When the tone's height, h, equals 0, we can determine when the tone will fall to the ground. The equation that expresses the height of the tone as a function of time is as follows:
h = -16t^2 + 32t + 40
where t is the number of seconds since the tone was launched, and h is the tone's height in feet.
We can set the formula equal to 0 because we are aware that h = 0 when the tone strikes the ground:
-16t^2 + 32t + 40 = 0
Here is the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
where a = -16, b = 32, and c = 40.
With these values entered into the formula, we obtain:
t = (-32 ± √(32^2 - 4(-16)(40))) / 2(-16)
t = (-32 ± √(1024 + 2560)) / (-32)
t = (-32 ± √(3584)) / (-32)
t = (-32 ± 64) / (-32)
t = (32) / (-32) or (-96) / (-32)
t = -1 or 3
The duration of the tone before it reaches the ground is -1 or 3 seconds.
However, as there is no such thing as a negative amount of time, it takes 3 seconds for the tone to reach the earth.
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An experienced bricklayer can work twice as fast as an apprentice bricklayer. after the bricklayers work together on a job for 4 hours, the experienced bricklayer quits. the apprentice requires 14 more hours to finish the job. how long would it take the experienced bricklayer, working alone, to do the job?
The total time taken by the experienced bricklayer to complete the job as per given condition is equal to 13 hours.
As given in the question,
Let the time taken by experienced bricklayer be 't' hours
Then time taken by apprentice bricklayer be '2t' hours
Time to complete 1 complete work is
Experienced bricklayer worked for 4 hours
Apprentice bricklayer worked for ( 4 + 14 ) = 18 hours
Required equation to complete 1 work is :
( 4/x) + ( 18 /2x) = 1
⇒( 8 + 18 )/ 2x = 1
⇒26/2 = x
⇒ x = 13 hours
Therefore, time taken by the experienced bricklayer to complete the job is equal to 13 hours.
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34 entre 250.6 con operacion
De acuerdo con la información del enunciado, el resultado de esta operación matemática (división) es 0,13
¿Cómo solucionar la división?Para solucionar la división, debemos realizar el siguiente procedimiento:Identificar las partes de la división (dividendo y divisor), en este caso como el divisor es más grande, debemos añadir un cero y una coma en el cociente para añadir un cero en el dividendo.Una vez hemos agregado un cero al dividendo, debemos identificar un número que al multiplicarlo con el divisor no de menor o igual al dividendo, en este caso sería 1, porque 250.6 * 1 = 250.6Entonces debemos hallar la diferencia entre 250.6 y 340, este procedimiento se hace con una resta y daría 89,4.Una vez hallamos este número, debemos identificar otro número para el cociente que multiplicado por 250,6 no de inferior o igual a 894, en este caso sería 3, 3 * 250,6 = 751.8En este paso debemos realizar otra resta para identificar la diferencia entre estos dos número. 894 - 751,8 = 142,2Esta división da como resultado un número decimal de varios valores por lo que podemos repetir este procedimiento tantas veces sea necesario dependiendo de la exactitud de nuestras necesidades.
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Your shifts productivity is slow because one person is not pulling his shares. the rest of the team is getting upset. what should you be most and least likely to do?
The diagram shows a cuboid ABCDEFGH
ABCD is a square 25cm^2
CG=12cm
Find the volume of the cuboid
Answer:
Step-by-step explanation:
Volume of cuboid = AC x CD x CG. (Cuboid formula is l x b x h)
Now, given, area of ABCD is 25.
Area of square = a² or AC x CD
Therefore, substituting that in the first line, we get,
25 x CG = volume,
or 25 x 12 = 300 cm³. (Given CG is 12cm)
50% of what number is 140?
Answer:280
Step-by-step explanation:
Hello I need some help with math
Answer:
y = 136
x=15
Step-by-step explanation:
to work this question out you must know the angles on a straight line add up to 180 degrees. By doing that we can find the top angle inside of the triangle.
