a) To find the domain of the equation 3x = 12, we need to solve for x, i.e. x = 4
b) x = 2.83
What is domain?The collection of all x-values that the function is specified for and that result in a real number as the output is known as the domain of a function.A finite collection of values, like the collection of positive integers, can serve as the domain.The range of real numbers between -5 and 5 would be considered the domain for this example.The domain may be the set of all real numbers, represented by the letter R.Square root, logarithmic, and reciprocal functions are only a few examples of functions whose domain may be constrained. Because the output must be a real number, several limitations frequently result. By looking at the x-values of the locations where the graph meets the x-axis, it is possible to visually identify a function's domain.By using the function specification and looking for any limitations on the input values, the domain can also be identified analytically.Divide both sides by 3:
3x/3 = 12/3
x = 4
The domain of this equation will be all real numbers.
b) To find the domain of the equation 1.06x = 3, we need to solve for x.
Divide both sides by 1.06:
x = 3 / 1.06
x = 2.830188679245283
The domain of this equation will be all real numbers.
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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 17)(0,17) and (2, 153)(2,153).
The locations (0, 17) and are traversed by an exponential function of the type y = abx, where a and b are constants (2, 153). We can utilise these points to solve for the values of a and b in order to determine the equation of the exponential function.
Since we now know that y = abx when x = 0, we can change the first point to read as follows:
17 = a(b^0)
We can simplify this to: since anything raised to the power of 0 is 1,
17 = a
We can now determine b using the second point (2, 153):
153 = ab^2
By applying the formula:
153/a = b^2
taking square root
b = sqrt(153/a)
Substitute a = 17
b = sqrt(153/17)
The equation will now look like this when we add the value of a back in:
y = a * b^x
y = 17 * sqrt(153/17)^x
y = 17 * sqrt(9)^x
Consequently ,y = 17 * 3^x, is the exponential function that passes between the positions (0, 17) and (2, 153).
Therefore , the exponential function is y = 17 * 3^x .
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Which subtraction expression does the number line model show?
The subtraction equation the inequality solve is
-9 + -4 = -13
What is a number line?A number line is a horizontal line with uniformly spaced numerical increments.
The number on the line can are represented depending on the numbers that are provided. A number is used to plot a point depending on the question that goes with it and the number type.
For the problem one unit represent a digit number with intervals of 1.
The shorter line is as -4 and the longer is at +9
adding bot together will be
= -9 + -4
= -9 - 4
= -13
hence the subtraction equation is -9 - 4 = -13
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What is the solution to the system of equations y equals 1. 5 x 4?.
The solution to the system of equations y = 1.5x - 4 and y = -x is (1.6,-1.6)
The coordinates of the ordered pair (s) that satisfy all of the system's equations make up the solution set to an equational system. This means that the equations will be true for those x and y values. The intersection of all of the graphs, when a system of equations is graphed, is the solution.
These are the equations:
y = 1.5x - 4
y = -x
Put y = -x in place of y in the first equation.
-x = 1.5x - 4
Assemble similar terms
-1.5x - x = -4
This results
-2.5x = -4
Add -2.5 to both sides.
x = 1.6
Change y = -x to x = 1.6.
y = -1.6
As a result, the system of equations solution is (1.6,-1.6).
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a train track slopes upward at an angle of 12 degrees how many feet does the track rise over a horizontal distance of 150 ft estimate ur answer to two decimal places
The track rises 31.88 feet over a horizontal distance.
What is tangent function?One of the six fundamental functions in trigonometry is the tangent function. As stated, Tan A = Opposite Side/Adjacent Side is the Tangent Formula. Tangent may be modeled using sine and cosine as follows: Tan A = Sin A / Cos A.
Given:
A train track slopes upward at an angle of 12°.
The track rise over a horizontal distance of 150 feet.
From the attached image:
tan(12)° = AB/OA
AB = 150 x tan12°
AB = 31.88 feet.
Therefore, the required distance is 31.88 feet.
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What is a commutative property in math?.
