Using the basic identities, find the value of cosΘ if cotΘ = -12/5.

Answer:

9 and 27

Step-by-step explanation:

let me know if you want an explanation

The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].

From the principle of indices we get,

Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]

Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]

Multiplication, [tex]a^{mn}=(a^m)^n[/tex]

negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]

Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

Calculating we get,

[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]

[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae

[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]

[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices

[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula

Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].

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Answer:

b

Step-by-step explanation:

edge 23

Answer:

[tex]3^x=5[/tex]

Step-by-step explanation:

Given:

[tex]9^x=25[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^x=25[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2x}=25[/tex]

Apply the same exponent rule:

[tex]\implies (3^x)^2=25[/tex]

Square root both sides:

[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]

[tex]\implies 3^x=5[/tex]

A function assigns the values. The input value that produces the same output value for the two functions is 1.

A function assigns the value of each element of one set to the other specific element of another set.

For the given tables the x is the input while f(x) and g(x) are the outputs of the respective functions. Therefore, the input for which the two given functions will return the same output is 1.

Hence, the input value that produces the same output value for the two functions is 1.

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Answer:

(fog)(a)​ = a³ - 3a² + 4a - 2

           = (a - 1)×(a² - 2a + 2)

Step-by-step explanation:

Given :

g(a) = a -1 

f(a)= a³ +a

…………………………

(fog)(a)​ = f(g(a)​))

           = g(a)³ + g(a)

           = (a - 1)³ + (a - 1)

           = (a³ - 3a² + 3a - 1) + (a - 1)

           = a³ - 3a² + 3a - 1 + a - 1

           = a³ - 3a² + 3a + a - 1 - 1

           = a³ - 3a² + 4a - 2

Second method :

(fog)(a)​ = f(g(a)​))

           = f(a - 1)

           = (a - 1)³ + (a - 1)

           = (a - 1)×[(a - 1)² + 1]

           = (a - 1)×[a² - 2a + 1 + 1]

           = (a - 1)×(a² - 2a + 2)

Firstly, let’s assume the the whole capacity the work requires is 1.

Then, let’s see how 1 man can do in 50 days: 1/5.

Further, let’s see how 1 man can do in 1 day : 1/(5×50) = 1/250.

Similarly, let’s see how 1 woman can do in 1 day: 1/(10×50) = 1/500.

Now, we have 8 men, and they can do 8*1/250 in 1 day, which is 4/125.

Besides, we have 4 women, and they can do 4×1/500 in 1 day, which is 1/125.

Therefore, all people we have can do 4/125 + 1/125 of the work in 1 day, which is 1/25.

As a result, the work takes 1/(1/25)= 25 days.

Answer:

18, 36, 54

Step-by-step explanation:

Find the least common multiple of 6 and 9:

Multiples of 6: 6, 12, 18, ......

Multiples of 9: 9, 18, 27, ......

We see that 18 is the least common multiple of 6 and 9.

Additional multiples of 18 are 36 and 54.

If an integer is divisible by 6 and by 9 , then the integer must be divisible by 54.

Consider the statement as a contradiction.

The assertion exists that any natural number divisible by 6 and 9 exists also divisible by 54.

Let us consider divisible to mean that the outcome of the division of the number and 54 provides another natural number. We can take the prime factors of 6 and 9 which are {2,3} and {3,3}. We can consider that the product [tex]$2 \times 3 \times 3=18$[/tex] exists a number that exists divisible by 6 and 9 but exists not divisible by 54. Another instance exists the product of [tex]$2 \times 2 \times 3 \times 3=36$[/tex] which exists also not divisible by 54.

Therefore, the correct answer is option e) 54.

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Answer: 62.8 cubic feet

Step-by-step explanation:

R is radius

H is height

R=2ft

H=5ft

V=(3.14)(2)^2(5)

V=62.8 cubic feet

Answer:

m=3

b=(0,5)

Step-by-step explanation:

If Five hundred ten of 650 high school students said that pizza was their favorite food. The margin of error is 0.0322.