180 - 104 = 76
to find x we need to know that angles in a triangle add up to 180 degrees.
180 = (3x-1) + 4x + 76
To solve for x, we can first simplify the equation.
180 = (3x-1) + 4x + 76
This can be re-arranged as:
(3x-1) + 4x = 104
and then combined as:
7x = 105
Finally, we can solve for x by dividing both sides by 7:
x = 105/7
x = 15
So the value of x that satisfies the equation is 15
to find y we need to know that angles on a line equal 180
180 = (3(15)-1) + y
180 = 44 + y
To find the value of y, we can subtract 44 from both sides
y = 180-44
y = 136
if xy + 8ey = 8e, find the value of y'' at the point where x = 0.
The value of y'' at the point where x = 0 is 8.
A derivative is a mathematical concept that measures how much a function changes as its input (or independent variable) changes. It is often represented by the symbol "dy/dx" or "f'(x)", and is used to calculate the slope of a function at a particular point.
To find the value of y'' at the point where x = 0, we first take the derivative of the equation with respect to x. This gives us y' + 8exy' = 0. Then, we take the derivative of this equation with respect to x again, which gives us y'' + 8exy'' + 8ey' = 0. Substituting x = 0 into this equation gives us y'' + 0 + 8e(0) = 0, which simplifies to y'' = 8.
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(a) A parallelogram has base (2x - 1) metres and height (4x-7) metres.
The area of the parallelogram is 1 m².
(i) Show that 4x² - 9x +3=0.
Answer (a)(i)
“please show steps and thank you”
Answer:
See below.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a parallelogram}\\\\$A=bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given:
[tex]b = (2x - 1)\;\sf m[/tex][tex]h = (4x - 7)\;\sf m[/tex][tex]A=1\;\sf m^2[/tex]Substitute the expressions for b and h and the value of A into the formula for area:
[tex]\implies 1=(2x-1)(4x-7)[/tex]
[tex]\implies (2x-1)(4x-7)=1[/tex]
Expand the brackets:
[tex]\implies 8x^2-14x-4x+7=1[/tex]
[tex]\implies 8x^2-18x+7=1[/tex]
Subtract 1 from both sides of the equation:
[tex]\implies 8x^2-18x+7-1=1-1[/tex]
[tex]\implies 8x^2-18x+6=0[/tex]
Factor out 2 from the left side:
[tex]\implies 2(4x^2-9x+3)=0[/tex]
Divide both sides by 2:
[tex]\implies 4x^2-9x+3=0[/tex]
Hence, showing that 4x² - 9x + 3 = 0.
The triangle below has a total perimeter of 450 cm: picture of a triangle with sides 128 and 150. Third side unknown Write an equation and solve it to find the length of the longest side of the triangle. (1 point)
For the given perimeter and side length of the triangle , the equation and the measure of the longest side length of the triangle is given by :
Equation : x + 278 = 450 and side length = 172cm.
As given in the question,
The given measurements of the triangle are :
Perimeter of the triangle = 450cm
Measure of the two side length are :
Side length 1 = 128 cm
Side length 2 = 150 cm
let 'x' be the measure of the longest side length of the triangle we have,
Perimeter of the triangle = Side length 1 + Side length 2 + side length 3
⇒ 450 cm = 128 + 150 + x
⇒ 450 = 278 + x
Equation to represent the relation :
x + 278 = 450
Measure of the longest side of the triangle is :
⇒ x = 450 - 278
⇒ x = 172 cm
Therefore, the equation and the measure of the longest side length of the triangle with given perimeter and other side length is equal to
Equation : x + 278 = 450 and side length = 172cm.
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A forest covers 51,000 acres. A survey finds that 0.4% of the forest is old-growth trees. How many acres of old-growth trees are there?
If a forest covers 51,000 acres. A survey finds that 0.4% of the forest is old-growth trees. The number of acres of old-growth trees that are there is: 204 acres.
How to find the number of acres?Using this formula to find the number of acres that are there.
