Evaluate the integral: f csc²x(cotx-1)³ dx Find the solution to the initial-value problem. y' = x²y-¹/2; y(1) = 1

Answer:

$425

Step-by-step explanation:

Let the dryer cost x

and the dish washer cost y

x+y=784-----------1

y=x-66-------------2

put the value of y=x-66 in 1

x+x-66=784

2x= 784+66

2x=850

x=850/2

x=425

Hence the dryer cost $425

Answer:

70 × g2

Step-by-step explanation:

Answer:

y=(x/2)+5

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept form. To get that, we need y by itself so we have to add 3x to both sides: 6y=30+3x. Now we divide by 6 and rearrange the right side: y=(3x+30)/6.

y = (3x/6)+(30/6) => y = (x/2)+5. We also know that the slope is 1/2 and the y-intercept is 5 because of the slope-intercept equation.

Answer:

y = 1/2x + 5

hope this helps :)

Answer:

Step-by-step explanation:

To solve this problem you have to complete the square. To do that, set the quadratic equal to 0, then move the constant over to the other side. That's 2 steps in one, but they're simple ones:

\(-5t^2+10t=-65\)

The first picky rule that completing the square has to follow is that the coefficient on the squared term has to be a 1. Ours is a -5, so we factor it out:

\(-5(t^2-2t)=-65\) . Now it gets even pickier. To create a perfect square binomial on the left, we take half the linear term, square it, and add it in to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is 1, so we add 1 into the set of parenthesis. BUT the -5 out front is a multiplier and refuses to be ignored. To offset the addition of the 1 inside the parenthesis, we have to multiply it by the -5 out front to get -5:

\(-5(t^2-2t+1)=-65-5\)

The perfect square binomial on the left side and simplifying the right:

\(-5(t-1)^2=-70\) . Now we'll move the 70 over and set the quadratic back equal to y:

\(-5(t-1)^2+70=y\)

That's the quadratic in vertex form. The vertex here is (1, 70) which serves to answer 2 questions for us: the max height of the ball along with the time it was at that max height. For us, the ball reached a max height of 70 m after 1 second in its travels.

You could also do it the "calculus way" which is to find the derivative of the position function, which is

-10t + 10 = 0 and solve for t:

-10t = -10 so

t = 1. That's the time that the ball is at its highest point, and to find the highest point, sub that value in for t in the position function:

\(h(t)=-5(1)+10(1)+65\) which comes to 70 m. I'm not sure what class you're taking so I did both! Calculus is way easier.

The fraction of the total price that the torch is is 4/5.

Let x be the cost of the battery.

We know that the torch cost is 1.50 more than the battery cost. So, the cost of the torch is

x + 1.50

The total cost is the sum of the cost of the battery and the torch, so:

x + (x + 1.50) = 2.50

2x + 1.50 = 2.50

Solving this equation we get,

x = 0.50

Therefore the cost of the battery is 0.50 and the cost of the torch is 2.00.

To find the fraction of the total price that the torch is, we divide the cost of the torch by the total cost:

= (2.00) / (2.50)

= 4/5

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Answer:

true

Step-by-step explanation:

Answer:

y=4/3x +7

Step-by-step explanation:

4x - 3y = -21

Move 4x to the other side

-3y = -21 -4x

Next divide the other side by -3

y= 7 +4/3x

Move numbers around

y = 4/3x + 7

The correct answer is option a). The variable "the mileage of a car" is not a categorical variable.

A categorical variable, also known as a nominal variable, is a variable that can be divided into categories or groups. These categories can be any non-numeric values such as names, labels, or yes/no answers.

The variables "a person's gender," "the make of a laptop," and "whether a person is a college graduate" are all examples of categorical variables because they can be divided into categories such as "male," "female," "Dell," "HP," "yes," and "no."

However, the variable "the mileage of a car" is not a categorical variable because it is a numeric variable that represents a specific numerical value, such as the number of miles a car has driven. Unlike categorical variables, numeric variables can be ordered, compared, and manipulated mathematically.

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If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.

Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.

Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.

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Answer:

Step-by-step explanation:

See image

Answer:

let width be x

area of rectangle =l*x

Step-by-step explanation:

52=8*x

52=8x

x=52\8

x=7

again

permeter=2(l+b)

=2(8+7)

=2*15

=30cm

Answer:

4) -14/5

Step-by-step explanation:

Answer:

When plotting points on the coordinate plane below, which point would lie on both the x-axis and the y-axis? the answer is its the origin  (0, 0)

Step-by-step explanation:

The variance is the correct option of property of Poisson distribution.

The Poisson distribution has the property that its mean is equal to its variance. This means that the average number of occurrences, represented by λ, is equal to the spread of the distribution.

The Poisson probability is calculated as P (x, λ) = (e^-λ * λ^x) / x! where e is approximately equal to 2.71828. The mean, represented as E(X), is equal to the variance, V(X). In a Poisson distribution, λ is the expected value of the distribution.

When certain conditions are met, there is a table available to make calculating probabilities easier using the Poisson distribution.

