The pressure gradient is a function of the pressure itself, the local acceleration due to gravity, and the density of the fluid.
The sum-of-forces equation is 0=∑ify,i=pa−(p dp)a−ρagdy. Rearranging the equation to isolate dp yields the following expression:
dp = (pa - ρagdy) / p
Differentiating both sides with respect to y yields the differential equation for pressure:
dp/dy = (a(pa - ρagdy) - (dp)(pa)) / p
This equation can be further simplified using the product rule to yield:
dp/dy = pa2/p2 - ρag/p.
This differential equation shows that the pressure gradient is a function of the pressure itself, the local acceleration due to gravity, and the density of the fluid.
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consider the case in which the constant a equals 16. plot the graph of y=16x2 .
The graph of y=16x2 is a parabola that is symmetric about the y-axis and opens upwards. Its vertex is at (0,0) and its intercepts are at (0,0) and (±√16,0). As x increases, the graph increases at a faster rate.
The graph of y=16x2 is a parabola that is symmetric about the y-axis and opens upwards. The vertex of the parabola is the point (0,0), which is the point where the parabola changes direction. The y-intercept of the graph is the point (0,0) and the x-intercepts are the points (±√16,0). This means that the graph crosses the x-axis at x=±√16. As x increases, the graph increases at a faster rate. This is because the exponent of x is 2, meaning that the graph is a quadratic equation. When x=0, the graph is at 0, and as x gets larger, the graph increases more quickly. The graph reaches its maximum at x=√16, where y=16. From this point, the graph decreases until it reaches 0 again at x=-√16.
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evaluate the function f(x)=5x+2 for f(-4)
Answer:
The answer is -18
Step-by-step explanation:
You plug in -4 and solve
f(-4)= 5(-4) +2
Simplify: 15²
(pls hurry)
Answer:
225
Step-by-step explanation:
15 x 15 = 225
PICKUP TRUCKS You can register a pickup truck as a passenger vehicle if the
truck is not used for commercial purposes and the weight of the truck with
its contents does not exceed 8500 pounds.
a. Your pickup truck weighs 4200 pounds. Write an inequality to represent the
number of pounds your truck can carry and still qualify as a passenger vehicle.
Then solve the inequality.
b. Acubic yard of sand weighs about
1600 pounds, How many cubic yards of
sand can you haul in your truck and still
quality as a passenger vehicle? Explain
your reasoning
Show your work.
Question 26
The solution to the inequality in question is less than or equal to 4300 pounds and 2.6875 cubic yards of sand can be hauled in the truck to still classify as a passenger vehicle.
From the question itself, we can deduce that the inequality is -
Let us assume that the amount of stuff carried by the vehicle is = x
So, the inequality becomes -
= 4200 + x ≤ 8500 pounds
So, if we solve this we will find that the weight of stuff to be carried is going to be -
= x ≤ 8500 - 4200
= x ≤ 4300
It should be no more than 4300 pounds.
We can still classify it as a passenger vehicle by carrying only 1.4655 pounds of sand because -
= 2.6875 *1600 = 4300 pounds
This means that by carrying 2.6875 pounds we maintain the rules to remain a passenger vehicle.
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A factory sampled hundreds of 9oz bags of chips off of one of their production lines to make sure the bags had the appropriate
amount of chips. They found the amount of chips to be normally distributed with = 9.12 ounces and o= .05 ounces.
PART A
Given this information, fill out the normal distribution chart below for the weight of 9oz bags of chips from this factory.
The normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.
What is standard deviation?The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a small variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the values deviate from the mean. The most popular way to assess dispersion is standard deviation, which is based on all values.
From the given samples of 9oz of chips we have the following values:
Mean = 9.12 ounces
SD = 0.05 ounces
The normal distribution of the chart below will have the following values:
The mean or the center value of the graph with the highest peak is:
Mean = 9.12
The value to the right of the mean value will be:
Mean + SD = 9.12 + 0.05 = 9.17
Mean + 2(SD) = 9.12 + 2(0.05) = 9.22
Similarly, the value to the left of the mean value will be:
Mean - SD = 9.12 - 0.05 = 9.07
Mean - 2(SD) = 9.12 - 2(SD) = 9.02
Hence, the normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.
