Under certain conditions, the velocity of a liquid in a pipe at distance r from the center of the pipe is given by V = 400(3.025 x 10-5--2) where Osrs5,5x10 -3. Writeras a function of V.r=where the domain is a compound inequality(Use scientific notation. Use integers or decimals for any numbers in the expression.)Le
Answers
Solving the equation for r:
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-r^2) \\ r^2=9.025\cdot10^{-5}-\frac{V}{400} \\ r=\sqrt[]{9.025\cdot10^{-5}-\frac{V}{400}} \end{gathered}[/tex]With the first equations, we can establish some limits for V:
With the lowest value for r (r=0):
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-0^2) \\ V=400(9.025\cdot10^{-5}) \\ V=3.61\cdot10^{-2} \end{gathered}[/tex]With the highest value for r (r=9.5x10^-3)
[tex]\begin{gathered} V=400(9.025\cdot10^{-5}-(9.5\cdot10^{-3})^2) \\ V=400(9.025\cdot10^{-5}-9.025\cdot10^{-5}) \\ V=400(0) \\ V=0 \end{gathered}[/tex]According to the radius range, velocity can be between 0 and 3.61x10^-2
It is also necessary to check the domain of the function considering it is a square root. The argument of an square root cannot be less than 0. Then:
[tex]\begin{gathered} 9.025\cdot10^{-5}-\frac{V}{400}\ge0 \\ 9.025\cdot10^{-5}\ge\frac{V}{400} \\ V\leq400(9.025\cdot10^{-5}) \\ V\leq3.61\cdot10^{-2} \end{gathered}[/tex]This is the same limit for velocity obtained before. Then, we can say for velocity that:
[tex]0\leq V\leq3.61\cdot10^{-2}[/tex]Related Questions
quick!! will give brainliest!! Given g(x) = -x + 3, solve for a when g(2) = -1
Answers
We have the following:
[tex]g(x)=-x+3[/tex]replacing when x is 2:
[tex]g(2)=-2+3=1[/tex]URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Answers
Answer:
translated 8 units down and then reflected across the y-axis
Point S is on line segment \overline{RT} RT . Given RT=3x,RT=3x, RS=3x-5,RS=3x−5, and ST=3x-1,ST=3x−1, determine the numerical length of \overline{RT}. RT .
Answers
The numerical length of the line segment RT is 6.
Length:
Length is the measuring unit used to identifying the size of an object or distance from one point to the other.
Given,
There is a point on the line segment RT.
And the values of the pots are,
RT = 3x, RS = 3x - 5 and ST = 3x - 1.
Now we need to find the length of the line segment RT.
To find the line of the line segment RT,
We have to add the length of the segments,
That can be written as,
=> RT = RS + ST
Now, we have to apply the values of the point to the equation, then we get,
=> 3x = 3x - 5 + 3x - 1
=> 3x = 6x - 6
=> 6x - 3x - 6
=> 3x - 6
=> 3x = 6
=> x = 2
If the value of x is 2, then the length of the line segment RT is,
RT = 3x => 3 x 2 = 6
Therefore, the length of the line segment RT is 6.
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Give the slope and y - intercept for each of the following equations, then sketch the graph. Give the slope ofany line perpendicular to the given line.y =22 +5Slope =y - intercept = (0,_ ) Slope of a Line Perpendicular =
Answers
The slope is 2.
The y-intercept is 5 or (0, 5)
See graph below
Explanation:Given:
y = 2x + 5
To find:
the slope, y-intercept, and plot a graph
To determine the slope and y-intercept, we will use the equation of line formula:
y = mx + b
m = slope
b = y-intercept
Comparing both equations:
y = y
2x = mx
m = 2
The slope = 2
5 = b
The y-intercept = 5
To plot the graph, we will assign values to x in order to get values to y that will be plotted:
let x = -4, 0, 4
when x = -4
y = 2(-4) + 5 = -3
when x = 0
y = 2(0) + 5 = 5
when x = 4
y = 2(4) + 5 = 13
Plotting the points:
Each line on the graph represents 1 unit
What are the slope and the y-intercept of the linear function that is represented by the table? -- Nicol у 3 2 1 0 -2 / 0 Nlw 3 1 2 -1 The slope is -3, and the y-intercept is 3 The slope is -3, and the y-intercept is z. 1 The slope is 3, and the v-intercept is -
Answers
We will assume the next table to answer this question (a linear function) (since the data in the question is not clear):
Having this information, we can find the slope using the formula for it:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]If we pick up from the table the next points:
x1 = 1, y1 =6
x2 = 2, y2 = 8
Then
[tex]m=\frac{8-6}{2-1}=\frac{2}{1}\Rightarrow m=2[/tex]We can use the slope-point formula to find the y-intercept. We can use the point (3, 10). Then, we have:
[tex]y-y_1=m\cdot(x-x_1)\Rightarrow y-10=2\cdot(x-3)\Rightarrow y-10=2x-6[/tex][tex]y=2x-6+10\Rightarrow y=2x+4[/tex]We end up with the slope-intercept formula for the line. Then the y-intercept is 4. In other words, if we have x = 0, then y = 4.