Given:

Sample proportion=Five hundred ten=510

Sample size=650

Hence:

Margin of error=z×√p×(1-p)/n

Margin of error=2√510/650× (1-510/650)÷650

Margin of error=2√0.78461538×(1-0.78461538)÷650

Margin of error=2√0.78461538×0.21538462÷650

Margin of error=2√0.168994085÷650

Margin of error=2√0.0002599909

Margin of error=0.0322

Therefore the correct option is D.

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Answer:

This point is not on the line, NOT TRUE

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

           b represents the y-intercept

where the format of a point is (x, y)

Given: y = x - 1/2, (-5, -2)

we can plug in the point (-5, -2)

-2 = (-5) - 1/2

-2 = -5.5

-2 does not equal -5.5 so this point is not on the line

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Answer:

1/2

Step-by-step explanation:

since every time you divide by 2, the common ratio is 1/2

Step-by-step explanation:

im sorry but im not sure about this question

Answer:

334.488 miles

Step-by-step explanation:

You don't have a specific request on what I should answer, if it was distance then here's your answer

Answer:

Step-by-step explanation:

If two ratios make a proportion then it can be shown as:

Let's verify the answer choices with this method

A. 1/4 and 5/25

B. 1/4 and 7/24

C. 1/4 and 10/48

D. 1/4 and 9/36

If the given differential equation is

[tex]\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1[/tex]

then multiply both sides by [tex]\frac1{\cos^2(x)}[/tex] :

[tex]\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)[/tex]

The left side is the derivative of a product,

[tex]\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)[/tex]

Integrate both sides with respect to [tex]x[/tex], recalling that [tex]\frac{d}{dx}\tan(x) = \sec^2(x)[/tex] :

[tex]\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx[/tex]

[tex]\sin(x) y = \tan(x) + C[/tex]

Solve for [tex]y[/tex] :

[tex]\boxed{y = \sec(x) + C \csc(x)}

which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}[/tex].

After calculating the value, l & w could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].

The inquiry relates to the laws of indices

where, [tex]x^{a} * x^{b}=x^{a+b}[/tex]

Provided the query, A= [tex]24x^{6}y^{15}[/tex]

[tex]2* 12[/tex] might be used to calculate the length and width of 24.

Hence,

[tex]x^{6}=x^{5} * x^{1} =x^{5+1}[/tex]

& [tex]y^{15}= y^{8} * y^{7} =y^{8+7}[/tex]

So, it can be written as,

A=l * w

⇒ [tex]24x^{6}y^{15}[/tex] = [tex]2x^{5}y^{8}[/tex] * [tex]12xy^{7}[/tex]

Therefore, it is concluded that the dimensions of the rectangle could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].

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The cross-section parallel to the base of a cone is a circle

The cross-section parallel to the base of a cylinder is a circle

The cross-section perpendicular to the base of a cone is a triangle

The cross-section perpendicular to the base of a cylinder is a rectangle

Answer:

shown below

Step-by-step explanation:

a) V = h(pi)r²

let x = height

and c = the constant radius

V1 = 2x(pi)c²

V2 = x(pi)c²

let c = random number, such as 2

let x = 3

2x(pi)4

x(pi)4

pi(4) = 12.57

3 x 12.57 = 37.7

6 x 12.57 = 75.4

We can compare these ans realise that the cylinder with double the height will also have double the volume.

b) SA = h(pi)2c

SA1 = 2x(pi)2c

SA2 = x(pi)2c

let c = 2

let x = 3

2(3)(pi)(2(2))

6(pi)4

24(pi)

3(pi)(2)(2)

3(pi)(4)

12(pi)

I don't need to finish the calulation to see that this is also halved. So the surface area of the one with the double length is twice the surface area of the one with a smaller height.

Comparatively, both the volume and surface area are doubled when the height is doubled.

QED.

The answer to the question is 5 units up.

Answer:

the answer is 4 units im pretty sure

Step-by-step explanation:

The height of the prism is 6 units.

The correct option is C.

A prism is a polyhedron in three dimensions with two identical ends.

