Anything helps. Thank you for the help.

If f(x,y,z) = x²+y²+z² and W is the solid cylinder with height 5 and base radius 2 that is centered about z-axis with its base at z=-1 then the integral value is 432π.

They want f inside the integral so your integer and is: (x² + y² + z²) rdzdrdt

Note that you need another r because you are integrating in cylindrical

coordinates.

conversion equations:

x = rcost

y = rsint

x² + y² = r²

(x² + y² + z²)rdzdrdt becomes (r² + z²)rdzdrdt

W is the solid cylinder with height of 3, radius of 4, and centered about the z-axis, starting from z = -1.

Around the z-axis, cylinders take the forms of circles: x² + y² = r²

This cylinder will have the equation: x² + y² = 16

Its height is 3 so from z = -1 to z = 2

z bounds: -1 <= z <= 2

r bounds (based on the circle): 0 <= r <= 4

t bounds (based on the circle): 0 <= t <= 2pi

\(\int_{0}^{2\pi}\int_{0}^{4}\int_{-1}^{2}(r^{2}+z^{2})rdzdrdt\)

(r² + z²)r = r³ + rz²
dz integral gives: r^3*z + (1/3)rz^3 --> 2r^3 + (8/3)r - (-r^3 - (1/3)r)

= 2r^3 + (8/3)r + r^3 + (1/3)r

= 3r^3 + 3r

dr integral gives: (3/4)r^4 + (3/2)r^2 --> 216

dt integral gives: 216t --> 432pi

Hence we get the integral value as 432π

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Answer:

  55.5°

Step-by-step explanation:

You want the angle in a right triangle that has opposite side 16 and adjacent side 11.

The tangent relation is ...

  Tan = Opposite/Adjacent

In this geometry, that means ...

  tan(x) = 16/11

Taking the inverse tangent, we have ...

  x = arctan(16/11) ≈ 55.49° ≈ 55.5°

The angle x is about 55.5°.

Answer:

Step-by-step explanation:

x>y

-x<-y

98>59

-98<-59

59>1

-59<-1

any negative value <any positive value (including 0)

combining

-98<-59<-1<51

The value of the composite function is (f + g)(x) = -3x + 1

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x - 3x

g(x) = 1 - 2x

The composite function is given as

(f + g)(x)

Mathematically, this can be represented as

(f + g)(x) = f(x) + g(x)

Substitute the known values in the above equation, so, we have the following representation

(f + g)(x) = 2x- 3x + 1 - 2x

Evaluate the like terms

(f + g)(x) = -3x + 1

Hence, the composite function is (f + g)(x) = -3x + 1

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90% confidence interval for positive difference between means that there is a 90% probability that the confidence interval will contain the true population mean

The difference in sample means is used to calculate the difference in population means. A confidence interval reveals how accurate the estimate is.

We will make three assumptions in order to build a confidence interval:

1. The variance between the two populations is equal. The second assumption of homogeneity of variance is what this premise is known as.

3. The populations are evenly distributed.

4. Each value is sampled separately from every other value.

The following formula is used to construct a confidence range for the mean difference:

[tex]Lower Limit = M_1 - M_2 -(t_{CL})(S_{M1} - S{M2})\\Upper Limit = M_1 - M_2 +(t_{CL})(S_{M1} - S{M2})[/tex]

where [tex]S_{M1} - S{M2}[/tex] is the expected standard error of the difference between sample means, tCL is the desired level of confidence, and M1 - M2 is the difference between sample means.

The given question is incomplete So, I've answered in general according to my knowledge

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Condense the expression:

Used property:

Expand the expression:

Used property:

Answer:

[tex]\ln(3x)^{-4}[/tex]

[tex]\ln2 + \ln x[/tex]

Step-by-step explanation:

Given expression:

[tex]-4\ln(3x)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]

[tex]\implies \ln(3x)^{-4}[/tex]

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

Given expression:

[tex]\ln(2x)[/tex]

[tex]\textsf{Apply the product law}: \quad \ln xy=\ln x + \ln y[/tex]

[tex]\implies \ln2 + \ln x[/tex]

The average rate of change of the temperature from 6 to 10 pm is given as -1.5. Option C is correct

From 6 pm to 10 pm we have a total of 4 hours that is in between this period of time.

