If bc=3y-15 and be=4y-26, find the value of y in rectangle CDEF

The provided statement indicates that the differential equation's solution will be y = c₁ + c₂ e⁻ˣ - 1/2 cos x

Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variable x and y are related because y is an unidentified function of x. The component of y is also on the equation's left-hand side.

The analytical solution is, given that.

⇒ y'' + y = sin x

Now,

The system of equations as follows:

The difference between these two is,

⇒ y'' + y = sin x

Find its auxiliary equation as;

⇒ m² + m = 0

⇒ m (m + 1) = 0

⇒ m = 0 or m = - 1

Therefore, the auxiliary equation is c1 e0 + c2 ex.

                                     = c₁ + c₂ e⁻ˣ

And, Particular integral = 1/(D² + D) (sin x)

                                  = 1/2D (sin x)

                                  = 1/2 (- cos x)

                                  = - 1/2 cos x

Consequently, the differential equation's solution will be;

⇒ y = A.E + P.I

⇒ y = c1 + c2 e x - cos x / 2

As a result, the differential equation's solution is;

⇒ y = c1 + c2 e x - cos x / 2

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The complete question is-

Solve the differential equation by variation of parameters.

y'' + y = sin x

in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf

A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.

The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
Thus, in this case, correct option is:b

in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf

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Answer:

Step-by-step explanation:

The algebraic expression representing the total cost of the rental after d additional days is 75 + 10d.

An algebraic expression is a combination of constants, numbers, values, and variables.

Algebraic expressions are not the same as equations because they lack the equation symbol and do not lay claim to the equality of mathematical expressions.

The rental cost on the first day = $75

The rental cost per additional day = $10

The number of additional days Clyde uses the tuxedo = d

Algebraic expression to represent the situation:

75 + 10d

Thus, an algebraic expression we can use to represent the total cost that Clyde incurred for renting the tuxedo after d additional days is 75 + 10d.

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Answer:

3 cm

Step-by-step explanation:

The formula of a cylinder is given by:

[tex]\pi r^{2} h[/tex]

where r is the radius and h is the height of the cylinder.

Given information from the question:

Volume of cylinder = [tex]90cm^{3}[/tex]

Radius of cylinder = 3cm

We can derive an equation to find the height:

[tex]90=\pi 3^{2} h\\9\pi h=90\\h = \frac{90}{9\pi } \\h = 3.18cm[/tex]

Given the height is 3.18cm, we will choose the closest answer which is 3 cm.

The number of dimes are 2 and number of nickels are 8 according to the sum and number of coins.

Let the number of dimes be x. The number of nickels will be 4x. Also, as per the known fact, the value of dimes is 0.1 and value of nickels is 0.05. Keeping the values in formula -

0.05x + 0.1×4x = 0.90

0.05x + 0.4x = 0.90

Performing addition on Left Hand Side of the equation

0.45x = 0.9

Rewriting the equation

x = 0.9/0.45

Performing division on Right Hand Side of the equation

x = 2

Number of dimes = 2

Number of nickels = 4×2

Performing multiplication

Number of nickels = 8

Thus, there 2 dimes and 8 nickles.

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Yes, you can assume both statements. In the diagram, planes W and X intersect at the line KL.

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Class limits indicate the largest and smallest data values that can be included in the class. Class limits are referred to actual data values. On the other hand, class boundaries give values that remove gaps between the classes in the frequency distribution. Class boundaries are considered to be one decimal place more accurate in comparison to the data. Options A, B, D, and F correctly describe differences between a class boundary and a class limit.

Following are the potential differences between a class boundary and a class limit.

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Answer:

Step-by-step explanation:

the answer is 44

The percentage change in the Touchdown passes is 28 %

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.

