What is the expanded form for 45 squared?

In mathematics, a differential equation is an equation involving one or more functions and their derivatives. The derivative of a function defines the rate of change of the function at some point.

According to the given Question:

Differential equation:

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.  In applications, a function generally represents a physical quantity, a derivative its rate of change, and a differential equation defines the relationship between the two. Such relationships are common. Therefore, differential equations play an important role in many fields such as engineering, physics, economics and biology.

The study of differential equations consists primarily of studying their solutions (the set of functions that satisfy each equation) and the properties of those solutions. Only the simplest differential equations can be solved with explicit formulas. However, many properties of solutions to particular differential equations can be determined without exact computation. In many cases, when a closed formula for the solution is not available, the solution can be approximated numerically using a computer. Although the theory of dynamical systems focuses on qualitative analysis of systems described by differential equations, many numerical methods have been developed to determine solutions with some degree of accuracy.

A first-order linear differential equation is an equation that can be written in the form y0 + p(x)y = q(x). where p and q are continuous functions on the interval I. The second-order linear differential equation has a similar form.

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The constant of proportionality, given that this is a proportional relationship, is 11. 7

To find the constant of proportionality, the following formula is used :

= Y value / Corresponding x value

The constant of proportionality can only be found for proportional relationships.

In this instance, we have x and y of ( 7, 81. 9 ).

The constant of proportionality is:

= 81 .9 / 7

= 11. 7

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On solving the provided question, we can say that we have two triangle, in which only one angle is same and all other angles and sides are not equal, so they are not similar.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

we have two triangle,

in which only one angle is same and all other angles and sides are not equal, so they are not similar.

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Answer: ok what is it

Step-by-step explanation:

The antithesis of an exponential function is a logarithmic function. A logarithmic function and an exponential function both use the same base.

Writing y = log2 x or f(x) = log2 x represents the logarithmic function for the equation x = 2y. Even today, the base is still 2. Y equals log base b of x, or more simply, "y equals log to the base b of x," is how y = logb x is typically read. Similarly to exponential functions, b > 0 and b 1.

Consequently, the table's data is represented by the logarithmic function f(x) = log3(x).

Table provided:

                    x           f(x)

                    25          2

                   125          3

                   625         4

We can write x in this case as powers of 5, so that

[tex]$25=5^2$$125=5^3$$625=5^4$$\Rightarrow f(x)=5^{f(x)}$[/tex]

After dividing the log in half, we now have

[tex]$\log x=\log 5^{f(x)}$$\Rightarrow \log x=f(x) \log 5 \ldots .\left[\log (a)^m=m \log (a)\right]$[/tex]

[tex]$\Rightarrow f(x)=\frac{\log x}{\log 5}$$\Rightarrow f(x)=\log _5 x \ldots \ldots\left[\log _a b=\frac{\log b}{\log a}\right]$[/tex]

A base-log function [tex]$f(x)=\log _5 x$[/tex], then, reflects the data in the table.

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Answer:

51,328

Step-by-step explanation:

5 11 12+2 1 6=51328

Answer:

21 cm

Step-by-step explanation:

An equilateral triangle has all 3 sides equal.

So the perimeter of the equilateral triangle

= 3 x side

= 3 x 7

= 21 cm

Hence,

The perimeter of the equilateral triangle is 21 cm.

Answer:

a. Write an inequality that demonstrates this situation

Let x be the number of $5 t-shirts Tyrone can buy

The inequality that demonstrates this situation is:

x*5 + 22 <= 95 - 15

b. solve your inequality

x5 + 22 <= 80

x5 <= 58

x <= 11.6

x <= 11

c. Explain what your answer means to Tyrone

Tyrone has $95 to spend, he already bought pants for $22, so he has $95-22 = $73 left to spend. He wants to have at least $15 left over after buying t-shirts, so he can buy up to $73-15 = $58 worth of t-shirts. Each t-shirt costs $5, so he can buy a maximum of 11 t-shirts (58/5=11.6) with no remainder. So Tyrone can buy 11 t-shirts and he will have $73-11*5 = $18 left. This means that Tyrone can buy 11 t-shirts and still have $18 left over.

Step-by-step explanation:

Answer:

2.5 Tons to lb

1 ton = 2,000 lb

2.5 tons x 2000 lb = 5,000 lb

The domain of the graphed function in this problem is given as follows:

2 <= x <= 5.

The domain of a function is the set composed by all the input values that the function accepts.

On the graph, the domain of the function is given by the values of x.

For this problem, the values of x are a closed interval between x = 2 and x = 5, hence the domain of the function is defined by the interval presented as follows:

2 <= x <= 5.

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The final solution after reducing the given number radical is; 9√2

The radical of a number is defined in the same way we define the root of a number. The root can be a square root, fourth root or even cube root, up to the nth root.

Now, we are given the number radical as; √162

Now, 162 can be broken down into its' factors as √(81 * 2)

We know from properties of surds that;

√(a * b) = √a * √b

Thus, we now have;

√162 = √81 * √2

This can be simplified further to get;

9√2

Thus, that is the final solution to the number radical simplification.