From the table the temperature at 6 pm is 34, the temperature at 10 pm is 28 degrees

Such that we would have:

[tex]\frac{28-34}{4}[/tex]

= -6 / 4

= - 1.5

Hence we would have that Negative 1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.

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Answer:

58 degrees

Step-by-step explanation:

a - 15 + a + 43 + 36 = 180

2a - 15 + 79 = 180

2a + 64 = 180

2a = 180 - 64

2a = 116

2/2 a = 116/2

a = 58 degrees

Answer:

  f(x) = x³ -9x² +28x -30

Step-by-step explanation:

You want a monic polynomial f of least degree with zeros 3 and 3-i.

For zero x=a, the polynomial has a factor (x -a). Complex zeros come in conjugate pairs, so another one is 3+i. This means the factored form is ...

  f(x) = (x -3)(x -3 +i)(x -3 -i)

  f(x) = (x -3)(x² -6x +9 +1) . . . . . combine the two right factors

  f(x) = x³ -9x² +28x -30

__

Additional comment

When multiplying polynomials mentally, it can be useful to consider the coefficients of the product terms in order of decreasing powers:

  f(x) = (1)x³ +(-3 -6)x² +(10 +(-3)(-6))x +(-3)(10)

The following statement is true is a) All the rhombuses are squares .

Given :

In contrast to a square, the lengths of all four sides of a rhombus are equal, the diagonals of a rhombus bisect each other, and all four angles of a rhombus are not equal to 90 degrees.

Parallelograms are not all squares. Parallelograms have equal length opposite sides, hence squares with all sides equal are parallelograms. Rhombuses are the only kites that fly.

Because a parallelogram contains two pairs of parallel sides, a trapezium is not a parallelogram. A trapezium, on the other hand, has only one pair of parallel sides.

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Answer:4^50

Step-by-step explanation:

Since 4 is twice as much as 2, you would divide 100/2 which would equal 50. Therefore, you get 4^50.

The correct options are

B.) GJ / MP = GH / MN

C.) ∠H≅∠N

By using the property of similarity of triangles, We get

The corresponding sides of the similar triangles are proportional to each other and the corresponding angles are congruent to each other.

So, given △GHJ∼△MNP  

⇒ GH/MN = HJ/NP = GJ/MP , and

∠G ≅ ∠M , ∠H ≅ ∠N , ∠J ≅ ∠P........(1)

The given options are :

A.) m∠J=m∠P

B.) GJ / MP = GH / MN

C.) ∠H≅∠N

D.) HJ ≅ NP

E.) GH=MN

Now, from equation (1)

The correct options are

B.) GJ / MP = GH / MN

C.) ∠H≅∠N

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(a) The component form of the velocity of the airplane is (-453.01 i + 79.88 j) mph.

(b) The actual ground speed and direction of the airplane is 392.76 mph and 30 degrees respectively.

The component form of the velocity of the airplane is calculated as follows;

Vy = V sinθ

Vx = V cosθ

where;

Vy = 460 mph x sin (170 - 90) = 79.88 mph

Vx = 460 mph x cos (170) = -453.01 mph

The bearing of the two speeds forms a triangle and the angle of the triangle is calculated as follows;

θ = θ₁ + θ₂

θ = (180⁰ - 170⁰) + (200⁰ - 180⁰)

θ = 30⁰

The resultant speed of the airplane is calculated as follows;

Vr² = V₁² + V₂² - 2(V₁)(V₂) cos(θ)

Vr² = (460²) + (80²) -  2(460 x 80) x cos(30)

Vr² = 154,260.53

Vr = √(154,260.53)

Vr = 392.76 mph

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The following are parallelograms' essential characteristics: The opposing sides are parallel. The opposing parties are in agreement (they have the same length).