Andy Dalton's throw is 18 touchdaown

In last saeson he threw 25 touchdown

So, the percentage change = (25-18)/25 * 100 = 28 %

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Answer:

k - 2n = x

Step-by-step explanation:

4^n = 2 ^ 2n

2^k/2^2n = 2^(k-2n) = 2^x

k - 2n = x

Thanks

Answer:

x = k - 2n

Step-by-step explanation:

The main exponent properties

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex]         ........ (1)

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] ........ (2)

[tex](a^{m} )^{n}[/tex] = [tex]a^{m*n}[/tex] = [tex]a^{mn}[/tex]   ........ (3)

~~~~~~~~~~~~~~~~~~

[tex]\frac{2^{k} }{4^{n} }[/tex] = [tex]2^{x}[/tex]

Let apply (3) and (2) exponent properties

L.H. = [tex]\frac{2^{k} }{(2^2 )^{n} }[/tex] = [tex]\frac{2^{k} }{2^{2n} }[/tex] = [tex]2^{k-2n}[/tex]

[tex]2^{k-2n}[/tex] = [tex]2^{x}[/tex]  ⇒  x = k - 2n

Rounded answers In Your calculations to find missing measures is given below.

Given: a = 8.72, b = 11.1, c = 11.7

Using the Law of Cosines, we can calculate angle A:

A = arccos((b2 + c2 - a2)/2bc)
A = arccos((11.12 + 11.72 - 8.722)/(2*11.1*11.7))
A = arccos(2.61/265.57)
A = arccos(0.00984)
A = 89.8°

Using the Law of Sines, we can calculate angle B:


Using the Law of Cosines, we can calculate side c:

c2 = a2 + b2 - 2abcos(C)
c2 = 8.722 + 11.12

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Step-by-step explanation:

(9-12)×5+13-2

=(-3)×5+13-2, (frist bracket )

=-15+13-2

=-4

Answer:

(9-12)x5+13-2= -4

Step-by-step explanation:

1. Solve the equation in parenthesis. 9-12 is -3. If you use a number line and add 9, then subtract twelve, you'll be three behind zero!

2. Then multiply -3 by five which is -15. -15+13 is -2, (since the thirteen is positive, it cancels out thirteen negative ones, and leaves us with two negative ones)

3. -2 -2=-4 (Negative two, subtracted by positive two, is negative four) subtracting a positive number, is the same as adding its opposite. Example. 8-5=3 (as we all know). And 8+-5=3. Numbers that have the same absolute value are opposites. AKA Numbers that are the same distance away from zero. -5 and 5 are both 5 spaces from zero!

The function c(x)  models the number of cookies sold each day by a bakery during a 10-day period between (c) days 02 and 03 did the number of cookies sold by the bakery increase.

Cox Proportional hazards Model:

Sir David Cox observed that if the proportional hazards assumption holds (or, is assumed to hold) then it is possible to estimate the effect parameter (s), denoted β₁  below, without any consideration of the full hazard function. This approach to survival data is called application of the Cox proportional hazards model, sometimes abbreviated to Cox model or to proportional hazards model. However, Cox also noted that biological interpretation of the proportional hazards assumption can be quite tricky.

Let Xi = ([tex]X_i1[/tex] , … , [tex]X_in[/tex]) be the realized values of the covariates for subject i. The hazard function for the Cox proportional hazards model has the form:

λ (t I [tex]X_i[/tex]) = λ₀(t) exp( β₁[tex]X_i1[/tex] +...... + βₙ[tex]X_in[/tex])

             = λ₀ (t) exp( [tex]X_i . \beta[/tex])

This expression gives the hazard function at time t for subject i with covariate vector (explanatory variables) Xi. Note : that between subjects, the baseline hazard is identical (has no dependency on i). The only difference between subjects' hazards comes from the baseline scaling factor exp [tex](X_i . \beta)[/tex].

⁡

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Answer:

$1.44

Step-by-step explanation:

9kg costs $12.96

1kg costs ($12.96*1kg)÷9kg

=$1.44

Answer:

Step-by-step explanation:

ask if you don't understand my answer

Answer:

Shaded area = 42.1 cm^2

Shaded perimeter = 44 cm

Step-by-step explanation:

See the attached worksheet.  The approach is the subtract the 4 semicircle areas from the total quare area to obtain the area of the shaded region.  The perimeter is calculated by the perimeter of one complete circle.  Since all four semicircles are 1/4 of the full circle, the total perimeter is equivalent to one full circle.

This is an example of a triangle with two missing sides.

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Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Big boxes have 1/4 of 20 gigabytes of ram.

