Solving a system of equations we will see that they sold 80 adult tickets.
how many adult tickets were sold?
To solve this, we need to solve a system of equations. To define said systems of equations, we first need to define the variables, we will use:
x = adult tickets sold.y = student tickets sold.They sold 20 more adult tickets than student tickets, then:
x = y + 20
And they collected a total of $880, then:
x*$8 + y*$4 = $880
The the system of equations is:
x = y + 20
x*$8 + y*$4 = $880
Isolating y on the first equation we get:
y = x - 20
Replacing that on the other equation we get:
x*$8 + (x - 20)*$4 = $880
Now let's solve that for x.
x*$12 - $80 = $880
x*$12 = $880 + $80 = $960
x = $960/$12 = 80
They sold 80 adult tickets.
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Which of the following are true statements about waves?
A. All waves carry matter but not energy.
B. All waves have both an amplitude and frequency.
C. All waves have a repeating pattern.
Answer:
B,C
Step-by-step explanation:
B. All waves have both an amplitude and frequency.
C. All waves have a repeating pattern.
A statement A is incorrect, Waves are a disturbance that transfer energy through space without transferring matter.
B is true, All types of waves have an amplitude, which is the measure of the maximum displacement of a point on the wave from its rest position and a frequency, which is the number of complete oscillations of a point on the wave per unit of time.
C is also true, All types of waves have a repeating pattern, which is known as a waveform. The shape of the waveform determines the type of wave. For example, sine waves have a smooth, curved shape, while square waves have sharp, angular edges.
Merge onto Highway 40 and drive 3/5
mile. Stop and pay the toll. Then
continue on Highway 40 for twice this.
distance. How much longer will you be
on Highway 40 after you pay the foll?
Distance traveled after toll payment is 1.2 miles on highway 40.
What is Distance ?The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.
Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.
Distance traveled before toll payment =3/5 miles on highway 40
Distance traveled after toll payment =2*3/5 = 6/5 =
1.2 miles on highway 40.
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You throw a ball straight up from a rooftop 70 feet high with an initial speed of 80
feet per second. The functions s(t)=â16t2+80t+70models theâ ball's height above theâ ground,s(t)
inâ feet, t seconds after it was thrown. During which time period will theâ ball's height exceed that of theâ rooftop?
When will the ball exceed the height of theâ rooftop?
On solving the provided question we can say that the value of equation here will be as duration is 0<t<5 seconds.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions
Information given in the query:
Rooftop height is 70 feet.
Speed at start: 80 feet per second
s(t ) = - 16t² + 80t + 70
s(t) in feet here
now,
for the balls to touch the rooftop
[tex]s(t ) = - 16t^2+ 80t + 70 > 70\\ - 16t^2 + 80t + 70 > 70\\ - 16t^2 + 80t > 70 - 70\\ - 16t^2 + 80t > 0\\ 16t^2 - 80t < 0\\t( 16t - 80 ) < 0\\t < 0 and 16t - 80 < 0 or 16t < 80 or t < 5\\[/tex]
Hence,
since time cannot be negative, the time period is 0 t 5 seconds.
0<t<5
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p divided by 9=4 is what
Answer:
36
Step-by-step explanation:
p/9=4
p=4*9
p=36
Give me 2 rational exponent world problem that contains sustainability
1. A city wants to reduce its carbon footprint by switching to renewable energy sources. The city's current energy consumption is measured in gigawatt hours (GWh) and they want to reduce it by 20% in the next 5 years. The city's current energy consumption is 2,000 GWh per year. What is the target energy consumption in GWh per year that the city should aim for to achieve their goal?
2. A company wants to reduce its water consumption by 50% in the next 10 years. The company currently consumes 500,000 gallons of water per day. How many gallons of water per day should the company aim to consume in 10 years to achieve their goal?
Create Write a real-world problem that could be represented by the equation 12(x+2.50)=78 .
Algebraic expression explaining real world problem is - A store is having a sale where all items are marked down 12% and an additional $2.50 is taken off the final price.
If a customer wants to find out the original price of an item before the sale, they can use the equation 12(x+2.50)=78, where x is the original price of the item.
What are algebraic expressions?Algebraic expressions are known as expressions made up of :
VariablesConstantsAddition,SubtractionDivisionOther algebraic operationsWhat are some examples of algebraic expression?A mathematical statement with variables, constants, coefficients, and algebraic operations is known as an algebraic expression. A good example of an algebraic expression is 5x2+6xyc. Algebraic expressions do not use equal signs, in contrast to algebraic equations. In contrast, since they are not derived from integer constants and algebraic operations, transcendental numbers like and e are not algebraic.