Then the slope for the values represented in the proposed table is m = 2, and the y-intercept is y = 4.
In 2011, the average daily temperature in Darrtown was 65°F. In 2012, the average daily temperature increased by 3% but then decreased by 4.5% in 2013.What was the daily average temperature in Darrtown in 2013?A.62°FB.64°FC.68°FD.74°F (thank you in advanced for who helps i was having trouble with this question)
Answers
Solution
In 2011 The temperature in Darrtown is
[tex]65^{\circ}F[/tex]The temperature increased by 3% in 2012
The temperature will be
[tex](1+\frac{3}{100})\times65=(1.03)(65)=66.95^{\circ}F[/tex]The temperature decreased by 4.5% in 2013
The temperature will be
[tex]\begin{gathered} (1-\frac{4.5}{100})\times66.95=0.955\times66.95=63.93725 \\ \\ (1-\frac{4.5}{100})\times66.95=64^{\circ}F\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore, the temperature in 2013 is 64 degrees Fareheint
Option B
solve for x and y (2x+7)(x+1)(y+5)(x-4)
Answers
Answer:
I am assuming you are looking for the x-intercepts and y-intercepts...here they are.
x-intercepts: (-7/2,0) , (-1,0) , (4,0)
y-intercepts: (0,-5)
Hope this helps...if not, please expound your question more.
Suppose a charity received a donation of $19.4 million. If this represents 43% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Answers
Given :
a charity received a donation of $19.4 million
Which represents 43% of the charity funds
Let the total funds = x
So,
43% of x = 19.4 million
So,
[tex]\begin{gathered} 43\%\cdot x=19.4 \\ \\ 0.43\cdot x=19.4 \\ \\ x=\frac{19.4}{0.43}\approx45.12 \end{gathered}[/tex]Rounding to the nearest million ,
The answer is : total donated funds = 45 million
A school debate team has 4 girls and 6 boys. A total of 4 of the team members will be chosen top participate in the district debate. What is the probaility that 2 girland 2 boys will be selected?
Answers
The probability that 2 girls and 2 boys are selected is given by:
[tex]P(\text{ 2 boys, 2 girls })=\frac{4C2\times6C2}{10C4}=\frac{6\times15}{210}=\frac{3}{7}[/tex]Therefore, the correct choice is option D) 3/7.
Solve for the Limit of Function by applying appropriate Limit Theorems
Answers
Answer:
Given to solve,
[tex]\lim _{x\to-1}(2x+2)(x+2)[/tex]From the rules for limits, we can see that for any polynomial, the limit of the polynomial when x approaches a point k is equal to the value of the polynomial at k.
The given function of the limit is a quadratic function, the limit of the quadratic equation when x approaches a point -1 is equal to the value of the quadratic equation at -1.
we get,
[tex]\lim _{x\to-1}(2x+2)(x+2)=(2(-1)+2)((-1)+2)[/tex][tex]=(-2+2)(1)=0[/tex][tex]\lim _{x\to-1}(2x+2)(x+2)=0[/tex]
Answer is : 0
Answer this, please
Zachariah and Khai collect stamps. Zachariah has 7 American stamps out of 12 stamps. Khai has 15 American stamps out of 24 stamps. Which statement is correct?
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is greater than 15 over 24.
Khai has a higher ratio of American stamps than Zachariah because 7 over 12 is less than 15 over 24.
Zachariah has a higher ratio of American stamps than Khai because 7 over 12 is less than 15 over 24.
Zachariah and Khai have the same ratio of American stamps.
Answers
The last statement would be true, because you would convert 7/12 into a fraction and 15/24 into a fraction. From their fraction eyes to State you would turn them into decimals and then percentiles.