Then the multiplication of the numbers 1/4 and 20 will be given by putting a cross sign between them. Then we have

⇒ (1/4) x 20

⇒ 20 / 4

⇒ 5 gigabytes

Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

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Answer: Keep it in the calculation

Step-by-step explanation:

The ratio that represents the sine of angle C is 65/97

From the given information, we are to determine the ratio that represents the sine of angle C

From SOH CAH TOA, we know that

sin(angle) = Opposite / Hypotenuse

Given triangle CDE with C as reference angle,

DE = Opposite

CD = Hypotenuse

Then,

We can write that

sin(C) = DE/CD

From the given information

DE = 65

CD = 97

Thus,

sin(C) = 65/97

Hence, the ratio is 65/97

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The statement 2 is true i.e. He  is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be root multiplicities or complex.

Understanding the fundamental theorem of algebra, the number of roots of a polynomial equation must be equal to the degree of the equation. While been given any polynomial in factored form, we must expand the parentheses to find the highest-degree term.

For the equation  provided, simplified form could be x⁵ + 2x² = 0, and as looking at this polynomial and graphing it, it is evident that the total roots or solutions is equal to the highest exponent of the term x which is 5. Hence, Josh makes an incorrect statement.

The multiplicity of a root is the number of occurrences of the said root in the entire complete factorization of the polynomial, as by the means of the fundamental theorem of algebra. The root multiplicities are thus the repeated roots as involved in the full factorization process of a single equation of a polynomial.

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The correct question is:

Josh graphs a system of equations to determine the roots of the polynomial equation x⁵ = -2x²  . From the graph, he determines that there are two solutions to the equation. Which statement is true?

On solving the provided question we cans ay that the upper bound for the integral is 1/(n+1).

In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.

The maximum value of the integrand on the interval [0, 1] is:

f(x) = 5x(1 + x)^(0.5)

At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.

Therefore, an upper bound for the integral is:

In ≤ 5√2∫x^n dx

Using integration by parts, we obtain:

In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1

= 5√2/ (n + 1)

Therefore, the upper bound for the integral is 1/(n+1).

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Answer: C. [tex]2.8[/tex]

Step-by-step explanation:

Using the distance formula, [tex]\sqrt{(-1-1)^2 +(-1-1)^2} \approx 2.8[/tex].

Therefore ,2.113 is the deemed appropriate of the greatest square that could be inscribed with in area between the square and the triangle.

A triangle is considered a polygon since it has four vertices or segments. It is a basic geometric form. Triangle ABC refers to a triangle the with ends A, B, and C. In Euclidean geometry, a singular plane plus square are produced when the sides are not collinear. A triangle is a polygon if it has three parts and three corners. The points where the three sides of the triangle meet are known as its corners. Three triangle angles add up to 180 degrees.

Here,

The midpoint of foot FE, G, is where we start by measuring the side length of the equilateral triangle.

Given that DE=GB and G is the midpoint, let GE equal x.

As a result, DGGB=x3 using fundamental trigonometry.

DB=2x3 follows.

We may then construct the equation 2x3=102 because DB is the orthogonal of ABCD and has length 102. Thus, the triangle's side length is

2x=(10√2)/√3.

Now, observe the diagonal AC. It is composed of the triangle's side length and the little square's diagonal multiplied by two. Let the little square's side length be y:

Let the little square's side length be y:

AC=y√2 + [(10√2)/√3]+y√2=10√2.

How to find y?

=>y√2+y√2 + (10√2√3)/3=10√2

=>y√2+y√2 + (10√6)/3=10√2

=> [3y√2+3y√2 + (10√6)] /3=10√2

=>6y√2+10√6=30√2

=>6y√2 = 30√2-10√6

=>y√2 = (30√2-10√6)/6

=>y = (30√2-10√6)/6√2

=>y = (60-20√3)/12

=>y= 5(3−√3)3  or 2.113