A real-world problem:A store is having a sale where all items are marked down 12% and an additional $2.50 is taken off the final price. If a customer wants to find out the original price of an item before the sale, they can use the equation 12(x+2.50)=78, where x is the original price of the item.
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A math club has 30 members. The number of girls is 2 less than 3 times the number of boys. How many members are boys? How many members are girls?
Answer:Well, we already see that the number of girls is greater than the number of boys, to find the result of girls, just do the division that is 30:2= 15 and boys is 30:3= 10
i hope i have helped you
Step-by-step explanation:
Answer:
8 boys, 22 girls
Algebraic ExpressionsTo solve, you must isolate the variable. This means moving the variable and it's coefficient to the other side of the equation with only the same variable on the same side with all the constants on the other side.
If you multiply, divide, add, subtract, square root, exponent both sides of the equation by the same value, that end value stays the same.
Q)
Lets set the amount of boys to x.
The amount of girls is 3x-2 as the amount of boy is x.
Set up an equation.
x+3x-2 = 30
30 is the amount of members.
Add 2 on both sides.
x+3x+2-2=30+2
Simplify by combining like terms.
4x = 32
Divide 8 on both sides.
[tex]\frac{4x}{4} =\frac{32}{4}[/tex]
x = 8
There are 8 boys in the class.
Plug back into the equation or subtract from 30 to solve for the amount of girls.
30 - 8 = 22
8(3) - 2 = 22
There are some counters in a bag.
The counters are red or white or blue or yellow.
Bob is going to take at random a counter from the bag.
The table shows each of the probabilities that the counter will be blue or will
be yellow.
Colour
Probability
red white blue yellow
0.45. 0.25
There are 18 blue counters in the bag.
The probability that the counter Bob takes will be red is twice the probability that the
counter will be white.
(a) Work out the number of red counters in the bag.
The number of red counters in the bag is given as follows:
8.
How to obtain a probability?A probability is obtained by the division of the number of desired outcomes by the number of total outcomes.
The probabilities for this problem are given as follows:
Red: 2x.White: x.Blue: 0.45.Yellow: 0.25.The sum of the probabilities is of one, hence the value of x is obtained as follows:
2x + x + 0.45 + 0.25 = 1
3x = 0.3
x = 0.1.
Hence the proportion of red is given as follows:
0.2.
There are 18 blue counters in the bag, which is of 0.45 of the total amount, hence the total amount is obtained as follows:
0.45n = 18
n = 18/0.45
n = 40.
Meaning that the number of red counters is given as follows:
0.2 x 40 = 8.
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There are 80 Students in the marching band.
Can they match in 2,5, and /or 10 equal rows? Explain.
Answer:
Step-by-step explanation: Yes, they can match in 2, 5, and/or 10 equal rows. This is because the number of items in the set can be divided evenly by 2, 5, and 10. For example, if there are 20 items in the set, it can be divided into 2 rows of 10, 5 rows of 4, or 10 rows of 2.
The sales tax in the town where Gina lives is 8%. Gina wants to buy a table saw that costs $300. How much sales tax will she pay?
Given the coordinates below, what is the scale factor of a dilation centered at the origin where "overline"(A'B') is the image of "overline"(A'B')
A(6,-4), B(2,-8)
A'(9,-6), B'(3, -12)
A.1/2
B.3/2
C.2/3
D. 3
Considering the coordinates of the preimage of line AB represented by A (6, -4), B (2, -8) and coordinates of the image of line A'B' represented by A' (9, -6), B'(3, -12) the dilation factor is 3/2
How to find the dilation factorThe transformation rule for dilation is as follows
(x, y) for a scale factor of r → (rx, ry)
following similar procedure for the given problem we have
A (6, -4) transformed to A' (9, -6)
B (2, -8) transformed to B' (3, -12)
hence 6r = 9, and -4r = -6
r = 9/6 = -6/-4
r = 3/2
The dilation factor of the transformation is 3/2
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What is the vertex of y = |x-9| +7?
Answer:
Step-by-step explanation:
The vertex (h, k) is always in the format of "x-" so if we have a positive h value for the vertex, it would be written as "x-(h)" and if we have a negative h value for the vertex, it would be written as "x-(-h)" which is the same as "x+h". Since our sign inside the absolute value symbols is negative, the h value for the the vertex is 9. The k value is always what's outside the absolute value symbols, including the sign. Ours is a positive 7. Thus the vertex is (9, 7).
