its rotation is infinite.
Name this triangle by its sides and angles. This is a(n) ____________________ triangle.
a triangle with one right angle and three non-congruent sides
right triangle
Hope this helps! :)
what is the value of a?
Hope this help!!!
Have a nice day!!!
This exercise involves the formula for the area of a circular sector. The area of a circle is 700 m2. Find the area of a sector of this circle that subtends a central angle of 3 rad.
Answer:
334.4 m²
Step-by-step explanation:
The formula for the area of a sector is given as:
1/2 × r² × θ
Where θ = Central angle
Area of a Circle = 700 m²
The formula for the area of a circle = πr²
r = Radius of a circle
r² = Area / π
r = √Area / π
r = √700/π
r = 14.927053304 m
Approximately, r = 14.93 m
Therefore, the area of the sector
= 1/2 × r² × θ
= 1/2 × 14.93² × 3 rad
= 334.35735 m²
Approximately, Area of the sector = 334.4 m²
write 0.824 as a fraction in the simplest form
What is the vertex of the absolute value function below?
Answer:
(-3,2)
Step-by-step explanation: The bottom most point of the graph is 3 back from 0 and 2 up from 0
I really need help please
Answer:
11
Step-by-step explanation:
3/7*14=6
5/8*8=5
6+5=11
How do I uses these
Answer:
To understand a graph you need to interpret a graph or a chart, read the title, look at the key, read the numbers and lables. then study the graph to understand what it shows. read the title graph or chart. the title tells what information is being displayed.
Step-by-step explanation:
Point Q is the midpoint of GH¯¯¯¯¯¯. GQ=2x+3, and GH=5x−5 .
What is the length of GQ¯¯¯¯¯?
Answer:
[tex]GQ =25[/tex] --- GoTV
Step-by-step explanation:
Given
[tex]GQ = 2x + 3[/tex]
[tex]GH= 5x - 5[/tex]
Required
Find GQ
Since Q is the midpoint, then:
[tex]GH = 2 * GQ[/tex]
This gives:
[tex]5x - 5 = 2[2x+3][/tex]
Open bracket
[tex]5x - 5 = 4x+6[/tex]
Collect like terms
[tex]5x - 4x = 5+6[/tex]
[tex]x =11[/tex]
We have:
[tex]GQ =2x+3[/tex]
This gives:
[tex]GQ =2*11+3[/tex]
[tex]GQ =25[/tex]