Number of acres = Number of forest covers acres × Forest old growth tree percentage
Where:
Number of forest covers acres = 51,000 acres
Forest old growth tree percentage = 0.4% or 0.004
Let plug in the formula
Number of acres = 51,000 acres × 0.004
Number of acres = 204 acres
Therefore we can conclude that the number of acres is 204 acres.
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Give each trig ratio as a fraction in simplest form.
Answer:
[tex]df = \sqrt{ {29}^{2} - {20}^{2} } = 21 \\ \sin(d) = \frac{20}{29} \\ \cos(d) = \frac{21}{29} \\ \tan(d) = \frac{20}{21} \\ \sin(e) = \frac{21}{29} \\ \cos(e) = \frac{20}{29} \\ \tan(e) = \frac{21}{20} [/tex]
Answer:
Step-by-step explanation:
First, use the pythagorean theorem to complete the vales of each sides of the triangle. Then, use the respective trigonometric formulas and inverse the answer to compute the degree of every corners.
the purpose of this lab is to find several types of samples given a population. your population is described below: population: the 24 students in a math 152 class. the following is the seating chart for the class. when choosing your sample only use the subject id not their name. describe how you found the sample fully including the technology you used and all steps you took.
To select a sample from the population of 24 math 152 students, I used stratified random sampling.
Stratified random sampling is when a population is divided into groups or strata, then a random sample is taken from each group. In this case, the population of 24 students was divided into two groups of 12. The first group was selected by randomly assigning each student a number from 1-12, then I used a random number generator to choose numbers from 1-12. The numbers that were chosen were the subjects for the first group. I repeated this process for the second group of 12, assigning each student a number from 13-24, then using the random number generator to choose the subjects for the second group. I repeated this process until I had a sample of 10 students. This process allowed me to create a sample that was representative of the entire population.
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I got a word problem for you maths people that I need help with
Answer: sometimes
Step-by-step explanation:
a system of linear equations that do not rely on each other for the algebraic or graphic form of the equation
Independent system of linear equations that do not rely on each other for the algebraic or graphic form of equations.
The collection of two or more linear equations involving the same variables is known as a system of linear equations. The number of orders in a system of linear equations can range from one to n.
If a consistent system only has one solution, it is regarded as independent.
Elimination or substitution are two algebraic methods for solving a system of linear equations. and was also graphically solved.
Hence Independent system of linear equations that do not rely on each other for the algebraic or graphic form of equations.
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how to calculate multiplier in economic
Answer:
1/1-mpc and 1-mps
Step-by-step explanation:
to get the multiplier effect you use the formula
M=1/1-MPC
Harley has 6 pints of lemonade. Rosie has 3 times as many pints of
lemonade as Harley.
a) How many pints of lemonade does Rosie have?
b) How many more pints of lemonade does Rosie have than Harley?
Give your answers as whole numbers or as fractions in their simplest form.
Answer: So in order to get a) you need to multiply 3 times 6 because Rosie has 3 times more pints than Harley so you would get 18. And to find b) you need to subtract the 6 from the 18 and you get 12. Rosie has 12 more pints than Harley.
Step-by-step explanation:
A device for training astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m. If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating? Express your answer in both m/s and rev/s
The velocity of the trainee is 94.2/m m/s and 0.15 x m rev/s.
The centripetal force (Fc) felt by the trainee can be calculated using the following equation:
Fc = mv2/r
Where m is the mass of the trainee, v is the velocity and r is the radius of the circle.
Therefore, the velocity (v) required to produce a centripetal force of 7.85 times the mass of the trainee can be calculated as follows:
v =√(Fc x r/m)
=√(7.85 x 12.0/m)
=√(94.2/m)
For a given mass, the velocity is therefore 94.2/m m/s.
Converting to revolutions per second (rev/s), the velocity can be calculated as follows:
v = (2πr)/T
= (2π x 12.0)/(94.2/m)
= (14.14 x m)/94.2
= 0.15 x m rev/s
Therefore, the velocity of the trainee is 94.2/m m/s and 0.15 x m rev/s.