A commutative property in math is
with respect to Addtion : x + y = y + x With respect to Multiplication : xy = yx.Commutativity says that the numbers we are dealing with can be shifted or swapped without affecting the answer. This property applies to addition and multiplication, but not to subtraction and division.
Commutative law of addition:a + b = b + a; where a and b are
integers. Example: 3 + 4 = 4 + 3 = 7.
Commutative law for multiplication:a × b = b × a; where a and b are
non-zero integers. Example :
2×3 = 3×2 = 6
So this rule simply states that you can change the order of numbers in a question by adding or multiplying them without affecting the answer.
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what is the value of x? WILL MARK BRAINLIEST FOR CORRECT ANSWER!!!
Answer:
x = 49Step-by-step explanation:
are two similar triangles, we can solve with a proportion between the corresponding sides
42 : x = 12 : 14
x = 42 x 14 : 12
x = 49
-------------------
EXERCISES INTEGRALS
INTEGRALS EXERCISES PLEEASEEEE HELPPP I’LL GIVE U A CROWN PLEASEEE
The solution of the integral are:
(a) ∫tanx secx dx = sec(x) + C,
(b) [tex]\int\limits{ \frac{y^3}{(1 - 2y^4)^5} \, dy = -\frac{1}{32(1 - 2y^4)^4}[/tex]
What is integral?
Integrals are used to evaluate such quantities as area, volume, work, and, in general, any quantity that can be interpreted as the area under a curve.
We have given,
∫tanx *secx dx = ?
∫y³/(1-2y⁴)⁵ dy = ?
∫tan(x)sec(x)dx
Rewrite the expression
∫ sin(x)/cos²(x) dx
Use the substitution dx = − 1/sin(x) dt to transform the integral
∫ sin(x)/cos²(x) ×(− 1/sin(x))dt
Simplify
∫− 1/cos²(x)dt
Use the substitution t=cos(x) to transform the integral
∫−t⁻²dt
= −(−t⁻¹)
Calculate
t⁻¹
Substitute back
1/cos(x)
Rewrite the expression
1 × sec(x)
Multiply the terms
sec(x)
Solution
sec(x) + C, C ∈ R
∫y³/(1-2y⁴)⁵ dy =
[tex]= \int\limits {-\frac{1}{8u^5} } \, du[/tex]
[tex]= \frac{1}{8} \int\limits {-\frac{1}{u^5} } \, du[/tex]
[tex]= \frac{1}{8} (-\frac{1}{4u^4} )[/tex]
by substituting u = (1 - 2y⁴)⁴
[tex]= \frac{1}{8} (-\frac{1}{4(1-2y^4)^4} )[/tex]
[tex]= -\frac{1}{32(1 - 2y^4)^4}[/tex]
Hence, the solution of the integral are:
(a) ∫tanx secx dx = sec(x) + C,
(b) [tex]\int\limits{ \frac{y^3}{(1 - 2y^4)^5} \, dy = -\frac{1}{32(1 - 2y^4)^4}[/tex]
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Need help with this
Gross profit is the profit that a business makes after the manufacturing and selling costs are subtracted from the total sales.
What is Gross profit?Gross profit is the profit a company makes after deducting the costs associated with making and selling its products, or the costs associated with providing its services. Gross profit will appear on a company's income statement and can be calculated by subtracting the cost of goods sold (COGS) from revenue (sales). These figures can be found on a company's income statement. Gross profit may also be referred to as sales profit or gross income.Gross profit=Net sales−CoGS.Gross margin is the difference between revenue and cost of goods sold, divided by revenue. Gross margin is expressed as a percentage. Generally, it is calculated as the selling price of an item, less the cost of goods sold, then divided by the same selling price.To learn more about Gross profit refer to:
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A rectangular garden has a length of 20 yards and a width of 42 yards. A diagonal path runs from one end of the garden to the other. How long is the diagonal path? a. B. C. 50 yd. D.
When the rectangular garden has a length of 20 yards and a width of 42 yards the diagonal path will be [tex]\sqrt{2164}[/tex] .