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The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.

The p(z ≥ 2.11) is 0.0177.

To calculate the p(z ≥ 2.11), you can use a z-table to look up the z-score. This z-score falls in the area of the tail of the distribution, which means it is the area to the right of 2.11.

The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.

The p(z ≥ 2.11) is 0.0177.

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Answer:

Step-by-step explanation:

[tex] \: \: \: \: \: \: \: \: \: \huge \color{green}{ \fbox \colorbox{black}{ \fbox{ \green {Answer} \: }}}[/tex]

[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + 2 \cos(x) + 1} = 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + \cos(x) + \cos(x) + 1} = 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ \cos {}^{} (x) ( \cos(x) + 1)+ 1(\cos(x) + 1} )= 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ ( \cos(x) + 1)(\cos(x) + 1} )= 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{2} = 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{} = 0[/tex]

[tex] \longrightarrow \sf \color{teal}{ \cos(x) {}^{} }= - 1[/tex]

[tex]\longrightarrow \sf \color{teal}{ x{}^{} }= \cos {}^{ - 1}( - 1)[/tex]

[tex]\longrightarrow \sf \color{teal}{ x = (2n + 1) \pi \: \: \: \: rad}[/tex]

where, [tex]{ n \in \{whole \:\; number\}} [/tex]

Principle value -

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \cos {}^{ - 1} ( - 1) [/tex]

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2n + 1) \pi \: \: \: \: rad \: [/tex]

put n = 0

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2(0) + 1) \pi \: \: \: \: rad \: [/tex]

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (0 + 1) \pi \: \: \: \: rad \: [/tex]

[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \pi \: \: \: \: rad \: = 180 \degree[/tex]

The correct value of r is 2.

What is the power inverse variation?

Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.

The equation for a power inverse variation is y = kx^r,

where k is a constant, x is the independent variable, y is the dependent variable, and r is the power.

We have given the set of ordered pairs,

we can find the value of r by substituting in the known values of x and y and solving for r.

(1/2,20) => 20 = 5 * (1/2)^r => r = log(20)/log(1/2) = -2

So the answer is:

r = 2

Hence, the correct value of r is 2.

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A 1-factor graph is a graph that can be decomposed into one or more 1-factors. In other words, a 1-factor graph is a graph that can be partitioned into disjoint perfect matchings.

In graph theory, a 1-factor is a subgraph of a graph that forms a perfect matching, or 1-factorization. A perfect matching is a set of edges in a graph such that each vertex is incident to exactly one edge in the set. A 1-factorization of a graph is a collection of perfect matchings such that every vertex is included in exactly one perfect matching.

The study of 1-factors and 1-factorizations is an important area of graph theory because of its connections to other areas of mathematics such as algebra, combinatorics, and statistical physics. It has various applications including coding theory, scheduling, and transportation networks.

1-factor graph theory is the study of graphs that can be decomposed into 1-factors and the properties of such graphs. This field of study helps to understand the conditions under which a graph can be decomposed into 1-factors and the properties of such graphs.

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The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.

What is the empirical rule?

If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.

It is given that the heights of a large population of ostriches are normally distributed. The percentage of these heights is within 3 standard deviations of the mean.

As we know from the empirical rule:

It is the rule of 68-95-99.7.

From the data given in the question: The height of a large population of ostriches is normally distributed.

X ~ (u, б²)

Normal distribution.

P{u - 3б < X < u + 3б}

From the distribution table:

P{u - 3б < X < u + 3б} = 99.7%

Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.

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