The four most crucial characteristics of a parallelogram are: A parallelogram has two opposed sides that are parallel to one another and have equal measurements. A parallelogram has equal opposite angles. The interior angles of a parallelogram sum to 360°. A parallelogram's subsequent angles should be supplementary (180°).

A quadrilateral having opposite sides that are equal and parallel is called a parallelogram. A parallelogram's opposing angle is also equal. A parallelogram is essentially a twisted rectangle.

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Since the test statistic is not greater than the critical value, the null hypothesis cannot be rejected. Therefore, the claim that the mean score is 71 is not rejected.

1. We are given the population of statistics final exams and asked to test the claim that the mean score is 71 using an alternative hypothesis that the mean score is different from 71. We are also given the sample statistics including the sample size (n = 26), the sample mean (ã = 72), and the sample standard deviation (s = 18). We are asked to use a significance level of α = 0.05.

2. Since we are assuming that the population is normally distributed, we will use a two-tailed z-test to test the claim.

3. The null hypothesis is that the mean score is 71 and the alternative hypothesis is that the mean score is different from 71.

4. The test statistic is calculated as:

Test statistic = (sample mean - population mean) / (standard deviation/√n)

= (72 - 71) / (18/√26)

= 0.283

5. The critical values for a two-tailed z-test with a significance level of α = 0.05 are 1.645 for both the positive and negative critical values.

6. Since the test statistic (0.283) is not greater than the critical value

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Answer:

The Tree diagram here is given as:  {HRR,HRB,HRW,HRG,HBB,HBW,HBG,HWG,HGG,TRR,TRB,TRW,TRG,TBB,TBW,TBG,TWG ,TGG}

Sample space for the compound experiment is : {HRR,HRB,HRW,HRG,HBB,HBW,HBG,HWG,HGG,TRR,TRB,TRW,TRG,TBB,TBW,TBG,TWG ,TGG}

Probability of 2nd ball drawn is green = 8/18=4/9

Probability of a head is flipped on the penny = 9/18=1/2

Step-by-step explanation:

Part A tree diagram: Document attached below

Part B:

Sample space for the compound experiment is : {HRR,HRB,HRW,HRG,HBB,HBW,HBG,HWG,HGG,TRR,TRB,TRW,TRG,TBB,TBW,TBG,TWG ,TGG}

N(s)=18

Part c:

A=Choosing Head

P(A)=n(a)/n(s)

P(A)= 1/18

B= Choosing tail

P(B)=n(B)/n(s)

P(B)= 1/18

c=Choosing red balls

P(C)=n(C)/n(s)

P(C)= 3/18=1/6

D= Choosing blue balls

P(D)=n(D)/n(s)

P(D)= 4/18=2/9

E=Choosing white balls

P(E)=n(E)/n(s)

P(E)= 1/18

F = Choosing green balls

P(F)=n(F)/n(s)

P(F)= 2/18=1/9

Part D:

Probability of 2nd ball drawn is green = 8/18=4/9

Part E:

Probability of a head is flipped on the penny = 9/18=1/2

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The power series of the given function  is 1 + (2x) + (2x)² + (2x)³+ --------------------- + (2x)ⁿ

We know very well that sum of n terms who are in geometric progression their sum of expression is given by  a/1-r where a is first term and r is common ratio between the terms.

Now, we have function f(x)=[1 / (1-2x)]

On comparing with a/1-r with f(x),we get

=>a=1 and r=2x

Now, we know that first term of geometric progression is given by =1

second term of geometric progression is given by=a × r= 1 ×2x

third term of geometric progression is given by =a×r² =1×(2x)²

fourth term of geometric progression is given by=a×r³ =1 × (2x)³

nth term of geometric progression is given by =a×(r)ⁿ = 1 × (2x)ⁿ

Therefore, according to the given formula progression series of given function is=a+ ar +ar² + ar³ + -----------arⁿ

=>progression series = 1+ 2x + (2x)² + (2x)³ + --------- + (2x)ⁿ.

