Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8.
27y= x³, y=0, x=6

The cos, tan, sec, csc and cot of the angle θ in quadrant IV are 3/5, -4/3, 5/3, -5/4 and -3/4 respectively

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Given that: sin(θ) = -4/5 and θ is in quadrant 4.

Using this information, we can sketch the location of the angle θ in the quadrant (See the attached image). Therefore:

(a) cos(θ) = 3/5     (adj/hyp)

(b) tan(θ) = -4/3     (opp/adj)

(c) sec(θ) = 1/cos(θ) = 5/3

(d) csc(θ) = 1/sin(θ) = -5/4

(e) cot(θ) = 1/tan(θ) = -3/4

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Using the definition of isosceles and equilateral triangles:

12. x = 77°; y = 58°; z = 122°

13. x = 60°; y = 120°; z = 60°

All three sides and angles of an equilateral triangle are equal in measure. On the other hand, two sides and two base angles of an isosceles triangle are equal to each other.

12. x = 1/2(180 - 26) [based on the definition of isosceles triangle]

x = 1/2(154)

x = 77°

y = 1/2(180 - (90 - 26)) [based on the definition of isosceles triangle]

y = 1/2(180 - 64)

y = 1/2(116)

y = 58°

z = 180 - 58 [base angles of isosceles triangle are equal]

z = 122°

13. Each interior angle of an equilateral triangle is equal to 60 degrees.

Therefore, x = the measure of one interior angle

x = 60°

y = 180 - 60 [linear pair]

y = 120°

The base angles of the triangle that has two equal sides would be 60° [180 - 120]

Therefore:

z = 180 - 2(60)

z = 60°

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The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.

What is a transformation of a shape?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.

From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

If the geometry is rotated, then there is no change in angles.

The translation does not change the shape and size of the geometry. But changes the location.

The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.

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Disclaimer

The question given by you is incomplete, so a similar question have been solved here and the image is attached.

Determine a series of transformations that would map Figure M onto Figure N.

El polígono regular tiene las características de un pentágono, cuya medida de ángulo central es 72° y la suma de todos los ángulos centrales es igual a 360°.

En este problema debemos determinar que polígono regular tiene un ángulo central con medida de 72°, la suma de todos los ángulos centrales de un polígono es igual a 360°. El número de lados del polígono se puede determinar mediante la siguiente operación:

n = 360° / θ

Donde θ es la medida del ángulo central, en grados.

Si sabemos que θ = 72°, entonces el número de lados del polígono:

n = 360° / 72°

n = 5

El polígono regular es un pentágono.

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Answer:

22/27

Step-by-step explanation:

5 play nothing.

27 - 5 = 22

22 play basketball only or baseball only or both.

p(plays baseball or basketball) = 22/27

The functions representing exponential growth or decay are f(x) = 3²ˣ⁺¹, f(x) = 0.8ˣ⁻⁰, f(x) = π⁴ˣ, f(x) = (4/9)ˣ, f(x) = -(3)ˣ, f(x) = (-3)ˣ

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form f(x) = aˣ

Where a>0 and a is not equal to 1, and x is any real number.

If the variable is negative, the function is undefined for -1 < x < 1.

Here,

An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.

In the question, the functions that are exponential are

f(x) = 3²ˣ⁺¹, f(x) = 0.8ˣ⁻⁰, f(x) = π⁴ˣ, f(x) = (4/9)ˣ, f(x) = -(3)ˣ, f(x) = (-3)ˣ

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Answer:

7650 rupees

Step-by-step explanation:

Use I = Pnr

Here P = Principal = 20000 rupees

n = time = 4.5 years

r = rate of interest = 8.5% = 8.5/100

The exponential function f(x)=(1/8)^-x can be evaluated to give us:

An exponential function  serves as Mathematical function in the form f (x) = ax hving “x” as  variable,the conceptis the concept of  exponential function.

The given function is f(x)=(1/8)^-x

Then f(2)=(1/8)^-2 = 1/(1/8)^2 =1/(1/64) =64

f(-3)=(1/8)^-(-3) = 1/512

f(-3)=(1/8)^-(1/2) =[tex]\frac{1}{\sqrt{\frac{1}{8} } }[/tex]

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The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8) thus option (A),(B) and (D) are correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given equation,

3x - y = 1

Substitute, x = -2

3(-2) - y = 1

y = -7 thus  (-2,-7) satisfied.

Similarly (-1,-4) and (3,8) are also satisfied.

Hence "The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8)".

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The given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).

The given trigonometric expression is 1-tan(a).

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

We know that, tanθ=sinθ/cosθ

Now, 1-tan(a) =1-sin(a)/cos(a)

= (cos(a)-sin(a))/cos(a)

Therefore, the given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).