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What single factor made the Hindu arabic number system superior
Invention of 0
What are the two purposes of numerals or digits
Show the cardinal value (how many)
And show the place value (10s, 100s, 1000s)
Natural numbers in a counting process
Does not include 0
1-2-3-4-5-6-7-8-9-10-11- infinity
Principle of closure
Addition- if you add any two natural numbers, the result will always be a natural number. Called closed under addition
Multiplication- if you multiply any two naturals, you get naturals. Called closed under addition
Subtraction- you cannot achieve closure when subtracting larger number from smaller number (i.e. 6-7)
Division - when you divide two natural numbers, it is possible to get a fraction. Not closed by division.
Integers
Positive and negative numbers, start at 0 and expand infinitely at both ends.
Closed under addition, multiplication, subtraction. NOT DIVISION
Rational numbers
Numbers that can be expressed as fractions, that is the quotient of two integers
Irrational numbers
Non terminating, repeating decimals
Three axioms of equality
Reflexive- law of identity. Any number reflects itself or is equal to itself (i.e. A=A)
Symmetric- any equality is reversible (i.e. A=B, then B=A)
Transitive property - possible to identity two numbers as being equal to a third quantity (a=b and b=c then a=c)
Commutative property
When adding, it doesn't matter the order
a+b=b+a
Order in which things are multiplied does not affect product (a*b=b*a)
Associative property
Law states that the order in which Addends are grouped, the sum will be unaffected. (a+b)+c = a + (b+c)
(A*b)*c = a(b*c)
Distributive property
Multiplication can be distributed over addition.
a(b+c)= (a*b) + (a*c)
Unity element
Number 1 is the identity element of multiplication. Any number multiplied by one equals itself
Zero element
Identity element for addition
Will destroy number, anything multiplied by 0 =0
Dividing by 0 is error.
0 /# = 0
The Hindu-Arabic numeral system is superior to other numeral systems because of its invention of the number 0. This allows for the representation of the concept of nothingness or absence, which allows for the development of more advanced mathematical operations such as negative numbers and decimal fractions.
The two purposes of numerals or digits are to show the cardinal value (how many) and to show the place value (10s, 100s, 1000s). The cardinal value is the actual quantity of a number, while the place value is the position of a digit in a number, which determines its value in relation to other digits.
The natural numbers are the numbers used in a counting process and do not include 0. They include the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on to infinity. The principle of closure is the idea that certain operations, such as addition and multiplication, will always result in a natural number when performed on natural numbers. However, subtraction and division do not result in natural numbers in all cases.
Integers are positive and negative numbers that start at 0 and expand infinitely in both directions. They are closed under addition, multiplication, and subtraction. However, division is not closed under integers.
Rational numbers are numbers that can be expressed as the quotient of two integers. Irrational numbers are non-terminating, non-repeating decimals.
The three axioms of equality are the reflexive property (A = A), the symmetric property (if A = B, then B = A), and the transitive property (if A = B and B = C, then A = C).
The commutative property states that the order of the numbers does not affect the result in operations such as addition and multiplication. The associative property states that the grouping of numbers does not affect the result in operations such as addition and multiplication. The distributive property states that multiplication can be distributed over addition.
The unity element for multiplication is the number 1, which serves as the identity element for multiplication. The zero element for addition is 0, which serves as the identity element for addition. Dividing by 0 is an error and not allowed.
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how do you find the answer to this super hard question which is,
2(1/3^2)
Step-by-step explanation:
Square the 3 first, which gives you 9 (use the 9 as the denominator), then do 2 X 1/9. Which leaves you with 2/9
nine times the sum of a number and 4 is equal to 7
Use the variable w for the unknown number. Write it into an equation
Answer:
9(w+4)7
Step-by-step explanation:
I got this answer too, just like the person before me
Given the points (3, -9) and (-9, 5) find the slope
Answer:0.5
Step-by-step explanation:
Is Ishmael or Ian correct?