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The Area of the given sector is 14.1 yd²

Define Sector of a Circle

A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.

Given,

radius = 6 yd

Angle θ = 45°

The formula for,  Sector Area = (θ / 360°) * πr²

Now, plug in the values

Sector Area = (45 / 360) * 3.14 * 6²

                    = 14.1 yd²

Hence, the Area of the given sector is 14.1 yd²

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Answer: 4.5

Step-by-step explanation:

sector area = 4.5 on 14.143 yd ^2

Rotational symmetry about the origin is present in odd functions. By substituting x with -x and computing f, we can determine algebraically if a function is even, odd, or neither (-x). The function is odd if f(-x) = f(x).

If -f(x) = f(-x), then the function f is said to be odd for all values of x. When studying additive inverses, the functions even and odd are those that satisfy particular symmetry relations.

Evenness or oddness in a function does not imply continuity or differentiability. For instance, the Dirichlet function is even but in no way continuous.

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There are two points, 4 units from the origin and 2 units from the line x = -1.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given point is at a distance of 4 units from origin,

that is √x² + y² = 4

x² + y²= 16 is the equation of the locus of the point.

The given point is also 2 units from the line x =-1

that is √(x+1)² + y² = 2

(x+1)² + y²= 4 is the equation of the locus of the point.

Subtracting the second given equation from the first one,

we get x² - (x+1)² = 12

simplifying, x = 11/2

So the common coordinate point for these 2 points which is 11/2.

Substituting this value to the first equation,

(11/2)²+ y² = 16

Simplifying, y = ±(i√57)/2.

There are 2 points whose coordinates are;

( i√57/2 , 11/2 ) and ( -i√57/2 , 11/2 ).

Therefore there are two points, 4 units from the origin and 2 units from the line x = -1.

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The distance between the line segment from P to RQ is 2.83 units

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x₂ – x₁)² + (y₂ – y₁)²).  This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

In this case, we need to find the coordinate of P and RQ

From P to the line RQ, we will meet the midpoint of the line RQ which has a coordinate of (3, 3)

Let's use the formula of distance of a line segment and solve this

d = √((x₂ - x₁)² + (y₂ + y₁)²)

d = √(3 - 1)² + (3 - 1)²

d = √(2)² + (2)²

d = √8

d = 2√2

d = 2.83 units

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The complete diagram map is given as,
1 - 3
2 - 5,
3 - 7,
8 - 17,
10 - 21
100 - 201

Given that,
To complete the map diagram,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
The given map diagram follows the general term as nth term = 2n + 1
So for n = 3
= 2 [3] + 1
= 7
Similarly,

10th = 21
100th = 2001

For the value 17

17 = 2n + 1
n = 8
So the 8th term is 17 in the map diagram,

Thus, The complete diagram map has been shown.

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The amount premium on bond selling is $83.75. Option A is correct.

Given that,
Exxon sells its bonds at 108.375%. The amount of premium or discount the bond is selling for is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Face value of bonds         = $1000

The selling price of bond = 1000 × 108.375%

                                       =$1083.75

Premium on bonds = difference in the selling price - value of a bond

                              = 1083.75-1000

                              = $83.75.

Thus, the amount of the premium on bond selling is $83.75. Option A is correct.