Answer:
D: They are both the same
Step-by-step explanation:
I took the test
Dejah is comparing two numbers shown in scientific notation on her calculator. The first number was displayed as 7.156E25 and the second number was displayed as 3.498E-10. How can Dejah compare the two numbers?
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The first number is about
2 x 10¹⁵
2 x 10³⁵
2 x 10‐¹⁵
2 X 10‐³⁵
times bigger than the second number.
Answers
Answer:
2 x [tex]10^{35}[/tex]
Step-by-step explanation:
7 ÷ 3 is about 2
[tex]\frac{10^{25} }{10^{-10} }[/tex] = [tex]10^{35}[/tex] When you are dividing powers with the same bases, you subtract the exponents
25 - -10 = 25 + 10 = 35
Imagine you are four years old. A rich aunt wants to provide for your future. She hasoffered to do one of two things.Option 1: She would give you $1000.50 a year until you are twenty-one.Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amounteach year until you were 21.If you only received money for ten years, which option would give you the most money?
Answers
Given the situation to model the arithmetic and the geometric sequences.
Imagine you are four years old. A rich aunt wants to provide for your future. She has offered to do one of two things.
Option 1: She would give you $1000.50 a year until you are twenty-one.
This option represents the arithmetic sequence
The first term = a = 1000.50
The common difference = d = 1000.50
The general formula will be as follows:
[tex]\begin{gathered} a_n=a+d(n-1) \\ a_n=1000.50+1000.50(n-1) \\ \end{gathered}[/tex]Simplify the expression:
[tex]a_n=1000.50n[/tex]Option 2: She would give you $1 this year, $2 next year, and so on, doubling the amount each year until you were 21.
This option represents the geometric sequence
The first term = a = 1
The common ratio = r = 2/1 = 2
The general formula will be as follows:
[tex]\begin{gathered} a_n=a\cdot r^{n-1} \\ a_n=1\cdot2^{n-1} \end{gathered}[/tex]Now, we will compare the options:
The first term of both options is when you are four years old that n = 1
you only received money for ten years so, n = 10
So, substitute with n = 10 into both formulas:
[tex]\begin{gathered} Option1\rightarrow a_{10}=1000.50(10)=10005 \\ Option2\rightarrow a_{10}=1\cdot2^{10-1}=2^9=512 \end{gathered}[/tex]So, the answer will be:
For ten years, the option that gives the most money = Option 1
A box contains 4 red balls and 6 green balls. If a ball is drawn at random, then find the probability that the ball is red.1/102/104/106/10
Answers
To calculate the probability of event A, divide the number of outcomes favorable to A by the total number of possible outcomes.
[tex]P(A)=\frac{favourable\text{ outcomes}}{total\text{ outcomes}}[/tex]so
Step 1
a)let
[tex]\begin{gathered} favourable\text{ outcomes=red balls = 4 \lparen there are 4 red balls\rparen=4} \\ total\text{ outcomes= total balls= 4 red+6 green=10 balls=10} \end{gathered}[/tex]b) now, replace in the formula and simplify
.
[tex]P(A)=\frac{4}{10}=\frac{2}{5}[/tex]therefore, the answer is
[tex]\frac{4}{10}[/tex]I hope this helps you
how do you find the exponential equation for growth? or what is the exponential equation for growth?
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Answer:
The equation f(x) = a(1 + r)x can also be used to compute exponential growth, where:
The function is represented by the word f(x).
The initial value of your data is represented by the a variable.
The growth rate is represented by the r variable.
Time is represented by the variable x.
are these places correctly.and yes it is math. pls answer fast
Answers
we have that
Costs that stay the same from week to week or month to month
-savings for college
-Rent
Costs that cannot be adjusted within a budget
-Car insurance
-Health care
Costs that can be adjusted within a budget
-cell phone
-gasoline
-hair cut
-Groceries
O GRAPHS AND FUNCTIONSDomain and range from the graph of a piecewise function
Answers
ANSWER:
[tex]Domain:(-5,-4]\cup[-1,2][/tex][tex]Range:[-3,0)\cup[1,4][/tex]EXPLANATION:
Given:
To find:
The domain and the range
Recall that the domain of a function is the set of possible input values for which the function is defined.
To determine the domain of a function from a graph, we consider the possible x-values from left to right.
So the domain of the given function can be written as;
[tex]Domain:(-5,-4]\cup[-1,2][/tex]The range of a function is the set of possible output values.