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PLEASE HELP!!
look at screen shot for question.
Answer:
Step-by-step explanation:
To evaluate g(-5), you simply plug in -5 for x in the equation:
g(-5) = (-5)²-10 which is 25 - 10 which is 15. Therefore, g(-5) = 15
Use cylindrical shells to find the volume of the solid that is generated when the region that is enclosed by y=1/x^3, x=1, x=2, y=0 is revolved about the line x=-1
The volume of the solid that is generated is: [tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]
Now, According to the question:
The formula for the shell method is :
[tex]=\int\limits^a_b {2\pi rh} \, dx[/tex]
where, a and b are the x - bound, which are x=1 and x=2,
So, a = 1 and b = 2
r is the distance from a certain x-value in the interval [1, 2] and the axis of rotation, which is x = -1 .
r = x - (-1) = x + 1
h is the height of the cylinder at a certain x-value in the interval [1, 2], which is [tex]\frac{1}{x^{2} } - 0[/tex] = [tex]\frac{1}{x^{2} }[/tex] (because [tex]\frac{1}{x^{2} }[/tex] is always greater than 0 and h must be positive).
Plugging it all in volume
[tex]\int\limits^2_1 {(2\pi (x + 1)(\frac{1}{x^2} ))} \, dx[/tex]
= [tex]2\pi \int\limits^2_1 { (x + 1)(\frac{1}{x^2} ))} \, dx[/tex]
[tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]
Hence, The volume of the solid that is generated is: [tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]
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the area of a right triangle is 50° one of its angle is 45° find the length of its sides and hypotenuse of triangle
If the area of the triangle is 50m² the length of it's other two sides is 10m each and hypotenuse is 14.1m
What is area of a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
A right angled triangle is a triangle with 90°. Since of one of the angle is 45° , this means that the triangle is isosceles and the other two sides will be equal. This means a= b
Area of triangle = 1/2absinC
50 = 1/2 b²sin90
50× 2 = b²× 1
b² = 100
b = √ 100
b =10m
b = 10m
a= 10m
using Pythagoras theorem
c² = 10²+10²
c² =100+100
c²= 200
c =√200
c = 14.1m
therefore the measure of the other two sides is 10m each and the hypotenuse is 14.1m
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using the substitution u=5x−2, ∫x5x−2−−−−−√ⅆx is equivalent to which of the following?
using the substitution u=5x−2, ∫x5x−2−−−−−√ⅆx is equivalent to ∫u+2 /5 du/5
What is Derivative?
Calculus defines a derivative as the rate at which one quantity, y, changes in relation to another, x. The differential coefficient of y with respect to x is another name for it. Finding a function's derivative is the process of differentiation. A function's derivative is typically represented by d/dx (f(x)) (or df/dx (or Df(x) (or f')). Let's examine the technical definition of a derivative. Two points on a function f(x) curve are (x, f(x)) and ((x + h), f(x + h)), respectively. If so, [f(x + h) - f(x)]/(x + h - x) = [f(x + h) - f(x) / h] will be the slope of the secant line through these points. The second point overlaps the first point in the figure below when the distance between two points is nearly equal to 0 (i.e., as h approaches 0), and the secant line turns into the tangent line. Calculus refers to the slope of the tangent line as the function's derivative.
x = 1/y + 1
y + 1 = 1/x
y = 1/x - 1
differentiating y w.r.t to x
dy/dx=-1/x^2
using subsitution u= 5x-2
then x= u+2/5
∫u+2 /5 du/5
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If a triangle has either two equal sides or two equal angles, then it is an isosceles triangle. What is the contrapositive, converse, and inverse form of this statement?
Contrapositive: If not isosceles, then not two equal sides or angles. Converse: If two equal sides or angles, then isosceles. Inverse: If not isosceles, then not two equal sides or angles.