A capsule is in the form of a hollow cylinder surmounted by a hemispherical bowl of the same diameter, 12 cm on both ends. The total height of the capsule is 16 cm. Find the surface area of the capsule. п cm?
The surface area of the capsule is calculated by adding the surface area of the cylinder and the surface area of the hemispherical bowl.
What is the hemispherical bowl?A hemispherical bowl is a type of bowl with a rounded bottom that is shaped like half of a sphere. It is often used in laboratories, kitchens, and dining rooms. The bowl’s curved surface prevents the contents from spilling, which makes it an ideal choice for mixing, swirling, and scooping. Additionally, the bowl’s shape makes it look aesthetically pleasing, so it can be used as a decorative piece as well.
The surface area of the cylinder = 2πr2 + 2πrh
Where r is the radius of the cylinder and h is the height of the cylinder.
The radius of the cylinder = 12 cm
The height of the cylinder = 16 cm
Therefore, the surface area of the cylinder = 2π(12)2 + 2π(12)(16) = 1536π cm2
The surface area of the hemispherical bowl = 2πr2
Where r is the radius of the hemispherical bowl.
The radius of the hemispherical bowl = 12 cm
Therefore, the surface area of the hemispherical bowl = 2π(12)2 = 144π cm2
The total surface area of the capsule = 1536π cm2 + 144π cm2 = 1680π cm2
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A system of equations is graphed on this coordinate grid.
Which ordered pair is the best estimate of the solution of the system of equations?
(-1, -2)is the best solution of the system of equations.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A system of equations is graphed on this coordinate grid.
we need to find the ordered pair which is the best estimate of the solution of the system of equations.
(-1, -2) is the best solution of this graph because both the lines are intersecting at that point
Hence, (-1, -2)is the best solution of the system of equations.
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if x/y=z/w then show that x^m+y^m+z^m+w^m/x^m+y^-m+z^-m+w^-m= (xyzw)^m/2
On solving the provided question we can say that the inequality equation can solved as = [tex]\sqrt[4]{xyzw}[/tex]
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
here,
the inequality equation can solved as
[tex]x^m+y^m+z^m+w^m/x^m+y^-m+z^-m+w^-m= (xyzw)^{m/2}[/tex]
[tex]u = x+y/2 \geq \sqrt{xy}[/tex]
v = z+w /2 [tex]\geq \sqrt{zw}[/tex]
u+v/2 = x+y+z+w+/4 [tex]\geq \sqrt{uw} \geq \sqrt{\sqrt{xy} \sqrt{zw} }[/tex]
= [tex]\sqrt[4]{xyzw}[/tex]
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what is the average (mean) value of 3t^3-t^2 over the interval -1<=t<=2?
The average value of 3t^3-t^2 over the interval -1<=t<=2 is 11/4
Mean Value Theorem states if a function f(x) is continuous on the interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:
f '(c)=f(b)-f(a)/b-a
Average Value:
The average value of a function of a variable over a range represents the height of a rectangle of the same area as that defined by the function under the curve. This value can be calculated using a formula:
favg=1/b−a∫f(t)dt
consider f(x)=3t³-t² and limits are -1 to 2
Now, substitute these values in the above formula:
favg=1/2-(1)∫3t³-t²dt
favg=1/3∫(3/4t⁴-1/3t³)|₋₁²
favg=(12-8/3)-(3/4+1/3)
By solving the equation we get
favg=11/4
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Exhibit 2-3
The number of sick days taken (per month) by 200 factory workers is summarized below.
Number of Days Frequency
0 − 5 120
6 − 10 65
11 − 15 14
16 − 20 1
The number of workers who took more than 10 sick days per month is _____.
A summary of 200 factory workers' monthly sick days is provided. From this, we can tell that about 15 workers took more than 10 sick days per month.
The number of times an event or observation occurred during an experiment or research is referred to as its frequency in statistics. It can alternatively be described as a straightforward count of a specific occurrence. Relative frequency and cumulative frequency are the two main types of frequency seen in statistics.
The given table contains the number of sick days per month and the frequency of factory workers on sick days. Then, the number or frequency of workers who took more than 10 sick days per month is,
number of workers = frequency for 11-15 days + frequency for 16-20 days
=14+1
=15
The required answer is 15 workers.