To determine the range of a function from a graph, we consider the possible y-values from the bottom to the top.
So the range of the given function can be written as;
[tex]Range:[-3,0)\cup[1,4][/tex]Triangle RST has the coordinates R(0 , 2), S(2 , 9), and T(4 , 2). Which of the following sets of points represents a dilation from the origin of triangle RST? A. R'(0 , 2), S'(8 , 9), T'(16 , 2) B. R'(0 , 2), S'(2 , 36), T'(16 , 2) C. R'(4 , 6), S'(6 , 13), T'(8 , 6) D. R'(0 , 8), S'(8 , 36), T'(16, 8)
Answers
The set of points that represents a dilation from the origin of triangle RST are: D. R'(0 , 8), S'(8 , 36), T'(16, 8).
What is dilation?In Mathematics, dilation is a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
For the given coordinates of triangle RST, the dilation with a scale factor of 4 from the origin (0, 0) or center of dilation should be calculated as follows:
Point R (0, 2) → Point R' (0 × 4, 2 × 4) = Point R' (0, 8).
Point S (2, 9) → Point S' (2 × 4, 9 × 4) = Point S' (8, 36).
Point T (4, 2) → Point T' (4 × 4, 2 × 4) = Point T' (16, 8).
In conclusion, the other sets of points do not represents a dilation from the origin of triangle RST.
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As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
Given that,
Coordinates of the triangle, R(0 , 2), S(2 , 9), and T(4 , 2).
The scale factor for the dilation = 4
The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
According to the question,
The dilated coordinate is given as,
R' = (0×4 , 2×4) = (0, 8)
S' = (2×4, 9×4) = (8, 36)
T' = (4×4, 2×2) = (16, 8)
Thus, As of the given condition ordered pair in the option D R'(0 , 8), S'(8 , 36), T'(16, 8), represents the dilated coordinates of the former triangle.
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Use the following function rule to find f(48).
f(x) = 12 + x/4
Answers
Answer:
See image
depending on what is in the numerator of your question:
24 OR 15 SEE IMAGE!
Step-by-step explanation:
f(48) just means to use 48 in place of x in your work.
f(x) = 12 + x/4
f(48) = 12 + 48/4
Hopefully, your text/worksheet/screen is clear on which problem you are doing.
there are twelve inches in one foot,creating the equation y=12x. if a door frame is 6.5 feet tall,how many inches tall is it
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} 12in=1ft \\ y=12x \end{gathered}[/tex]The height of the door frame is 6.5 feet. To convert to inches, we have:
[tex]\begin{gathered} y=12(6.5)=78inches \\ y=78inches \end{gathered}[/tex]What is the domain for the following function? 2x . - 3 O A. (x+3) O B. {**-3) O c. {*#0 O D. all real number ers
Answers
Given,
y = 2x/x - 3
to solve this,
let's equate the denominator to 0
so,
y = 2x/0
this means undefined
recall,
Domain is the set of all possible values of x. Since the function is undeined when the denominator is zero, the domain is the set of all real numbers except the value which will make the denominator zero
so the domain for the function y = 2x/x - 3
is x is not equal to 3
therefore, the correct option is
[tex]A.\mleft\lbrace x\ne3\mright\rbrace[/tex]A pile of cards contains eight cards, numbered 1 through 8. What is the probability of NOT choosing the 6?
Answers
The probability of NOT choosing the 6 is 7/8.
What is the probability?Probability is used to calculate the likelihood that a random event would happen. The chances that the random event happens is a probability value that lies between 0 and 1. The more likely it is that the event occurs, the closer the probability value would be to 1. If it is equally likely for the event to occur or not to occur, the probability value would be 0.50.