What is triangle ?
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C.
Contrapositive: If a triangle is not an isosceles triangle, then it does not have either two equal sides or two equal angles.
Converse: If a triangle has either two equal sides or two equal angles, then it is an isosceles triangle.
Inverse: If a triangle is not an isosceles triangle, then it does not have either two equal sides or two equal angles.
Contrapositive: If not isosceles, then not two equal sides or angles. Converse: If two equal sides or angles, then isosceles. Inverse: If not isosceles, then not two equal sides or angles.
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the equality v · v = kvk 2 holds for all vectors v in r n . True or False
The formula v · v = kvk2 can be seen to hold for all vectors in Rn, as the dot product of a vector and itself is equal to the magnitude of the vector squared.
The formula v · v = kvk2 is true for all vectors v in Rn. This is because the dot product of a vector and itself is equal to the magnitude of the vector squared. The dot product of two vectors is defined as the sum of the products of their components. Therefore, when a vector v is multiplied by itself, the result is the sum of the squares of all its components. The magnitude of a vector is defined as the square root of the sum of the squares of its components. Thus, the formula v · v = kvk2 can be seen to hold for all vectors in Rn, as the dot product of a vector and itself is equal to the magnitude of the vector squared.
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If you cannot show the triangles are congruent from the given information leave the trianglges name black and write CNBD for Cannot be Determined in place of the rule.
Step-by-step explanation:
the triangle GAS is congruent with the triangle IOL (I know, it is tempting to say OIL, but it is important to show the sequence of the corresponding corners, so G corresponds to I, A to O and S to L) by AAS (angle-angle-side) : 2 angles and a not included but corresponding side are equal between the 2 triangles.
65 points
1. Find the pattern and then write a rule and an
equation that represents the pattern. Then
complete the table,
X= 0 2 10 16 20
Y= 0 1 5 8 10
Rule: Y is equal to the square root of X.
Equation: Y = √X
What is algebraic expression?
An algebraic expression is when we use b and words in solving a particular mathematical question.
In this table, the relationship between the values of X and Y appears to be Y = √X.
This can be expressed as a mathematical rule and equation as follows:
Rule: Y is equal to the square root of X.
Equation: Y = √X
We can use this rule to complete the table as following figure.
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f(n) = 100n log n, g(n) = n (log n)2.
Functions that take a positive integer n as input and return a real number are F(n) = 100n log n and g(n) = n (log n)2. A different algorithm's time complexity is represented by g(n), whereas another algorithm's time complexity is represented by F(n).
As n approaches infinity, F(n) and g(n) both expand as O(n log n), which indicates that the growth rate of the two functions is proportional to n log n as n gets very big. However, because the coefficient 100 in F(n) is smaller than the coefficient 1 in g, it develops more slowly than g(n) (n).
Hence, functions that take a positive integer n as input and return a real number are F(n) = 100n log n and g(n) = n (log n)2.
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How to convert 145 pounds to kilograms?
Multiply the mass in pounds by 0.45359237 to convert 145 lbs to kilogrammes.
How Do You Convert Lbs To Kg?Add 0.45359237 kg to the given number of pounds to convert it to kilogrammes. For instance, multiply the supplied 5 pounds by 0.45359237 kg to convert 5 lbs to kilogrammes. Consequently, 5 lbs is about equivalent to 2.26796185 kg.It is said that a kilogramme (kg) weighs 2.2 times more than a pound (represented as lbs). Thus, 2.26 pounds are equal to one kilogramme of mass. In light of this, we shall now examine some of the primary variations between the pound and the kilogramme.The imperial unit of mass or weight measurement is the pound.Multiply the mass in pounds by 0.45359237 to convert 145 lbs to kilogrammes. [kg] = 145 * 0.45359237 is the formula to convert 145 pounds to kilogrammes.To learn more about pounds refer to:
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Polygon X is a scaled copy of Polygon Y using a scale factor of 3. Which of the following statements is true?