In Poisson distribution, the mean is known as E(X) = λ.

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Answer:  \(\boldsymbol{4\sqrt{11}}\\\\\)

Work Shown:

\(\sqrt{176}\\\\\sqrt{4*44}\\\\\sqrt{4}*\sqrt{44}\\\\2*\sqrt{4*11}\\\\2*\sqrt{4}*\sqrt{11}\\\\2*2*\sqrt{11}\\\\\boldsymbol{4\sqrt{11}}\\\\\)

The idea is to factor the number such that we pull out perfect square factors. We use the rule that \(\sqrt{x*y} = \sqrt{x}*\sqrt{y}\) to help break up the root. We also use the idea that \(\sqrt{x^2} = x\) when x is nonnegative.

Answer:

\(\frac{\sqrt[8]{2} }{\sqrt[2]{8} } = \frac{1}{\sqrt[8]{2^{11} } }\)

\(\sqrt{\frac{5}{7} } *\sqrt{\frac{2}{5} } =\sqrt{\frac{2}{7} }\)

Step-by-step explanation:

Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Raise both sides of the equation to the index of the radical.

If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.

Answer:

Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Raise both sides of the equation to the index of the radical.

If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.

Step-by-step explanation:

To complete the square for the equation x2 - 16x + 60 = -12, add 64 to each side of the equation. This will give us x2 - 16x + 124 = 52.

Then, factor out the coefficient of x2 (1) and the coefficient of x (16). This will give us (x - 8)2 = 52. Finally, subtract 52 from both sides to get (x - 8)2 = 0. Solving for x yields x = 8.

Equations are mathematical statements that express the equality of two expressions. They involve one or more unknowns that are represented by variables and involve numbers, constants, and operators. An equation states that the expressions on either side of the equal sign have the same value.

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The remainder of the polynomial using the remainder theorem and factor theorem is 6.

Apply the remainder theorem,

When we divide a polynomial

f(x) by (x − c)

f(x) = (x − c)q(x) + r

f(c) = 0 + r

Here,

f(x)=(x−c)q(x)+rf(c)=0+r

and (x−c) is (x−(−2))

Therefore,

f(−2) = \((-2)^{4} - (-2)^3 - 3(-2)^2 + 4(-2) + 2\)

= 16 + 8 − 12 − 8 + 2

= 6

Hence, the remainder of the polynomial using the remainder theorem is 6.

Whereas using the factor theorem and doing synthetic division, we get,  

x = -2 is a zero of f(x), and x+2 is a factor of f(x). To factor f(x), we divide

the coefficients of the polynomial as follows -

         -2   |   1  -1    -3     4      2

                      -2   6    -6      4

        -----------------------------------------

                    1   -3   3    -2     6

Hence, we get that 6 is the remainder when (\(x^4-x^3-3x^2+4x+2\)) ÷ (x+2), using the factor theorem.

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The complete question is -

Find the remainder using the Remainder Theorem and Factor Theorem using the synthetic division of the given polynomial, \(x^4-x^3-3x^2+4x+2\) ÷ (x+2)

Answer if you work 20 hours to get 10 $ your whole pay is 200- 10% is 180

Step-by-step explanation:

The value of Double integral will be \(\mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\)

A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.

The integrals of a function in two variables over a region in R2, or the real number plane, are referred to as double integrals in mathematics. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as: R f (x, y) d A = R f (x, y) d x d y.

We know that by the property of integral \($\int u \mathrm{udv}=u v-v \int d u$\)

\($$\begin{aligned}& \mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}=\left[\mathrm{x} \ln (1+\mathrm{x})-\int \mathrm{x} \frac{.1}{1+\mathrm{x}} \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4\left[\mathrm{x} \ln (1+\mathrm{x})-\int\left(1-\frac{1}{1+\mathrm{x}}\right) \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4[\mathrm{x} \ln (1+\mathrm{x})-\mathrm{x}+\ln |1+\mathrm{x}|]_0^4 \\& \mathrm{I}=[4 \ln (5)-4+\ln (5)]-[0-0+0] \\& \mathrm{I}=4[5 \ln 5-4] \\& \mathrm{I}=20 \ln 5-16\end{aligned}$$\)

We have to evaluate the given double integral

\($$\iint_{\mathrm{R}} \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dA} \text { where } \mathrm{R}=[0,4] \times[0,1]$$\)

\($$\begin{aligned}& \mathrm{I}=\int_0^4 \int_0^1 \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dydx}=\int_0^4 4 \mathrm{x}\left[\frac{|1+\mathrm{xy}|}{\mathrm{x}}\right]_0^1 \mathrm{dx} \\& \mathrm{I}=\int_0^{44}[\ln |1+\mathrm{x}|-0] \mathrm{dx}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\end{aligned}$$\)

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The meaning of the y - intercept in the context of the problem of the snow level in Moose Wyoming is the level of snow at the beginning of the time period in question.

The y-intercept of the function y = 2x + 14 is the value of y when x = 0. Substituting x = 0 into the equation, we get:

y = 2(0) + 14

y = 14

Therefore, the y-intercept is 14.