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Answer:

Number 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

You need a take a picture so I know what question your talking about

Answer:

A) [tex]\frac{484}{7}[/tex]cm

B)[tex]44[/tex]in

C)[tex]\frac{880}{7}[/tex]mi

D)[tex]\frac{660}{7}[/tex]yd

Step-by-step explanation:

The formula for the circumference of a circle is:

[tex]C=2\pi r[/tex]

Within the problem it is stated to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex] so our equation will be:

[tex]C=2\frac{22}{7}r[/tex] which simplifies to  [tex]C=\frac{44r}{7}[/tex]

The variable [tex]r[/tex] in the equation for the circumference represents 'radius' which is half the diameter, for circle's A and C we are given a diameter. We can divide these numbers in half to get a radius. From there we plug in each radius to get circumference of each circle!

A)

[tex]\text{Diameter}=22\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{22}{2}=11\\\text{Circumference}=\frac{44(11)}{7}=\frac{484}{7}[/tex]

B)

[tex]\text{Radius {\it (r)}}=7\\\text{Circumference}=\frac{44(7)}{7}=\frac{308}{7}=44[/tex]

C)

[tex]\text{Diameter}=40\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{40}{2}=20\\\text{Circumference}=\frac{44(20)}{7}=\frac{880}{7}[/tex]

D)

[tex]\text{Radius {\it (r)}}=15\\\text{Circumference}=\frac{44(15)}{7}=\frac{660}{7}[/tex]

Remember to include units of measurement in your answers.

Answer:

simplify 8/6, and you get 4/3.

This is a coincidence, because this is a Pythagorean triple,

which means: opp = 4, adj = 3, hyp = 5

now, we can solve the rest easily

sin(0) = 4/5

cos(0) = 3/5

sec = 5/3 (opposite of cos)

x + 2 = 10

x + 2 - 2 = 10 - 2

x = 8

x - 2 = 10

x - 2 + 2 = 10 + 2

x = 12

2x = 10

2x/2 = 10/2

x = 5

x/2 = 10

x/2 × 2 = 10 × 2

x = 20

⇒Find the sum of  12t+8 and [tex]t^{2} -10t+3[/tex]

⇒For sum we add:

[tex]=(12t+8)+(t^{2} -10t+3)\\=12t-10t+8+3+t^{2} \\=2t+11+t^{2}[/tex]

⇒The next step is to subtract [tex]9t^{3} -3t+8[/tex] and [tex]t^{2} -8t+4[/tex] from the answer we got above.

[tex]=(2t+11+t^{2} )-(9t^{3} -3t+8)-(t^{2} -8t+4)\\=2t+11+t^{2} -9t^{3} +3t-8-t^{2} +8t-4\\=2t+3t+8t+11-8-4+t^{2} -t^{2} -9t^{3} \\=13t-1-9t^{3} \\[/tex]

⇒The answer  is shown above.

not defined because 848 has no unit

Answer:

f(x)

Step-by-step explanation:

the function g(x) has y-interception in point (0;0), the function f(x) has y-interception in point (0; 1/3). For more details see the attachment.

Answer: 105 words

Step-by-step explanation:

15x7=105

The given term of the arithmetic sequence is -18. The correct option is (A).

An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.

This difference is known as the common difference of the sequence.

The given arithmetic sequence is as below,

27, 22, 17, 12, 7, 2,...

Since the nth term of an arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

Where d is the common difference.

The common difference for the given sequence is,

d = 22 - 27

  = -5

Substitute d = -5 and n = 10 in the general form of nth term to obtain,

a₁₀ = a₁ + (n - 1)d

     = 27 + -5(10 - 1)

     = 27 - 45

     = -18

Hence, the value of the 10th term of the given sequence is -18.

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The first angle in a triangle is three times that of a second angle. The second angle is two times that of the third angle. The ratio of the angles in the triangle is 1:2:3.

When two rays are joined at one point, they produce the geometric shape known as an angle. The vertex is the shared point between the two rays, which are known as the arms or sides of the angle. When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolised by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees.

Given,

A first angle of let x

2x = 2nd angle

3x = 3rd angle

Angle sum = 180

x + 2x + 3x = 180

6x = 180

Dividing,

x = 30°

2x = 2(30)

2nd angle = 60

3x = 3(30)

3rd angle = 90

30°, 60°, and 90° are the three angles.

Ratio 1:2:3

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Answer:

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

Given is a quadratic equation:

A quadratic equation has no real solutions if its discriminant is negative.

The discriminant of ax² + bx + c is:

Apply to given equation:

Find the value of n when D < 0:

Answer:

-33

Step-by-step explanation:

just fill in the values

3-6^2

3-36

-33

Hopes this helps please mark brainliest

Answer:

-33

Step-by-step explanation:

a = 3; b = -6

a - b² = 3 - (-6)² = 3 - 36 = -33

Answer:

You can write a statement of proportionality without any additional information:

... weight = k × length . . . . . . . . for some constant k

If you need to know the specific weight of a specific length, then you need to know the constant of proportionality (the value of k).