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Answer:

10 and 16

Step-by-step explanation:

let on number be x then the other number is x + 6

sum the 2 numbers and equate to 26

x + x + 6 = 26

2x + 6 = 26 ( subtract 6 from both sides )

2x = 20 ( divide both sides by 2 )

x = 10

x + 6 = 10 + 6 = 16

the 2 numbers are 10 and 16

A two-dimensional (2D) coordinate system is a system used to define the position of points in a two-dimensional plane.

A 2D coordinate system can also be used to represent other kinds of data, such as temperature, elevation, or pressure. In this case, the two coordinates are usually called the x-axis and y-axis, and they are both used to measure the same physical quantity.

It is most commonly used in mathematics and engineering to plot graphical data such as graphs, charts, and diagrams. In a 2D coordinate system, each point is represented by two numbers, called coordinates, which indicate the position of the point in relation to a fixed reference point, called the origin. These coordinates usually describe the horizontal (x) and vertical (y) distances between the point and the origin. The set of all points in the 2D coordinate system is called the coordinate plane.

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The value of the equation A = LW is A = 750

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The value of L = 50

The value of W = 15

A = LW   be equation (1)

Substituting the values of L and W in the equation , we get

A = 50 x 15

On simplifying the equation , we get

A = 750

Therefore , the value of A is 750

Hence , the equation is A = 750

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The inequality  6 > x + 1 > 3  is 'And' type Inequality.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

An 'Or' inequality is also referred to as a disjunction.

In other words, there is no connection on the number line between the range of values that meet either component of the inequality. Finding a truthful statement that satisfies either one of the inequality conditions or both inequality conditions is the aim whenever 'Or' compound inequalities are solved.

For example, x > 7 OR x < 3

Another name for a compound inequality with a 'And' is a conjunction. Compound inequality of this kind is stated as a long inequality, such as

3 > x > 9. Similar to 3>x and x > 9, this is.

The solutions to this and other compound inequalities fall within a range of potential values between 3 and 9. The range of values used to solve "And" inequalities must meet both requirements. These inequalities display a range of overlapping values.

So, the inequality is 'And' type of Inequality.

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By solving the given inequality in question, i.e -8+2x>4 , the solution obtained is x>6, which means the inequality satisfies for all the values of x that are greater than 6.

An inequality is a statement that compares two values and asserts that one value is greater than, less than, or not equal to the other value. Inequalities are used to describe a range of values that a variable can take on. The most common symbols used to express inequalities are ">", "<", "≥" and "≤", which represent "greater than", "less than", "greater than or equal to" and "less than or equal to" respectively.

An example for inequality can be , the inequality x > 2 , which states that x is greater than 2, which means that any value of x that is greater than 2 satisfies the inequality.

Inequality can be solved either graphically or algebraically. The solution of an inequality is the set of all values that make the inequality true.

To solve the inequality -8 + 2x > 4, you can follow these steps:

So the solution of the inequality is x > 6.

This means that x is greater than 6. So any value of x that is greater than 6 satisfies the inequality.

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Therefore , the solution of polynomials problem is Grouping technique using the greatest common factor (GCF) and others given below.

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

There are several methods for factoring polynomials, but the most common methods are:

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The power and the r m s value for each of the following signals are a)p=50w and  r m s =7.07 b)p=178w,  r m s =√178 c)p=51w, r m s =√51
d)p=25w, r m s =√25 e)p=25w, r m s  =√25  and f)p=1/2, r m s =√1/2.

(a) 5+10cos(100t+π/3)
=A cos(w0t+θ)
power of the signal
P=10^ 2/2=100/2=50w
p=50w
r m s value of the signal
=√50
=7.07

b) 10cos(100t+π/3)+16sin(150t+π/5)
power of the signal.
p=10^ 2/2+16^ 2/2
p=178w
r m s value of the signal=√178

c) (10+2sin(3t)cos10t
=10cos10t+2sin3tcos210t
=2sin3tcos10t
=1/2(sin(3+10)+sin(3-10))
(sin a cos b=1/2(sin(a + b)+sin(a-b))
=2x1/2(sin13t-sin7t)
=sin13t-sin7t
=10cos10t+sin13t-sin7t
power of the signal is
p=10^ 2/2+1^ 2/2+1^ 2/2
p=51w
r m s value of the signal=√51

d) 10 cos(5t)cos(10t)
=10(cos(5+10)T+ cos (5-10)t/2
(cos a cos b=1/2(cos a+ cos b)+cos(a-b))
=10(cos(15)t+ cos (-5)t/2
=5cos15t-5cost
power value of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the signal=√25

e) 10 sin(5t)cos(10t)
=10(sin(5+10)t+ sin(5-10)t/2
=10/2(sin15t-sin5t)
=5sin15t-5sin5t
power of the signal
p=5^ 2/2+5^ 2/2
p=25w
r m s value of the =√25      

F) f) e^(jαt) cos(w0t)
=e jαt cos wot
=(cosαt+ cos wot+jsin2tcoswot
=(cos(α+wo)t+ cos(α-wo)t/2+j(sin(2+wo)t+ sin cos-wot/2
=1/2cos(α+wo)T+1/2cos(α-wo)T
power of the signal
p=(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2+(1/2)^ 2/2
p=1/2
r m s value=√1/2

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[tex]\pi[/tex]

Jee's trip from New York to Boston would take approximately time 4.5 hours.