The area of Polygon Y is [tex]\frac{1}{9}[/tex] the area of Polygon X.
The area of Polygon X is [tex]\frac{1}{9}[/tex] the area of Polygon Y.
The area of Polygon Y is 9 times the area of Polygon X.
The area of Polygon X is 9 times the area of Polygon Y.
Since Polygon X is a scaled copy of Polygon Y using a scale factor of 3, a statement which is true include the following: D. The area of Polygon X is 9 times the area of Polygon Y.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Therefore, the area of Polygon X with respect to Polygon Y based on the given scale factor of 3 is as follows;
Area of Polygon X/Area of Polygon Y = 3²
Area of Polygon X/Area of Polygon Y = 9.
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an ideal gas is contained in a cylinder of fixed length and diameter. 80 j of heat is added while the piston is held in place. the work done by the gas on the walls of the cylinder is
The work done by the gas on the walls of the cylinder is zero, since the piston is held in place. The heat energy added to the gas will cause it to expand, but since the cylinder has a fixed volume, the pressure of the gas will increase without the gas doing any work on the walls of the cylinder.
An ideal gas is a hypothetical gas which follows the ideal gas laws. These laws state that the pressure, volume, and temperature of an ideal gas are related to each other in a predictable and measurable way. In this case, the cylinder has a fixed length and diameter, and the piston is held in place. This means that the volume of the cylinder is fixed and cannot change, even if heat is added to the gas. Therefore, when 80 J of heat is added, the pressure of the gas will increase, but the gas will not do any work on the walls of the cylinder since it cannot expand. Therefore, the work done by the gas on the walls of the cylinder is zero.
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The coordinate of an object is given as a function of time by x = 4+2 - 3, where x is in meters and t is in seconds. Its average acceleration over the interval from t = 0 to t = 2 s is:
A. -4m/s^2
B. 4m/s^2
C. -10m/s^2
D. -13m/s62
The average acceleration over the given time interval is option C -10 m/s²
By dividing the change in velocity by the change in time, the average acceleration will be determined. Therefore, let's first determine the velocity function:
x = 4t² - 3t³
v = dx / dt
v = d( 4t² - 3t³) / dt
v = 8t - 9t²
Then,
at t = 0 sec , v = 0 m/s.
at t = 2 sec , v = 8(2) - 9(2²) = 16 - 36 = -20 m/s.
Average acceleration;
The rate of change in velocity is referred to as the average acceleration. To calculate the average acceleration of anything, we divide the change in velocity by the time since the initial measurement. A crazy ball's average acceleration, for instance, would be 20 cm/s/s if its velocity rose from 0 to 60 cm/s in 3 seconds.
avg.acc = (- 20 - 0) / (2 - 0) = -20 / 2 = -10 m/s²
That is,
-10 m/s² (option c) will be the average acceleration over the given interval.
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The given question is incomplete. Completed question is here;
The coordinates of an object is given as a function of time by x=4t^2-3t^3,where x is in meter and t is in second .what is its average acceleration over the time interval from 0 to 2 seconds
Factorise fully 3 ( x − 4 ) 2 + 15 ( x − 4 )
The factorization is given as 9x² - 9x - 44
How to factorize the equationFactorize fully 3 ( x − 4 )² + 15 ( x − 4 )
(3x - 4)² + 15(x-4)
(3x - 4)(3x - 4) + 15(x-4)
we have to open the bracket
9x² - 12x - 12x + 16 + 15x - 60
take the like terms in the equation
9x² - 24x + 15x +16 - 60
9x² - 9x - 44
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Solve the system of equations. –6x + y = –21 2x − 1 3 y = 7 What is the solution to the system of equations? (3, 3) (2, –9) infinitely many solutions no solutions
Answer:
x = 7/2
y = 0
Step-by-step explanation:
–6x + y = –21
2x − 13y = 7
Times the second equation by 3
-6x + y = -21
6x - 39y = 21
-38y = 0
y = 0
Now put -0 back for y and solve for x
-6x = -21
x = 7/2
Answer:
I think it would be infinitely many solutions
Step-by-step explanation:
if sqrt a / sprt b =, which statment must be true?