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A toy car and a battery together costs £44. The ratio of the cost of the car to the battery is 10:1. How much did the battery cost?
Answer:
4,4
Step-by-step explanation:
44x1/10
The two-way frequency table contains data on the preference of two school subjects among a group of 100 students. English Science Total Grade 5 24 36 60 Grade 8 16 24 40 Total 40 60 100 Based on this data, are "Grade 5" and "Science" independent events? (1 point) No, P(Grade 5 ∩ Science) ≠ P(Grade 5) ⋅ P(Science) Yes, P(Grade 5 ∩ Science) = P(Grade 5) ⋅ P(Science) No, P(Grade 5 ∩ Science) = P(Grade 5) ⋅ P(Science) Yes, P(Grade 5 ∩ Science) ≠ P(Grade 5) ⋅ P(Science)
The events Grade 5 and Science" are independent events, P(Grade 5 ∩ Science) = P(Grade 5) ⋅ P(Science) .Option B is the correct option.
What is frequency?
The frequency (f) of a specific value is the number of occurrences of the value in the data. The frequency distribution of a variable is the collection of all possible values and the frequencies associated with these values. Frequency distributions are represented graphically as frequency tables or charts.
Given table is
English Science Total
Grade 5 24 36 60
Grade 8 16 24 40
Total 40 60 100
Total students is 100.
Total student in grade 5 is 60.
The number of students who prefer science is 60.
The number of students who are in grade 5 and prefer science is 36.
The probability of grade 5 is P(grade 5) = 60/100 =0.6
The probability of science is P(science) = 60/100 = 0.6
The probability of Grade 5 ∩ Science is P(Grade 5 ∩ Science) = 36/100 =0.36.
Thus P(Grade 5 ∩ Science) =P(Grade 5) ⋅ P(Science).
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What is the slope for this
Answer:
-3
Step-by-step explanation:
rise over run method
3 up and 1 to the left which makes the slope negative
You have a cone whose height and base radius are equal and, inside it, you put the largest possible sphere that will completely fit inside. What is the exact fraction of the volume of the cone that is occupied by the sphere?
The exact ratio of of the volume of the cone that is occupied by the sphere is 4/(1+√2)³.
What is a cone?
A cone is a three-dimensional geometric shape that narrows smoothly from a flat base (typically circular base) to a point called the apex or vertex (which creates an axis to the centre of base).
Given that the height and radius of the cone is the same.
Assume that the radius of the cone is x.
Thus the slant height of the cone is √(x² + x²) = x√2.
Assume the radius of the sphere is r.
△OEC and △BDC are similar triangles according to AAA rule.
Thus, BD/OE =BC/OC
x/r = x√2/(x -r)
Cross multiply:
x(x - r) = xr√2
x² - rx = xr√2
x² = xr√2 + rx
rx( 1+√2) = x²
r = x²/[x( 1+√2)]
r = x/ (1+√2)
The volume of the sphere is 4/3 ∏ r³ = 4/3 ∏ [ x/ (1+√2)]³
The volume of the cone is 1/3 ∏r²h = 1/3 ∏x³
The ratio of the volume of the sphere to the cone is
4/3 ∏ [ x/ (1+√2)]³ : 1/3 ∏r³
= 4 : (1+√2)³
= 4/(1+√2)³
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Given the function: 1/(x + 1) - 4:
a. State the Domain using INTERVAL notation
b. State the Range using INTERVAL notation
c. Are there any asymptotes? If so, state their equations and draw them on the graph as dotted lines
Answer:
a) (-∞, -1) ∪ (-1, ∞)
b) (-∞, -4) ∪ (-4, ∞)
c) Vertical asymptote: x = -1
Horizontal asymptote: y = -4
Step-by-step explanation:
Given function:
[tex]f(x)=\dfrac{1}{x+1}-4[/tex]
Part (a)The domain of a function is the set of all possible input values (x-values).
When the denominator of a rational function is zero, the function is undefined.
Rewrite the function as one fraction:
[tex]\implies f(x)=\dfrac{1}{x+1}-\dfrac{4(x+1)}{x+1}[/tex]
[tex]\implies f(x)=\dfrac{1-4(x+1)}{x+1}[/tex]
[tex]\implies f(x)=\dfrac{-4x-3}{x+1}[/tex]
Set the denominator to zero and solve for x:
[tex]\implies x+1=0[/tex]
[tex]\implies x=-1[/tex]
Therefore, the given function is undefined when x = -1, so its domain in interval notation is:
(-∞, -1) ∪ (-1, ∞)Part (b)The range of a function is the set of all possible output values (y-values).