Answer:
Ian is correct
Step-by-step explanation:
The range of a function is the set of all possible values that the function can take. In other words, it is the values of y lying between minimum and maximum
From the graph we can see that the minimum value of y = 0
Maximum value of y = 30
So the range is 0 ≤ y ≤ 30
So Ian is correct
(Note that y ≤ 30 can include negative values which is not possible in this case)
A square and isosceles triangle of equal height are side-by-side, as shown, with both bases on the $x$-axis. The lower right vertex of the square and the lower left vertex of the triangle are at $(10, 0)$. The side of the square and the base of the triangle on the $x$-axis each equal $10$ units. A segment is drawn from the top left vertex of the square to the farthest vertex of the triangle, as shown. What is the area of the shaded region
According to the given statement the area of shaded region is is 20 units squared.
An isosceles triangle is just what?As an outcome, an isosceles triangle has two equal sides as well as two equal angles. As from Greek words iso (same) and skelos, the phrase is formed (leg). Except for a right triangle, which has quadrilateral on all sides, a scalene triangle lacks equal sides on each side.
The slope of the line connecting the bottom right vertex of something like the triangle to the top left vertex of both the square is equal to -1/2.
This line's equation is y = (-1/2)x + 10. (1)
The point at the triangle's top vertex is (15, 10)
The slope of the segment between (10, 0) and (15, 10) is 10/5, which equals two.
The line connecting these two locations has the equation y = 2(x - 10) y = 2x - 20. (2)
You may get the x coordinate of the point where these lines cross by putting (1) = (2)
(-1/2)x + 10 = 2x - 20
30 = [5/2]. x x equals 12 and y equals 2(12) - 20 = 4.
Therefore, the triangle's shaded area's height is 4 and its base is 10.
Its area is therefore (1/2)(4)(10) = 20 units squared.
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determine whether the series is convergent or divergent. 1 + 1 2 2 + 1 3 3 + 1 4 4 + 1 5 5 ⋯
We can see from the provided data that it is obviously divergent.
What in mathematics is convergent and divergent?Convergent sequence occurs when, as n approaches infinity, you arrive at a final as well as constant term through a number of terms. Divergent sequences are those in which individual terms never stabilize; instead, they constantly grow or decrease as n approaches infinity, approaching either infinity or -infinity.
Is divergence equivalent to infinity?A series diverges when it moves up, down, to infinity or minus infinity without settling on a value.
The series' parts are becoming larger and larger while being interrupted by some constant "1" (however they are useless in this situation since the series is divergent because there are always two numbers that follow an intercepting "1" that are greater by 1 than the two that came before it).
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What type of triangle is it if the lengths are 4 cm 5 cm and 6 cm?
A triangle with given lengths 4cm , 5cm , and 6cm is scalene and acute angled triangle.
As given in the question,
In the given triangle ,
Lengths of the sides of a triangle is given by :
4cm , 5cm , and 6cm.
All the sides are of different measure , it is a scalene triangle.
Apply cosine rule to find the measure of largest angle:
c = 6cm is the longest side opposite to largest angle.
c² = a² + b²- 2abcosα
⇒ 6² = 4² + 5² - 2(4)(5)cosα
⇒cosα = ( 16 + 25 - 36 ) / 40
⇒ cosα = 5/40
⇒ α = cos⁻¹( 1/8)
⇒ α = 82.8° < 90°
It is an acute angled triangle.
Therefore, for the given lengths of the triangle it is a scalene and acute angled triangle.
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4 Which number is included in the set of integers that when added to –4 gives a sum of less than zero? Select all that apply. A 3 B 7 C 9 D –2 E 4 F 0
The number included in the set of integers that when added to -4 gives a sum less than zero are 0, -2 and 3
How to find the integers in a word expression?The question wants us to find the numbers included in the set of integers that when added to -4 gives a sum less than zero.