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Since we have a right-angled triangle, we can use the Pythagorean Theorem to find our answer. The Pythagorean Theorem states the following:
[tex]a^{2} +b^{2} =c^{2}[/tex]
In this formula a and b represent the legs of the triangle and c represents the length of the hypotenuse.
Let's substitute our data from the question.
[tex]42^{2} +20^{2} =c^{2}[/tex]
Square.
1764 + 400 = [tex]c^{2}[/tex]
And finally take the root of both sides. We only need to use the positive solution, since the length of the hypotenuse can't be negative.
[tex]c = \sqrt{2164}[/tex]
When the rectangular garden has a length of 20 yards and a width of 42 yards the diagonal path will be [tex]\sqrt{2164}[/tex] .
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Answer: 53
Step-by-step explanation:
The length and width of the garden represent the legs of a right triangle, and the diagonal path represents the hypotenuse.
The Pythagorean Theorem states that a squared plus b squared equals c squared, where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse.
Let p equal the length of the diagonal path in yards.
Applying the Pythagorean Theorem gives us p squared equals forty-five squared plus twenty-eight squared.
Now square forty-five and twenty-eight to get p squared equals two thousand twenty-five plus seven hundred eighty-four.
Next, find the sum of two thousand twenty-five and seven hundred eighty-four, which is two thousand eight hundred nine.
Finally, calculate the square root of two thousand eight hundred nine to find that p equals fifty-three.
So the length of the diagonal path is fifty-three yards.
At a local print shop, 20 copies can be made for $8. At this rate, how much would it cost to make 75 copies?
Fill out the table of equivalent ratios until you have found the value of x.
At a local print shop, 20 copies can be made for $8. At this rate, it would cost $30 to make 75 copies.
What is the equivalent ratio?
Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.
To solve this problem, we can set up a ratio between the number of copies and the cost:
20 copies / $8 = 75 copies / x
We can cross-multiply to find the value of x:
20 copies * x = 75 copies * $8
20x = 600
x = 30
Therefore, it would cost $30 to make 75 copies.
Here's the completed table of equivalent ratios:
Number of copies Cost
20 $8
75 x
We know that these ratios are equivalent, so we can set up a proportion:
20/8 = 75/x
Then we cross-multiply:
20x = 75 * 8
20x = 600
And solve for x:
x = 600/20
x = 30
Therefore, it would cost $30 to make 75 copies.
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How do you find the roots of a quadratic equation in factored form?.
By setting one side of a quadratic equation to zero, factoring the resulting polynomial, and then using the Zero Product Property, you can obtain the solutions, or roots, of these equations.
According to the Principle of Zero Products, if ab = 0, then either an or b, or both a and b, are 0, or both are 0. The roots of a function (f (x) can be any function) are the answers to y = f (x) when y = 0. These are the locations where an equation's graph crosses the x-axis.
To use factoring to solve a quadratic equation:
1. Convert the equation to standard form with a zero on one side.
2. Factor the non-zero side.
3. Reset each component to zero.
4. Solve each of the ensuing equations.
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URGENT!
find the value of x in each supplementary angle pair
The value of x in the supplementary angle pair is obtained as x = 14°.
What is a supplementary angle?
The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.
Two angles are supplementary, if -
One of its angles is an acute angle and another angle is an obtuse angle.
Both of the angles are right angles.
The given angles are -
Angle 1, ∠1 = 156°
Angle 2, ∠2 = (x + 10)°
Since, both angles lie on same plane which a straight line it forms a supplementary angle.
The equation for supplementary angle pair is -
∠1 + ∠2 = 180°
Substituting the values in the equation -
∠1 + ∠2 = 180°
156° + (x + 10)° = 180°
166° + x = 180°
x = 180° - 166°
x = 14°
Therefore, the value of x = 14°.
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X/4 + 11 = 25
Solve for x
Answer: x=56 you can just look it up on
Answer:
[tex]x=56[/tex]
Step-by-step explanation:
[tex]\frac{x}{4}+11=25\\\\[/tex]
Mutiply by 4 every each number you see.
[tex]x+44=100[/tex]
Subtract -44 in both sides.