The statement that must be true is (c) x² = a/b
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
√a/√b = x
Take the square root of both sides
So, we have the following representation
a/b = x²
Rewrite the equation as
x² = a/b
Hence, the solution is x² = a/b
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Write an equation that represents the situation.
After the parade, Ameen had 300 pieces of candy. He was allowed to eat 8 pieces of candy each day. Write an equation that represents the number of days he had been eating candy if he has 82 pieces of candy left.
Ameen has been eating the candy for 27 days and now has 82 pieces left
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Let x represent the number of days he had been eating candy.
Ameen had 300 pieces of candy. He was allowed to eat 8 pieces of candy each day. He has 82 left. This can be represented by:
300 - 8x = 82
8x = 300 - 82
8x = 218
x = 27.25
He has been eating the candy for 27 days
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Find the surface area of the cylinder. Round your answer to the nearest tenth.
6 ft
7 ft
Surface area of the cylinder would be 231.1 sq ft.
How do you find a surface area of a cylinder?
A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².
The surface area of a cylinder with height h and radius r can be found using the formula:
2πr^2 + 2πrh
Given a cylinder with height 6 ft and radius 7 ft, the surface area is:
2π * 7^2 + 2π * 7 * 6 = 147.1 + 84 = 231.1 sq ft (rounded to the nearest tenth).
Therefore, Surface area of the cylinder would be 231.1 sq ft.
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you measure the radius of a sphere as (6.20 ± 0.30) cm, and you measure its mass as (1.81 ± 0.09) kg. what is the density and uncertainty in the density of the sphere, in kilograms per cubic meter?
The density and uncertainty in the density of the sphere is (1828.28 ± 0.0984) kg/m³
The radius of a sphere is (6.20 ± 0.30) cm
Mass of the sphere is (1.81 ± 0.09) kg
We know that the formula for the density,
Density = mass/volume
d = m/V
As we know tha volume of the sphere is, [tex]V=\frac{4}{3} \pi r^3[/tex]
[tex]V=\frac{4}{3} \pi r^3\\\\V=\frac{4}{3} \pi (6.2\times 10^{-2})^3\\\\V=0.00099~m^3[/tex]
So, the density would be,
d = (1.81) / (0.00099)
d = 1828.28 kg/m³
We can find the uncertainty in volume as follows :
[tex]\frac{\delta V}{V}=3\frac{\delta r}{r}\\\\\frac{\delta V}{V}=3\times \frac{0.003}{0.0620} \\\\\frac{\delta V}{V}=0.0484[/tex]
and the uncertainty in the mass would be,
[tex]\frac{\delta m}{m}=\frac{0.09}{1.81} \\\\\frac{\delta m}{m}=0.05[/tex]
The uncertainty in the density of the sphere would be,
[tex]\frac{\delta d}{d}=\frac{\delta V}{V}+\frac{\delta m}{m}\\\\\frac{\delta d}{d}=0.0484+0.05\\\\\frac{\delta d}{d}=0.0984[/tex]
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The pread of a flu viru through a certain population i modeled by y=500/1990e^-. 5(t) where y i the total number of people infected after t day. In how many day will 125 people be infected with the viru?
ln t = 145.69 days day will 125 people be infected with the virus (500/125)/-.005 = t
How many days will it take for 125 people to contract the virus?This question uses the theory of exponential growth and decay.
The equation y=500/1990e^-. 5(t) models the spread of a flu virus through a population, where y is the total number of people infected after t days.