As the domain is restricted to (-∞, -1) ∪ (-1, ∞), the range is also restricted.
To find the range of a rational function, first solve the equation for x:
[tex]\implies y=\dfrac{1}{x+1}-4[/tex]
[tex]\implies y+4=\dfrac{1}{x+1}[/tex]
[tex]\implies (y+4)(x+1)=1[/tex]
[tex]\implies x+1=\dfrac{1}{y+4}[/tex]
[tex]\implies x=\dfrac{1}{y+4}-1[/tex]
[tex]\implies x=\dfrac{1-(y+4)}{y+4}[/tex]
Set the denominator of the resultant equation ≠ 0 and solve for y:
[tex]\implies y+4 \neq 0[/tex]
[tex]\implies y \neq -4[/tex]
Therefore, the range is the set of all real numbers other than y = -4:
(-∞, -4) ∪ (-4, ∞)Part (c)A vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.
Therefore, there is a vertical asymptote at x = -1.
As the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the result of dividing the highest degree term of the numerator by the highest degree term of the denominator.
[tex]\implies f(x)=\dfrac{-4x-3}{x+1}[/tex]
Therefore, there is a horizontal asymptote at:
[tex]y=\dfrac{-4}{1}=-4[/tex]There are no slant asymptotes as there is a horizontal asymptote.
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a. Identify each sequence as arithmetic, geometric, or neither.
b. If it is arithmetic or geometric, describe the sequence generator
n t(n)
0 16
1 8
2 4
3 2
4 1
5 1/2
6 1/4
Answer:
a) The sequence is geometric,b) [tex]t(n) = 2^{4-n}[/tex]----------------------------------------
Given sequence from zeros to 6th terms:
16, 8, 4, 2, 1, 1/2, 1/4It is a GP with the common ratio of 1/2 as each term is half the previous one.
Use the nth term equation, considering the first term is t(1) = 8, and common ratio r = 1/2:
[tex]t(n) = t(1)*r^{n-1}[/tex][tex]t(n) = 8*(1/2)^{n-1}=8*2^{1-n}=2^3*2^{1-n}=2^{4-n}[/tex]Answer:
a) Geometric sequence
[tex]\textsf{b)} \quad t(n)=8 \left(\dfrac{1}{2}\right)^{n-1}[/tex]
Step-by-step explanation:
An Arithmetic Sequence has a constant difference between each consecutive term.
A Geometric Sequence has a constant ratio (multiplier) between each consecutive term.
Part (a)From inspection of the given table, t(n) halves each time n increases by 1.
Therefore, the sequence is geometric with a common ratio of 1/2.
Part (b)[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given:
a = 8r = 1/2aₙ = t(n)Substitute the initial value (when n = 1) and the common ratio into the formula to create an equation for the nth term:
[tex]\implies t(n)=8 \left(\dfrac{1}{2}\right)^{n-1}[/tex]
Which of the following describes the domain and range of the function?
The domain and range of the piecewise function is;
B) Domain: x < 2 or x ≥ 3.; range: y > -3
What is the domain and range of the function?The piecewise function is given as;
f(x) = {-¹/₂x - 2, if x < 2
{2x - 4, if x ≥ 3
The domain of a function is the set of all possible input values of the function and as such in this case the domain is x < 2 or x ≥ 3.
The range is defined as the set of all possible output values of the function and in this case, we have;
For -¹/₂x - 2; If x < 2
At x = 2; -¹/₂(2) - 2 = -3
Range is; y > -3
Similarly, for 2x - 4, if x ≥ 3
At x = 3; 2(3) - 4 = 2
Range is; y ≥ 2
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solve for x, given the rectangle below TNREO to= 3x+1 ro=2x+4
Answer:
Step-by-step explanation:
The length of the two diagonals of a rectangle are said to be equivalent.
From the Pythagorean theorem, the diagonal (a) will be the hypotenuse in the equation and the length (b) and width (c) will be its opposite and adjacent.
From the figure given, the length of half of two diagonal of rectangles are given.
We can simply solve for the value of x
Solution:TO = RO
3x + 1 = 2x + 4 (combine like terms by first transposing it to the other side of the equation and changing its sign from (+) to (-) or vice versa).