[tex]x+44-44=100-44[/tex]
So,
[tex]x=56[/tex]
Hope this helps :D
What is the value of x in the triangle?
Answer: 33
Step-by-step explanation:
66 - 33
Answer:
x is 33...........................
Step-by-step explanation:
33 +x =66
66-33=x
Think of a number, double the number and add 6. The answer is 3 times the number. Find the number.
Answer:
The number is 6
Step-by-step explanation:
"Think of a number," [I'm thinking of x]
"double the number" [OK, that would be 2x]
"and add 6 " [If you insist: 2x + 6] ["The Answer"]
"The answer is 3 times the number" [Answer = 3x]
We take the answer, 2x+6 and set it equal to 3x
2x+6 = 3x
x = 6what is the equation of the parabola with vertex (-1,-3) and the origin as zero
The equation of the parabola with vertex (-1,-3) and the origin as zero point is given by y = (x + 1)2 - 3.
What is Equation?An equation is a mathematical statement that expresses two expressions as being equal. It consists of two expressions, one on either side of an "equals" sign, and indicates that the expressions have the same value. For example, the equation "2 + 2 = 4" states that the value of the expression "2 + 2" is equal to the value of the expression "4".
This equation can be derived by transforming the standard form of a parabola, which is y = ax2 + bx + c, into a form where the vertex of the parabola lies at the origin of the coordinate system. The standard form of the equation can be written as y = (x - (-1))2 -3. When the terms inside the parentheses are multiplied out, the equation becomes y = (x + 1)2 – 3.
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Can you help please?
To be a function, each x-value (or input) can only be used once. Each x-value (or input) can only be paired with a single y-value (or output).
If any x-value (or input) is paired with more than one y-value (or output), it's not a function.
Top Left:
Not a function
"rock" and "leaf" are paired with two outputs.
Top Right:
Not a function
The one input goes to three outputs.
Bottom Left:
Function
Each x-value/input is used only once.
Bottom Right:
Not a function
The x-value of 4 is used twice and paired with two different y-values.
How to multiply 4 x 0.27
Solve the following quadratic equation, giving your answer accurate to 2 decimal places:
3x^2-16x+6=0
The solutions to the equation are x = 2.61 and x = -0.61
To solve the quadratic equation 3x² - 16x + 6 = 0, we'll use the quadratic formula:
x = (-b ± √(b²-4ac)) / 2a
Where a = 3, b = -16 and c = 6.
x = (-(-16) ± √((-16)²-4(3)(6)))/2(3)
x = 16 ± √(256-72) / 6
x = 16 ± √(184) / 6
x = 16 ± √184 / 6
x = (16 ± 4√23) / 6
So the solutions are:
x = (16 + 4√23) / 6 ≈ 2. 61 or x = (16 - 4√23) / 6 ≈ -0.61
Therefore, the solutions to the equation are x = 2.61 and x = -0.61.
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Vanessa earned $76:00 in 8 hours how much did she earn per hour
Answer: $9.50 per hour
Hope this helps :)
Step-by-step explanation:
Find the rate of change
76/8 = 9.5
8.50 cents per hour because 8.50 x 9 is close to 76
When Lavaughn moved into a new house, he planted two trees in his backyard. At the
time of planting, Tree A was 30 inches tall and Tree B was 15 inches tall. Each year
thereafter, Tree A grew by 2 inches per year and Tree B grew by 5 inches per year. Let
A represent the height of Tree At years after being planted and let B represent the
height of Tree B t years after being planted. Write an equation for each situation, in
terms of t, and determine which tree is taller after 6 years.
PLSSS HELPPPP
The height of Tree A t years after being planted can be represented by the equation:
A = 30 + 2t
This equation states that the initial height of the tree (30 inches) plus the annual growth of the tree (2 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.
The height of Tree B t years after being planted can be represented by the equation:
B = 15 + 5t
This equation states that the initial height of the tree (15 inches) plus the annual growth of the tree (5 inches per year) multiplied by the number of years that have passed (t) will give the current height of the tree.