The equation follows an exponential decay curve, where the number of people infected decreases with each passing day. In this case, the rate of decay is -.005.
given below
Step 1: Rearrange the equation to isolate t.
y = 500/1990e^-.005(t)
500/y = 1990e^-.005(t)
500/y = e^-.005(t)
ln(500/y) = -.005(t)
Step 2: Substitute the given values of y (125) and solve for t.
ln(500/125) = -.005(t)
ln(500/125)/-.005 = t
t = 145.69 days
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The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
Answer:
its "equally likely and unlikely" because since its 50% for the chocolate chip then its 25% for both oatmeal raisin, and sugar cookies, which both of their percentages are equivalent to 50% so its a 50/50 chance between getting chocolate chip cookies to getting oatmeal raisin and/or sugar cookies
Step-by-step explanation:
Elizabeth lives in san francisco and works in mountain view. In the morning, she has 3 33 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 33 choices for her trip home. If elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?.
The probability that she will choose to use a cab exactly one time is 4/9.
It has been given that In the morning she has 3 transportation choices. And in the evening the same 3 choices.
i) bus
ii) cab
iii) train
Since each choice have an equal chance of being chosen,
The probability of Choosing a bus will be 1/3
The probability of Choosing a cab will be 1/3
The probability of Choosing a train will be 1/3
Now, the Probability of Not Choosing the cab will be the sum of the probabilities of choosing a bus and train i.e, 2/3
Now there will be two possibilities-Either She chooses a cab in the morning and something else in the evening Or She chooses a cab in the evening and something else in the morning.
Therefore, the probability of choosing a cab exactly one time =
( Probability of cab in morning x Probability of no cab in the evening) + (Probability of no cab in morning x Probability of cab in evening)
Probability of choosing a cab exactly once
= 1/3 x 2/3 + 2/3 x 1/3
= 4/9
Therefore, the probability that she will choose to use a cab exactly one time is 4/9.
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PLS HELP AND SHOW WORK PLS
A librarian has 274 return books. 50 of the books are reserved at her desk, and the remaining books need to be shelved. Each shelf can hold 14 books. write and solve an equation to find the number of shelves needed.
Answer: 16
Step-by-step explanation:
274-50=224/14=16
Answer:
16
Step-by-step explanation:
the size of a bacteria population grows at a rate of p(t) where t is measured in weeks
The bacteria will reach its maximum size at t = 8.94 weeks.
To find when the bacteria will reach its maximum size, we need to find the maximum value of p(t). The first step is to find the derivative of p(t):
dp(t)/dt = -8000(t^2 - 80)/(80 + t^2)^2
Next, we need to find the critical points of this derivative by setting it equal to 0 and solving for t:
dp(t)/dt = 0
-8000(t^2 - 80)/(80 + t^2)^2 = 0
t^2 - 80 = 0
t = √80
t = 4√5
t ≈ 8.94
Since t = 4√5 is the only critical point, we can see that it is a local maximum. To confirm this, we need to find the second derivative and evaluate it at t = 0:
d^2p(t)/dt^2 = 16000t (t^2 - 240) / (80 + t^2)^3
d^2p(t)/dt^2 = 160000 * -160 / (80 + 80)^3 < 0
Since the second derivative at t = 4√5 is less than 0, it is a local maximum.
--The question is incomplete, answering to the question below--
"The size of a bacteria population grows at a rate of p(t) = 8000t/ (80 + t^2) where t is measured in weeks. Determine when the bacteria will reach its maximum size."
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Please help ASAP
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $5, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 5 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A package that weighs 15 pounds will cost $35 for both options.
A package that weighs 15 pounds will cost $25 for both options.
A package that weighs 10 pounds will cost $15 for both options.
A package that weighs 5 pounds will cost $15 for both options.
Answer:
A package that weighs 5 pounds will cost $15 for both options.
Step-by-step explanation:
The equation for the cost of the first shipping option is y = 5 + 2x, where x represents the amount of pounds of the package. The cost, y, increases by $2 per pound of the package. So, if the package weighs 5 pounds, the cost of the first option would be y = 5 + 2 * 5 = $15.
The equation for the second shipping option is y = 15, representing a one-time fee of $15 to send the box. The cost is fixed at $15 regardless of the weight of the package.
Therefore, if the package weighs 5 pounds, the cost of both shipping options would be $15, and the two options would cost the same.