The probability of NOT choosing the 6 = number of cards that are not 6 / total number of card
Cards that do not have a value of 6 = 1, 2, 3, 4, 5, 7, 8
Total is 7
The probability of NOT choosing the 6 = 7 / 8
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Find ( f+g ) (x) for each of the following functions
Answers
Answer:
(f + g)(x) = 2x³ + 3x² + x + 2
Explanation:
If f(x) = 2x³ - 5x² + x - 3 and g(x) = 8x² + 5, we can calculate (f + g)(x) as follows
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (2x³ - 5x² + x - 3) + (8x² + 5)
Then, we can simplify the expression adding the like terms, so
(f + g)(x) = 2x³ - 5x² + x - 3 + 8x² + 5
(f + g)(x) = 2x³ + (-5x² + 8x²) + x + (-3 + 5)
(f + g)(x) = 2x³ + 3x² + x + 2
Therefore, the answer is:
(f + g)(x) = 2x³ + 3x² + x + 2
10. Find the area of ABC. (A) 84 (B) 168 (C) 170 (D) 48 (E) 56A: 10B: 17C: 21Right angle: 8
Answers
we know that
the area of triangle ABC is equal to the area of two right triangles
so
triangle ABD and triangle BDC
D is a point between point A and point C
step 1
Find the length of segment AD
Applying Pythagorean Theorem in the right triangle ABD
10^2=AD^2+8^2
100=AD^2+64
AD^2=100-64
AD^2=36
AD=6
Find teh area of triangle ABD
A=AD*BD/2
A=6*8/2
A=24 units^2
step 2
Find the area of triangle BDC
A=DC*DB/2
DC=21-6=15 units
A=15*8/2
A=60 units^2
step 3
Find teh area of triangle ABC
Adds the areas
A=24+60=84 units^2
therefore
the answer is the option A 84 units^226.219 Miles in 128 minutes. what is speed in km per minute?
Answers
26.219 Miles in 128 minutes.
First we have to convert miles to km:
Since 1 mile = 1,609 km
26.219 x 1,609 = 42,041.561 km
Then divide the distance by the time:
42,041.561/ 128 = 192.85 km per minute
5. Which of the following expressions isequivalent to the expression below?2 394Х4AC29;woltON Alw94B+D1M
Answers
A) 9 cups of berries to 12 cups of juice
Explanation
to figure out this, we need to find the original ratio and then compare
Step 1
find the ratio:
ratio cups of berries to cups of juices
[tex]\text{ratio}=\frac{3\text{ cups of berries}}{4\text{ cups of juices}}=\frac{3}{4}[/tex]hence, the rario is 3/4
Step 2
now, check the ratio of every option
a)9 cups of berries to 12 cups of juice
[tex]\begin{gathered} \text{ratio}_a=\frac{9\text{ cups of berries}}{12\text{ cups of juice}}=\frac{3}{4} \\ \text{ratio}_a=\frac{3}{4} \end{gathered}[/tex]b) 12 cups of berries to 9 cups of juice
[tex]\text{ratio}_b=\frac{12\text{ cups of berries}}{9\text{ cups of juice}}=\frac{4}{3}[/tex]c) 6 cups of berries to 15 cups of juice
[tex]\text{ratio}_c=\frac{6\text{ cups of berries }}{15\text{ cups of juice}}=\frac{6}{15}=\frac{2}{5}[/tex]d) 15 cups of berries to 10 cups of juice
[tex]\text{ratio}_d=\frac{15\text{ cups of berries }}{10\text{ cups of juice}}=\frac{15}{10}=\frac{3}{2}[/tex]therefore, the option that haas the same ratio is a) 3/4
I hope this helps you
What 3D shape will be formed when the following are rotated around the axis
Answers
a)
A washer will be formed
b)
A cone will be formed
C)
A sphere will be formed
Which system of inequalities is shown?-5O A. y>xy<4OB. y> xy> 4C. y< xy<4OD. y< xy> 45
Answers
Given:
a graph of the inequalities is given.
Find:
we have to find the correct inequalities.
Explanation:
From the graph , it is observed that the value of y > x and y < 4,
Therefore, the correct inequalities are y > x,
y < 4.
Hence, correct option is A.
What is the missing coefficient of the x-term of the product (−x−5)^2 after it has been simplified?−25−101025
Answers
Given:
The terms is
[tex](-x-5)^2[/tex]Required:
What is the missing coefficient of the x-term of the product after it has been simplified?
Explanation:
We have to find the missing coefficient of the x term of the given product
We know
[tex](a-b)^2=a^2-2ab+b^2[/tex]So,
[tex](-x-5)^2=x^2+10x+25[/tex]Therefore, the missing coefficient of the x-term is 10.
Answer:
Therefore, the missing coefficient of the x-term is 10.
Solve the equation-3 + a = 13a = ???
Answers
ANSWER
a = 16
EXPLANATION
To solve for a we have to add 3 on both sides of the equation:
[tex]\begin{gathered} -3+3+a=13+3 \\ a=16 \end{gathered}[/tex]