To determine which tree is taller after 6 years, we can substitute t = 6 into each equation and compare the results:
A = 30 + 2(6) = 30 + 12 = 42 inches
B = 15 + 5(6) = 15 + 30 = 45 inches
Tree B is taller than Tree A after 6 years because 45 inches is greater than 42 inches.
Find the component form of the sum of u and v with direction angles u and v.
Magnitude
u = 14
Angle
u = 45°
Magnitude
v = 70
Angle
v = 180°
The component form of the vector u and v are < -60.11, 9.89 >
What is the Vector QuantityTo find the component form of the sum of u and v, we first need to express each vector in terms of its components in the x and y directions. To do this, we use the trigonometric relationships between the magnitude and direction angle of a vector and its x and y components.
The x and y components of u can be found using the following formulas:
x_u = u * cos(u)
y_u = u * sin(u)
where u is the magnitude of u and u is the direction angle of u measured in radians.
So, x_u = 14 * cos(45°) = 9.89
and y_u = 14 * sin(45°) = 9.89
The x and y components of v can be found using the following formulas:
x_v = v * cos(v)
y_v = v * sin(v)
where v is the magnitude of v and v is the direction angle of v measured in radians.
So, x_v = 70 * cos(180°) = -70
and y_v = 70 * sin(180°) = 0
Now, we can find the x and y components of the vector sum by adding the corresponding components of u and v.
x_sum = x_u + x_v = 9.89 + (-70) = -60.11
y_sum = y_u + y_v = 9.89 + 0 = 9.89
Therefore, the component form of the sum of u and v is given by the vector < -60.11, 9.89 >
Note: the direction angle is measured in radians and the angle given in the question was in degrees, so it's important to convert the angle from degrees to radians before use it.
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Is tan inverse equal to tan?.
No, the tan inverse is not equal to tan
A right triangle's opposing side to its adjacent side is calculated using the trigonometric function known as the tangent function (tan). It is described as tan(x) = adjacent/opposite. The opposite of the tangent function is called the inverse tangent function (tan-1). The angle whose tangent has the specified value is revealed. The formula for it is tan-1(y) = x, where tan(x) = y. An angle between -90 and 90 degrees is what is returned.
In other words, tan-1 undoes the tangent function because it is the inverse of the tangent function. In other words, the input of the tangent function is the output of the inverse tangent function. In conclusion, tan-1 and tan are inverse functions; they are not equal.
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What is the slope and the y intercepts of 3x 2y 5?.
The slope and the y intercept of the equation 3x + 2y = 5 is -3/2 and 5/2 respectively.
The term equation of the straight line is y = mx + c here m refers the slope and c refers the value where the line cuts the y-axis that is y intercept.
Here we have given that the equation 3x + 2y = 5.
In order to find the slope and the y intercept we have to rewrite the given equation as follows,
Here we need to find the value of y so we have to move the other terms to the next side then we get,
=> 2y = 5 - 3x
Then it can be rewritten as,
=> y = (5 - 3x)/2
Therefore, the resulting equation is written as,
=> y = -3x/2 + 5/2
So, the slope of the equation is -3/2 and the y intercept is 5/2.
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Write the equation g(x) by translating the following function 4 units to the right. Show your work.
f(x) = x^2 - 3x - 10
The equation g(x) by translating the following function 4 units to the right would be g(x) = (x+4)² - 3(x+4) - 10.
What is a function?
A function is a mathematical relationship between a set of inputs and a set of outputs. More formally, a function is a rule that assigns to each input exactly one output. In mathematical notation, a function is typically represented by an equation of form f(x) = y, where x is the input and y is the output. The symbol f(x) is called the function notation, and x is called the independent variable, and y is called the dependent variable.
To translate a function 4 units to the right, we can add 4 to the input variable (x) inside the function. Therefore, the equation for g(x) would be:
g(x) = (x+4)^2 - 3(x+4) - 10
Hence, the equation g(x) by translating the following function 4 units to the right would be g(x) = (x+4)² - 3(x+4) - 10.
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Triangle ABC with angle ACB a right angle and CD perpendicular AB at D
We have proved that BC² ×AD = AC² ×BD using AAA congruence rule.