Step-by-step explanation:

If two cones are similar, then the height of the larger cone will be equal to 3 cm.

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the data provided in the question,

For volume, the scale factor is,

k³ = 27/8

For length, the scale factor is,

k = ∛27/8

k = 3/2

Then the height of the larger will be,

h = 3/2 × 2

h = 3 cm.

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The cosine and sine functions are presented as follows;

(a) cosine function is; f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5

(b) f(x) = -5·sin((4/3)·x - 530/3) + 2.5

A sine function is a periodic function used bases on the sine of an angle.

(a) The cosine function is f(x) = a·cos(b·x - c) + k

Where;

a = The amplitude

The amplitude = (Max - Min)/2

Therefore;

a = (7.5 - (-2.5))/2 = 5

f = b/(2·π)

c = The phase shift

k = The vertical shift

The minimum is at x = 200° = (200/360)·(2·π) = 10·π/9

The period = 270° = 3·π/2

Frequency, f = 2/(3·π)

b = 2·π·f = 2·π×2/(3·π) = 4/3

When the function is at the minimum point, θ = π

Therefore;

(4/3)×(10·π)/9 - c = π

c = 13·π/27

k = The minimum value + a

Therefore, k = -2.5 + 5 = 2.5

The cosine function is therefore;

f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5

(b) The negative sine function is found as follows;

f(x) = a·sin(b·x - c) + k

b = 4/3

k = 2.5

Minimum point sin((4/3)200 - c) = 180

((4/3)200 - c) = 180

c = 260/3

Using a negative sign function, we get;

((4/3)200 - c) = 90

c = 530/3

The equation is therefore;

f(x) = -5·sin((4/3)·x -530/3) + 2.5

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The student who can write more words per minute is Marcus because he writes at a speed of 1.3 words per second, that is, in one minute he writes 79.8 words while Rhys writes at a speed of 1.1 words per second and in one minute he writes 66.66 words.

To identify the speed at which students write we must divide the number of words the student writes in time (seconds) as shown below.

Marcus

Rhys

Using the information above, we need to multiply the number of words each student types per second by the number of seconds that equals one minute.

Rhys

Marcus

According to the information above, Marcus has a faster typing speed than Rhys because he types 79.8 words in one minute, while Rhys types 66.6 words in the same time.

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Answer:

55 Hot dogs were sold

Step-by-step explanation:

Let d = hot dogs

Let h = hamburgers

d + h = 175

d + 1.50h = 235

Re-write

d + h = 175 for d and then substitute this into the second equation

d = 175 - h

d + 1.5 h = 235

175 - h + 1.50h = 235  Combine like terms

175 + .5h = 235  Subtract 175 from both sides

.5 h = 60  Divide both sides by .5

h = 120

120 Hamburgers were sold.  

Plug in 120 for h to solve for hot does

d + h = 175

d + 120 = 175  Subtract 120 from both sides

d = 55

Check

d + 1.5h = 235

55 + 1.5(120) = 235

55 + 180 = 235

235=235

y = 6x  + 1 is the line of the equation which has a gradient of 6 and passes through the point (3, 19)

What is a gradient?

A straight line's steepness can be determined by looking at its gradient. A line's gradient does not have to be a whole integer and might be positive or negative. A line's gradient can either be uphill (positive value) or downward (negative value).

Here, we have

Equation of line

y = mx  + c

m = Slope of line = Gradient  = 6

= y = 6x + c

a line passes through (3, 19)

so, we find the value of c

= 19 = 6(3)  + c

= c = 1

Now, we put the value of c in the equation and we get

= y = 6x  + 1

Hence,y = 6x  + 1 is the line of the equation which has a gradient of 6 and passes through the point (3  19)

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Answer:

A.  56

Step-by-step explanation:

Let the three consecutive integers be:

Given:

Create an equation with the given information and solve for x:

[tex]\implies x+(x+1)+(x+2)=2x+30[/tex]

[tex]\implies 3x+3=2x+30[/tex]

[tex]\implies 3x+3-2x=2x+30-2x[/tex]

[tex]\implies x+3=30[/tex]

[tex]\implies x+3-3=30-3[/tex]

[tex]\implies x=27[/tex]

Therefore, the three consecutive integers are:

So the sum of the first and last integer is:

[tex]\implies 27+29=56[/tex]

Answer:

a) 56 --- (27, 28, 29)

Step-by-step explanation:

Forming the equation,

→ x + (x + 1) + (x + 2) = 2x + 30

Now the value of x will be,

→ x + (x + 1) + (x + 2) = 2x + 30

→ x + x + 1 + x + 2 = 2x + 30

→ 3x - 2x = 30 - 3

→ [ x = 27 ]

The last integer will be,

→ x + 2

→ 27 + 2 = 29

Sum of first and last integer is,

→ x + (x + 2)

→ 27 + (27 + 2)

→ 27 + 29 = 56

Hence, required answer is 56.