In terms of the problem, this means that at midnight (when x = 0), there is already 14 inches of snow on the ground in Moose, Wyoming. The y-intercept represents the initial or starting value of the snow level function, which in this case is the amount of snow already on the ground at the start of the time period being modeled.

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The total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d. To calculate the total amount to be paid, we need to consider the compounded interest on the borrowed amount.

The nominal interest rate of 12% compounded quarterly means that interest is added to the principal four times a year. Using the formula for compound interest, we can calculate the future value of the loan. The formula is given as:

Future Value = Principal * (1 + (Nominal Interest Rate / Number of Compounding Periods))^Number of Compounding Periods * Number of Years

In this case, the principal is $7,500, the nominal interest rate is 12% (or 0.12), the number of compounding periods per year is 4 (quarterly), and the number of years is 10.

Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + (0.12 / 4))^(4 * 10) = $24,465

Therefore, the total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d.

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There are two types of classifications for triangles, Classification according to internal angles and Classification according to the length of its sides.

A geometrical shape with three vertices, angles and sides, whose sum of internal angles is 180° is considered as a triangle.

Classification of triangles :-

There are two ways to classify triangles,

1) Based on the Angle :-

a) Acute Angled Triangle :- A triangle that has all three angles less than 90° is an acute angle triangle.

b) Right-Angled Triangle :- A triangle that has one angle that measures exactly 90° is a right-angle triangle.

c) Oblique Angled Triangle :- A triangle that has one angle that measures more than 90° is an obtuse angle triangle.

2) Based on the Sides :-

a) Scalene Angled Triangle :- A triangle that has all three sides of different lengths is a scalene triangle.

b) Isosceles Angled Triangle :- A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle.

c) Equilateral Angled triangle :- A triangle that has all three sides of the same length is an equilateral triangle.

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The probability that their first child will have kidney disease is 1/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

Both parents must be heterozygous to have a 1/4 chance of having an

affected child. Parent 2 is heterozygous (her father was homozygous recessive, but she has unaffected).

For the child to have the disease, both Parent 1 and Parent 2 would need to be heterozygous

There is a 50% chance of this for Parent 1 and a 100% chance of this for Parent 2 and then, there is a 25% chance that their first child will be affected:

50%× 100% × 25% = 12.5%

1/2 × 1/4 = 1/8

Hence, the probability that their first child will have kidney disease is 1/8.

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Answer:

C

Step-by-step explanation:

We'll have to use trigonometry for this.

First, note that in right triangle ABC, if we look from the perspective of angle A, the opposite side is x, the adjacent side is y, and the hypotenuse is 18.

In order to find x, then, we must use sine, which is opposite/hypotenuse. So:

sin(A) = sin(60) = opposite/hypotenuse = x/18

sin(60) is equal to (√3)/2, so multiplying both sides by 18 gives:

[(√3)/2] * 18 = 9√3

Already, we can tell that the answer is likely C, but let's find y to make sure.

We will use cosine to find y because cos = adjacent/hypotenuse.

cos(A) = cos(60) = adjacent/hypotenuse = y/18

cos(60) = 0.5, so multiplying both sides by 18 gives:

0.5 * 18 = 9

So, y = 9.

Thus, C is our answer.

~ an aesthetics lover

Answer:

C

Step-by-step explanation:

Using the cosine/ sine ratio in the right triangle and the exact values

cos30° = \(\frac{\sqrt{3} }{2}\) and sin30° = \(\frac{1}{2}\) , then

cos30° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{x}{18}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2x = 18\(\sqrt{3}\) ( divide both sides by 2 )

x = 9\(\sqrt{3}\)

----------------------------------------------------------

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{y}{18}\) = \(\frac{1}{2}\) ( cross- multiply )

2y = 18 ( divide both sides by 2 )

y = 9

Thus

x = 9\(\sqrt{3}\) and y = 9 → C

Answer:

9+11i

Step-by-step explanation:

Answer:

B. 65 degrees

Step-by-step explanation:

The sum of angles in a triangle = 180 degrees

Given angles = 80 and 35

Sum of given angles = 115

Thus, the third angle = 180 - 115 = 65 degrees.

Hope this helps

Answer:

b

Step-by-step explanation:

As per the question, the answer is ∠CAB is congruent to ∠BAD.

An isosceles triangle named BDC is positioned within a circle. The segments of the circle they pass through are congruent because the faces of the triangles BC and BD are congruent, or identical.

Due to the triangle's faces BC and BD being identical and congruent

BC=BD

Additionally, the segments of the circle it goes across are congruent.

In the case of ΔBAC & ΔBAD

AC=AD= the radius of the circle

AB=BA

Thus, BAC is consistent with BAD according to SSS guidelines.

As a result, the central angles of the sections are also congruent; hence, BAD and CAB are congruent.

As a result, ∠BAD is equivalent to ∠BAC OR ∠CAB.

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Answer:

B on edge

Step-by-step explanation:

CAD