What is congruence rule?Triangles that are identical in size and shape are said to be congruent. This implies that the corresponding sides and angles are equal.
Without comparing each of the triangles' sides and angles, we can determine whether two triangles are congruent. The four rules that demonstrate triangle congruence will be discussed in this lesson. They are referred to as the SSS rule, SAS rule, ASA rule, and AAS rule.
We'll discuss the Hypotenuse Leg rule, a right triangle proof, in a later lesson. It is sufficient to demonstrate that the two triangles are congruent if only one of the rules is accurate.
Consider △ACD&△ABC
∠CAD=∠CAB
∠CDA=∠ACB
∴△ACD∼△ABC,{ By AA similarity criterion}
⟹ AC/AB = AD/AC
∴ AC ² =AB×AD
Similarly, △BCD∼△BAC { by AA similarity criterion}
⟹ BC/BA =BD/BC
∴BC² =BA×BD
∴ BC²/AC² = AB×BD/AB×AD
∴BC² ×AD = AC² ×BD
Thus, We have proved that BC² × AD = AC² × BD using AAA congruence rule.
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Complete question:
Triangle ABC is right angled at C and CD is perpendicular to AB. Prove that BC² ×AD = AC² ×BD
The sum of frequencies for all classes will always equal
a. 1
b. the number of items in a data set
c. the number of classes
d. a value between 0 and 1
The sum of frequencies for all classes will always equal to the number of element in a data set. Between 0-100 there will be 100 numbers.
So that it's 100 and correct option is b
What is frequencies ?
A frequency is a measurement of how frequently a certain value, occurrence, or feature takes place. It is employed in a wide range of disciplines, including science, engineering, mathematics, and statistics. Frequency is often expressed as a number, percentage, or ratio. For example, a frequency chart might show the number of times a particular product was purchased over a certain time period. Frequency can also refer to the number of times a particular wave pattern occurs in a given time period. In physics and engineering, frequency is used to measure the number of cycles per second of a wave or periodic phenomenon. For example, a wave with a frequency of 440 hertz (Hz) has 440 complete cycles per second.
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What does 0 [infinity] means?.
When we say "0" or "infinity," what we're really saying is that the number has no end.
The original value of zero corresponds to the logarithm, and the original value of infinity to the logarithm +. We consider the initial values 0 and infinity similarly when we treat both of the conceivable values and + as a single infinity. Georg Cantor, a mathematician, developed the concept of infinity into The Absolute Infinite. You can think of it as a number that is greater than any other possible or inconceivable amount, whether it be transfinite or finite. Infinity is the unfathomable end of the number line, according to mathematics. No actual number is bigger than infinity since it cannot be believed to exist beyond it.
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Is 64 a cube number?.
Yes, 64 a cube number.
64 is the cube of 4.
As, 4 x 4 x 4 = 64
The cubes are made up of values that are obtained by multiplying integers by themselves three or four times. The cube's original number can be found by raising any natural number to the power of three.
Cubes are the numbers that are produced when an integer is multiplied by itself three times. We can find cubes for any number, whether it be an integer or a fraction. In order for the cube of a whole number (x) to produce a perfect cube, the cube root of x3 must equal x. The procedure of locating cubes is thus the opposite of locating the cube root.
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The price of gold i often reported per ounce. At the end of 2005, thi price wa $513. At the end of 2015, it wa $1060. By what percentage did the price per ounce of gold increae?(Round to the nearet whole %)
An increase of 106.63 % in gold price is observed in that particular year.
What is percentage change?The original value multiplied by 100 is used to get the percentage change, which is the difference between the original and final values. It is expressed as a percentage and can be used to demonstrate an increase or decrease over time. A higher proportion indicates growth, whereas a lower percentage indicates a decline.
initial price of gold per ounce is $513
final price of gold per ounce is $1060
change in rate = final price of gold - inital price of gold
=> 1060 -513
=> 547
so the change in rate = $547
percentange change = (change in rate) / (inital rate of gold) *100
=> [tex]\frac{547}{513}[/tex] *100
=> 106.63 %
so the percentage change is 106.63%
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