To find the height of the prism, we need to use the formula for the volume of a prism, which is:

Volume = Base area x Height

Since the prism has two congruent hexagonal bases, we can find the base area by adding the areas of the two congruent isosceles trapezoids.

The area of an isosceles trapezoid is given by the formula:

Area = ((b1 + b2) / 2) x h

where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.

In this case, the two parallel bases have lengths of 5 and 8, and the height of each trapezoid is 3, so the area of one trapezoid is:

Area = ((5 + 8) / 2) x 3 = 19.5 square units

The base area of the prism is then:

Base area = 2 x 19.5 = 39 square units

We are given that the volume of the prism is 234 cubic units, so we can use the formula for the volume of a prism to find the height:

Volume = Base area x Height

234 = 39 x Height

Height = 6 units

Therefore, the height of the prism is 6 units.

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The solution to the equation is x = 7 , -2 , Option C and D is the right answer.

An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.

It is given that the equation is

[tex]\rm 3 +\sqrt{3x - 5}= x[/tex]

Taking square on both sides

3x-5 = (x-3)²

3x-5 = x² +9 -6x

x² -9x -14 = 0

x² -7x +2x -14 = 0

x(x-7) +2(x-7) = 0

(x-7)(x+2) = 0

x =7 , x = -2

Therefore the solution to the equation is x = 7 , -2 , Option C and D is the right answer.

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Answer:

450 N

Step-by-step explanation:

Since you have the VOLUME and the HEIGHT of the prism, you can calculate the AREA of the prism base :

 18 m^3 / 3 m =   6 m^2    area

Now you are given  pressure = force / area

                                      75 n/m^2 =  force / 6 m^2

        6 *75 = force = 450 N

Answer:

450 newtons

Step-by-step explanation:

To solve for the force, we first need to find the area. (Force = Pressure × Area)

[tex]Area = \frac{volume}{height} = \frac{18m^{3} }{3m} = 6m^{2}[/tex]

Now we just substitute this number into [tex]Force = Pressure * Area[/tex] and get that [tex]Force = 75newtons/m^{2} * 6m^{2} = 450 newtons[/tex]

(p.s. Units are very important! This question doesn't require any unit

conversions, but others might.)

The range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given that:-

The range for the given domain: {-2, -1, and 0} and the function is y = 3x².

The range will be the value of y at each given value of the domain.

Domain: { -2, -1, 0 }

y  =  3x²

At x = -2  →  y = 3 ( -2)² = 12

At x = -1   →  y = 3 (-1)²   = 3

At x = 0   →  y = 3 (0)    = 0

Therefore range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.

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Answer:

1.3 or 1.333333

Step-by-step explanation:

Just do it!

Answer:

it depends on whether the outlier is a high outlier or a low outlier

Step-by-step explanation:

The mean of a data set is the average of the data set. So if I had the data set {5, 2, 10} the average would be (5+2+10)/3 = 5.667. Now if I added an outlier like 10,000 it would increase the mean significantly. It changes it significantly but I cannot say whether it increases or decreases it without knowing the value of the outlier, since if I had the outlier -10,000 that would decrease the mean, but I had the outlier 10,000 it would increase it. So it depends on whether the outlier is a high outlier or a low outlier

Using limits, the end behavior of the functions are given as follows:

a. Rises to the left and falls to the right.

b. Rises to the left and rises to the right.

c. Falls to the left and rises to the right.

The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.

In item a, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -5x^3 = -5(-\infty)^3 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -5x^3 = -5(\infty)^3 = -\infty[/tex]

Hence it rises to the left and falls to the right.

In item b, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 3x^6 = 3(-\infty)^6 = \infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 3x^6 = 3(\infty)^6 = \infty[/tex]

Rises to the left and rises to the right.

In item c, we have that, respectively, to the left and to the right.

[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 20x^3 = 20(-\infty)^3 = -\infty[/tex]

[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 20x^3 = 20(\infty)^3 = \infty[/tex]

Falls to the left and rises to the right.

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[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]

Answer:

7

Step-by-step explanation:

14-a=19-12

14-a=7

14-7=a

7=a

Combine like terms