The options are 3, 7, 9, -2, 4 and 0.
Therefore,
let
the number added = x
Hence,
-4 + x < 0
Base on the options, the numbers that fits into the inequality are as follows:
The numbers are 0, -2 and 3.
Therefore,
-4 + 0 < 0
-4 + -2 < 0
-4 + 3 < 0
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State the center point and radius of the circle. Write the equation of the circle in standard and general form.
The equation of the circle is [tex](x-2)^2+(y+1)^2=16[/tex].
What is equation of the circle?
A closed curve that is drawn from a set point known as the center and has all of its points at exactly the same distances from it is termed a circle. The formula for a circle with the coordinates (h, k) in its center and radius is [tex](x-h)^2+(y-k)^2=r^2[/tex]
This represents the equation's conventional form. As a result, the equation for the circle is simple to find if we also know the coordinates for the radius of the circle.
Here according to the graph the center of the circle is (2,-1) and radius of the circle = 2+2=4 unit.
Now using circle equation then
=> [tex](x-p)^2+(y-q)^2=r^2[/tex]
Where p=2 , q=-1 and r=4 then
=> [tex](x-2)^2+(y-(-1))^2=4^2[/tex]
=> [tex](x-2)^2+(y+1)^2=16[/tex]
Hence the equation of the circle is [tex](x-2)^2+(y+1)^2=16[/tex].
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Geometry Unit 4 homework 3
Solve for x.
Answer: The answer is x = 34
Step-by-step explanation: The first triangle shows that the first angle is 84 and 36 which equals 120. Since both triangles are the same the second triangle also has to equal 120. Since you know this you simply subtract 86 from 120 which gives you 34.
Hope this helped
a rectangular field is to have 100 m2 in area. it was enclosed by fence. the north south sides costs $20/m, east-west sides cost $5/ m. what are the dimensions so that the cost is a minimum?
The dimensions of the rectangular field with a minimum cost are x = 50 m and y = 2 m.
Let x be the length of the north-south sides and y be the length of the east-west sides.
The area will be given by: A = xy
The cost will be given by: C = 20x + 5y
We have to find the dimensions (x and y) that minimize the cost C subject to the constraint that the area A is 100 m2.
Using the constraint, we have:
A = xy = 100
We can solve this equation for one of the variables in terms of the other, say x in terms of y.
We get: x = 100/y
Substituting this into the cost equation, we get:
C = 20(100/y) + 5y
Differentiating this equation with respect to y and equating it to 0, we get:
dC/dy = 20/y2 - 5 = 0
or, y2 = 4
or, y = ±2
We choose the positive value for y, so y = 2
Substituting this value of y in the equation for x, we get:
x = 100/2 = 50
Therefore, the dimensions of the rectangular field with a minimum cost are x = 50 m and y = 2 m.
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Math
B8.18 Evaluate a linear function: word problems
c = 18h + 63
4) This equation shows how the cost of renting a moving van depends on how many hours
it is rented for.
The variable h represents the number of hours the moving van is rented for, and the
variable c represents the cost in dollars. For $81, what is the maximum amount of time that a
moving van can be rented for?
Quizzes
DELL
pls help!!
Therefore , the solution of the given problem of equation comes out to be 1 hour is required to generate 81$ .
Clarify Equation.The equal symbol (=) is used to indicate equivalency in a statement for a mathematical model, which combines two statements. In algebra, an equation is a claim that establishes the similarity of two mathematics. The formula 78x + 5 = 14 connects the two numbers, for example. The statements on either face of a letter form a mathematical connection. Typically, the symbol is the lone element and the only variable. For example, 9x – 4 = 2.
Here,
Given :c = 18h + 63
Where c is cost in dollars
and h is hour spend.
Thus ,
To find the maximum amount of time to generate $81
So,
Using equation:
81 = 18h + 63
=> 18h = 81-63
=> 18h = 18
=> h =1
Therefore , the solution of the given problem of equation comes out to be 1 hour is required to generate 81$ .
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