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The sale price of the sweater is $2.7

From the question, we have the following parameters that can be used in our computation:

Markdown rate = 85% off

Original price of the sweater = $18

The retail price of the coat can be calculated using the following equation

Retail price = original price * (1 - Markdown rate)

Substitute the known values in the above equation, so, we have the following representation

Retail price = 18 * (1 - 85%)

Evaluate the products

Retail price = 2.7

Hence, the sales price is $2.7

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The factors of the function graphed in the given graph is option (C) (x-1)(x+5)

The function is the mathematical statement that shows the relationship between the dependent variable and independent variable

From the given graph

The given graph is a parabola and the equation of the graph will be a quadratic function

x intercepts of the lines are

x = -5 and x = 1

Then to find the factors of the function graphed

x = -5

x + 5 = 0

Similarly the second equation will become

x = 1

x-1 = 0

Then the factors function will be

(x+5)(x-1)

Therefore, the factors are option (C) (x-1)(x+5)

I have solved the question in general, as the given question is incomplete

The complete question is

Which of the following are the most likely factors of the function graphed above?

A. (x+1)(x-5)

B. (x)(x-5)

C. (x-1)(x+5)

D. (x)(x+5)

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The probability that the net weight is greater than 49.9 pounds is 0.44

What is probability?

Given f (x) = 2.0 for 49.62 < x < 50.12 pounds.

Our goal is:

a). We need to find the probability that a package weighs more than 50 pounds.

b). We need to find How much chemical is contained in 90% of all packages.

a). The probability of more than 49.9 pounds.

Given P(X>50).

P(X>49.9) = [tex]\int\limits^a_b {2} \, dx[/tex] (a=50.12, b= 49.9)

P(X>49.9) = [2x]₄₉.₉⁵⁰.¹²

P(X>49.9) = 2(50.12)-2(49.9)

P(X>49.9) = 100.24-99.8

P(X>49.9) = 0.44

Therefore, P(X>49.9) = 0.44

Hence, the probability that the net weight is greater than 49.9 pounds is 0.44

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The total time for the mass of the element to be 60 grams is 7.5 minutes

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ  for growth rate

x ( t ) = x₀ × ( 1 - r )ⁿ   for decay rate

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units = n

Given data ,

Let the total mass of element be = 520 grams

So , the value of x₀ = 520 grams

Now , the decay rate of element is given by r = 25.1 %

To calculate the time at which the amount of element left is 60 grams = n

where n is the total time = t

So , x ( t ) = 60

The decay rate formula is given by the equation ,

x ( t ) = x₀ × ( 1 - r )ⁿ

Substituting the values in the equation , we get

60 = 520 ( 1 - 25.1/100 )ⁿ

On simplifying the equation , we get

60 = 520 ( 1 - 0.251 )ⁿ

Divide by 520 on both sides of the equation , we get

( 0.749 )ⁿ = 6/52

Taking logarithm on both sides , we get

n × log ( 0.749 ) = log ( 6/52 )

Divide by log ( 0.749 ) on both sides , we get

n = log ( 6/52 ) / log ( 0.749 )

n = -0.9378 / -0.1255

n = 7.47 minutes

Therefore , the value of n time t = 7.5 minutes

Hence ,

The total time for the mass of the element to be 60 grams is 7.5 minutes

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Therefore the solution to the given problem is the roots of the given equation are -2,-4,+2

A mathematical statement that shows the equality of two mathematical expressions is the definition of an equation in algebra. As an illustration, the two equations 3x + 5 and 14 are joined by the equal sign to get the equation 3x + 5 = 14. Algebraic mathematical equations frequently have one or more variables.

Given:

[tex]x^{3} +2x^{2} -16x-32[/tex]

We are given a cubic polynomial.

Thus  find the roots of the polynomial. the roots can be find by solving the equation in terms of x

 => [tex]x^{3} +2x^{2} -16x-32[/tex]

[tex]x^{2}(x +2)-16(x+2)\\(x+2)(x^{2}-16)\\x+2=0\\x=-2\\x^{2}-16=0\\x^2=16\\x=+4,-4[/tex]

=so roots are -2,-4,+4

Therefore the solution to the given problem is the roots of the given equation are -2,-4,+2

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Answer:

-2,-4, 4

Step-by-step explanation:

Answer:

12d+12m+3a+6c

Step-by-step explanation:

distribute 3 by multiplying