To calculate the time it would take Jee to travel from New York to Boston, we need to divide the total distance (approximately 280 miles) by the average speed (42 mph). This gives us a total time of 6.67 hours. We then need to subtract the time it took Jee to travel from Boston to New York (6 hours) to get the total time for the return trip. 6.67 hours - 6 hours = 4.5 hours. Therefore, Jee's trip from New York to Boston takes approximately time 4.5 hours. Jee's trip from New York to Boston would take approximately 4.5 hours.

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Answer:

It is a function

Step-by-step explanation:

The vertical line test proves that it’s is a function because there is no place on the graph where a vertical line would pass through two points.

Answer:

  (c)  3x√(6x) -x⁴√(30x) +24x²√2 -8x⁵√10

Step-by-step explanation:

You want to simplify the product ...

  [tex](\sqrt{6x^2}+4\sqrt{8x^3})(\sqrt{9x}-x\sqrt{5x^5})[/tex]

As with a lot of problems of this type, the correct answer choice can be selected by examining a term or two.

Multiplying the last two terms of the binomials, we get ...

  [tex]4\sqrt{8x^3}\cdot (-x\sqrt{5x^5})=-4x\sqrt{40x^8}=-4x\sqrt{10(2x^4)^2}=\boxed{-8x^5\sqrt{10}}[/tex]

This term is only found in choice C.

__

Additional comment

The expression is simplified by making use of the radical relations ...

  (√a)(√b) = √(ab)

  √(a²b) = a√b

The given expression can be rewritten with squares taken out of the radicals as ...

  (x√6 +8x√(2x))·(3√x -x³√(5x))

Then, using FOIL or the distributive property, we have ...

  = 3x√(6x) +24x²√2 -x⁴√(30x) -8x⁵√10 . . . . . matches C

Answer: the total spent on the meal is $88.25875.

Step-by-step explanation:

The total spent on the meal can be calculated by adding the cost of the meal, the tax, and the tip.

First, we need to calculate the cost of the tax: 72.5 x 0.0675 = 4.88375

Then we need to calculate the cost of the tip: 72.5 x 0.15 = 10.875

Finally, we add the cost of the meal (72.5), the tax (4.88375) and the tip (10.875) to find the total cost of the meal: 72.5 + 4.88375 + 10.875 = 88.25875

Therefore, the total spent on the meal is $88.25875.

Answer:47.8125kg

Step-by-step explanation:

x: previous weight

x = 45+45x6.25% = 47.8125

When you multiply 4 with any number, you can use the doubling-up trick (that's the one you used for the two times table) twice. Here is an example: 2 x 4 is the same as 2 + 2 = 4 and then 4 + 4 = 8. So, 2 x 4 = 8.

Here is next double, double example are: 5 x 4 is the same as 5 + 5 = 10, so then 10 + 10 = 20. So, the answer is 5 x 4 = 20.

Here, is the table of four.

4×1=4

4×2=8

4×3=12

4×4=16

4×5=20

4×6=24

4×7=28

4×8=32

4×9=36

4×10=40

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The product of two complex numbers, with a result of 821, is given as follows:

(26 + 12.04i)(26 - 12.04i) = 821.

Complex numbers are numbers that are composed by a real part and by an imaginary part, and have the notation given as follows:

z = a + bi.

In which:

The most important complex numbers relation is given as follows:

i² = -1.

Meaning that the easiest way to obtain the desired product is multiplying complex-conjugate numbers, as follows:

(a + bi)(a - bi).

Applying the subtraction of perfect squares, we have that:

(a + bi)(a - bi) = a² - (bi)²

(a + bi)(a - bi) = a² - b²i²

(a + bi)(a - bi) = a² + b² (as i² = -1).

Then, attributing a = 26, the value of b is obtained as follows:

a² + b² = 821

26² + b² = 821

[tex]b = \sqrt{821 - 26^2}[/tex]

b = 12.04.

Meaning that the product is given as follows:

(26 + 12.04i)(26 - 12.04i) = 821.

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Answer: 1,176 miles

Step-by-step explanation:

490 / 5 = 98 miles

98 mph X 12 hours is 1,176

Answer:f = 57 g = 33

Step-by-step explanation:

Add f and g together and make them equal 90 and then solve for x and plug x back in to both angles 57 and 33

Answer:

m<F + m<G + m<H=180°[Sum of angles of traingle is Supplementary]

or,90°+(4x +13)°+(2x +11)°=180°

or,6x + 24°=180°-90°

or,6x=90°-24°

or,X=66°/6

:.X=11°

Now,

m<F=(4x+13)°=(4×11+13)°=57°

m<G=(2x+11)=(2×11+11)°=33°

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