3x - 2x = 4 - 1
x = 3
Find the range of the given function y=3x-2 for the domain (-1,2,4)
The range of the given function y = 3x - 2 for the domain (-1, 2, 4) is
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Domain of the function is the values of x for which the function is defined.
Range of the function is the value of the function when we put the values in the domain.
Given function,
y = 3x - 2
Given the domain (-1, 2, 4)
x = -1, then y = (3 × -1) - 2 = -5
x = 2, then y = (3 × 2) - 2 = 4
x = 4, then y = (3 × 4) - 2 = 10
Range is (-5, 4, 10).
Hence the range of the function is (-5, 4, 10).
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Find two positive numbers whose product is 192 and whose sum is a minimum.
A. 3 and 64
B. 4[tex]\sqrt{3}[/tex] and 16[tex]\sqrt{3}[/tex]
C. 8 and 24
D. 8[tex]\sqrt{3}[/tex] and 8[tex]\sqrt{3}[/tex]
E. 12 and 16
Two positive numbers whose product is 192 and whose sum is a minimum are; 8√3 and 8√3.
The correct option is (D).
What is minima?Minima is the minimum value of a function in given domain.
First Order Derivative Test
Let f be the function defined in an open interval I and f be continuous at critical point c in I such that f’(c) = 0.
If f’(x) changes sign from negative to positive as x increases through point c, then c is the point of local minima. And the f(c) is the minimum value.
Given,
Product of two positive numbers = 192
Sum should be minimum
Let x be the first positive number and y be the other positive number. So, the equation would be
x . y = 192
⇒ y = 192/x --------(a)
Let S be the sum of the two positive numbers.
S = x + y
substituting value of y in terms of x from equation(a)
S = x + 192/x
⇒ S = x + 192 . x⁻¹
Differentiating with respect to x
S'(x) = 1 + (-1)192x⁻²
S'(x) = 1 - 192/x²
S'(x) = (x² - 192)/x²
To determine the minimum S, equating first derivative of S with respect to x to zero.
S'(x) = 0
(x²-192)/x² = 0
x² - 192 = 0
x² = 192
x = ±√192
Rejecting negative root, since the numbers are positive
x = √192
Substituting value of x in equation (a)
y = 192/√192
y = √192
x and y can be written as
x = √192 = 8√3
y = √192 = 8√3
Hence , 8√3 and 8√3 are the two positive numbers whose product is 192 and sum is a minimum.
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Kiyo invites 5 friends to a sporting event.
Tickets cost $40 each. He knows at least one
friend will choose to attend the event.
Answer: 40 dollars
Step-by-step explanation:
i hope the explanation is right:)
If he invites 5 friends for 40 bucks each then one friend that he knows will go is 40 dollars. So the only thing you have to do for this problem is multiply 40 by the number of friends which in this case i believe is 1.
solve the given differential equation by undetermined coefficients.
y"+3y=-48x2e3x
The given differential equation by undetermined coefficients are y(x)=c1cos(31/2 x)+c2sin(31/2x)+(-4x2+4x-4/3)e3x
A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a place is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others. The study of solutions that satisfy the equations and the characteristics of the solutions is the main goal of the differential equation.
y'' + 3y=0
λ2+3 =0
λ 1=-i31/2,
λ 2=i31/2.
y0(x)=c1cos(31/2 x)+c2sin(31/2x),
yp(x)=(Ax2+Bx+C)e3x
yp'(x)=(3Ax2+(3B+2A)x+3C+B)e3x
yp''(x)=(9Ax2+(9B+12A)x+2A+6B+9C)e3x
x2e3x:3A+9A=-48,
xe3x:3B+9B+12A=0,
e3x:3C+2A+6B+9C=0.
=>A=-4,B=4,C=-4/3.
yp(x)=(-4x2+4x-4/3)e3x,
y(x)=y0(x)+yp(x)
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8,320 to 10,399 114,192 10,400 to 15,599 148,276 15,600 to 20,799 123,638 20,800 to 25,999 121,623 26,000 to 31,199 103,402 31,200 to 36,399 73,463 36,400 to 41,599 59,126 41,600 to 51,999 68,747 52,000 to 77,999 56,710 1. What is the modal-class interval? 2. Copy the table into your notebook and include columns to find the upper pulative frequencies and cumulative percentages.
Answer:
Copy the table into your notebook and include columns to find the endpoint (upper value) for each interval. Figure out the cumulative frequency and
Step-by-step explanation: