How do you find the amplitude, period, and shift for f(x)=−4cos(3x−π)+1?

Answer:

1) [tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } \approx 1.665[/tex]

2) [tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}[/tex]

3) [tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } \approx 1.317[/tex]

Step-by-step explanation:

1) [tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} }[/tex]

This integral can be solved easily by using algebraic substitutions:

[tex]u = \ln x[/tex], [tex]du = \frac{dx}{x}[/tex]

Then, the integral can rewritten as follows:

[tex]\int {\frac{dx}{2\cdot x\cdot \sqrt{\ln x}} } = \frac{1}{2}\int {\frac{du}{u^{1/2}} } = \frac{1}{2}\int {u^{-1/2}} \, du[/tex]

[tex]\int {u^{-1/2}} \, du = 2\cdot u^{1/2} + C = 2\cdot \sqrt{\ln x} + C[/tex]

Where [tex]C[/tex] is the integration constant.

[tex]\int\limits^{16}_{2} {\frac{dx}{2\cdot x \cdot \sqrt{\ln x}} } = F(16) - F(2)[/tex]

[tex]F(16) - F(2) = 2\cdot (\sqrt{\ln 16}-\sqrt{\ln 2})[/tex]

[tex]F(16) - F(2) \approx 1.665[/tex]

2) Let be [tex]y = \cosh^{-1} (2\cdot \sqrt{x+1})[/tex], then we obtain the expression by the definition of the derivative for the inverse hyperbolic cosine and the chain rule:

[tex]\frac{dy}{dx} = \pm\frac{1}{\sqrt{4\cdot x + 3}}\cdot \left(\frac{1}{\sqrt{x+1}} \right)[/tex]

[tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{(4\cdot x + 3)\cdot (x+1)}}[/tex]

[tex]\frac{dy}{dx} = \pm \frac{1}{\sqrt{4\cdot x^{2}+7\cdot x +3}}[/tex]

3) [tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} }[/tex]

This integral can be solved by the following trigonometric substitutions:

[tex]\frac{2}{\sqrt{4 + x^{2}}} = \cos \theta[/tex]

[tex]\frac{1}{\sqrt{4+x^{2}}} = \frac{\cos \theta}{2}[/tex]

[tex]\frac{x}{2} = \tan \theta[/tex]

[tex]x = 2\cdot \tan \theta[/tex]

[tex]dx = 2\cdot \sec^{2}\theta \,d \theta[/tex]

[tex]\int {\frac{dx}{\sqrt{4+x^{2}}} } = \int {\left(\frac{\cos \theta}{2} \right)\cdot (2\cdot \sec^{2}\theta)} \, d\theta = \int {\sec \theta} \, d\theta[/tex]

[tex]\int {\sec \theta}\,d\theta = \ln |\sec \theta + \tan \theta| + C[/tex]

[tex]\ln \left|\frac{\sqrt{4+x^{2}}}{2} + \frac{x}{2} \right| + C[/tex]

Where [tex]C[/tex] is the integration constant.

[tex]\int\limits^{2\sqrt{3}}_{0} {\frac{dx}{\sqrt{4 + x^{2}}} } = F(2\sqrt{3}) - F(0)[/tex]

[tex]F(2\sqrt{3}) - F(0) = \ln \left|2+\sqrt{3}\right|-\ln \left|1\right|[/tex]

[tex]F(2\sqrt{3}) - F(0) \approx 1.317[/tex]

Answer:

7=x

Step-by-step explanation:

6(x-3)=8(x-4)

Distribute

6x -18 = 8x-32

Subtract 6x from each side

6x-18 -6x = 8x-32-8x

-18 = 2x-32

Add 32 to each side

-18+32 = 2x-32+32

14 = 2x

Divide by 2

14/2 =2x/2

7=x

[tex]\sf\purple{x= 7}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

[tex]➺\:6(x - 3) = 8(x - 4)[/tex]

[tex]➺ \: 6x - 18 = 8x - 32[/tex]

[tex]➺ \: 6x - 8x = - 32 + 18[/tex]

[tex]➺ \: - 2x = - 14[/tex]

[tex]➺ \: x = \frac{ - 14}{ - 2} [/tex]

[tex]➺ \: x = 7[/tex]

Therefore, the value of [tex]x[/tex] is 7.

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]

[tex]➺ \: 6(x - 3) = 8(x - 4)[/tex]

[tex]➺ \: 6(7 - 3) = 8(7 - 4)[/tex]

[tex]➺ \: 6 \times 4 = 8 \times 3[/tex]

[tex]➺ \: 24 = 24[/tex]

➺ L. H. S. = R. H. S.

Hence verified.

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]

Answer:

B. x</=-3

Step-by-step explanation:

the arrow is pointed to the left which means less than and the end is shaded which means or equal to

Answer:

Answer is in bold form

Step-by-step explanation:

Given

radius = 3feet

Height = 6feet

Volume of the cylinder = πr²h

Volume of the cylinder = 3.14 * 3² * 6

Volume of the cylinder = 169.56ft³

volume of the cone = Volume of cylinder/3

volume of the cone = 169.56/3

volume of the cone = 56.52ft³

Volume of the sphere = 4/3πr³

Volume of the sphere = 4/3*3.14*(3)³

Volume of the sphere = 4 * 3.14* 9

Volume of the sphere = 113.04ft³

Answer:

f(-3) = -12

g(-2) = -19

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 3x - 3

g(x) = 3x³ + 5

f(-3) is x = -3 for function f(x)

g(-2) is x = -2 for function g(x)

Step 2: Evaluate

f(-3)

g(-2)

Answer:

f(-3) = -12

g(-2) = -19

Step-by-step explanation:

1.

f(x) = 3x - 3

One is asked to find (f(-3)), substitute (-3) into the given function (f) in place of (-3), and solve to evaluate,

f(-3) = 3(-3) - 3

Simplify,

= -9 - 3

= -12

2.

g(x) = [tex]3x^3+5[/tex]

The problem asks one to find (g(-2)), subtitute (-2) into the function in place of (x) and solve to find tis value,

g(-2) = [tex]3(-2)^3+5\\[/tex]

Remember any number raised to an exponent is equal to the base (the number that is being raised to the exponent) times itself the number of times that the exponent indicates,

[tex]=3(-8)+5\\=-24+5\\=-19[/tex]

Answer:

add all the numbers

which will get you 24

then divide by how many numbers you got which will give you 6

the answer is six

Step-by-step explanation:

Hope this helps :D

Answer:

The mean is equal to 4.

Step-by-step explanation:

To find the mean of any set of numbers, you have to add all of those numbers and divide the result by however many numbers their are.

For example, the mean of 2,5,6, and 7 would be the following: 2+5+6+7/4

The mean of 5,3,6,8,1, and 1 is the following: 5+3+6+8+1+1/6=24/6=4

The mean is equal to 4.

Answer:

C D E

Step-by-step explanation:

They are the options that are clear enough

Answer:

The Answer for your question is B

Answer:

78%

Step-by-step explanation:

They are asking for spotted animals and dogs so

Spotted animals=40%

Dogs=38%

So just add them to get 78%

(Don’t get confused by the 12% spotted dogs those are from the 38%)

Answer:  30 boys

Step-by-step explanation:

Boys:Girls

3       : 1

Let no. of girls =x

⇒ no. of boys =3x.

⇒ no. of students in class =4x

                                            =   4/3×3x

                                            =  4 /3  ×no. of boys

  40=4/3* no.of boys

40* (3/4)=no.of boys

30=no of boys

Answer:

Cross sectional study

Step-by-step explanation:

Cross sectional study, also known as traverse or prevalence study caloukdnbe defined as a form of observational study which involves analysing a certain sample of data which is selected based on a variable of interest. This data is collected at a given point in time across the sample population. In the scenario described above, the record of viewing habit of 7500 household smoke obtained today(point in time) will be used to determine the proportion tuned to a particular sport programme. (data collected is based on the variable to be analyzed).

Step-by-step explanation:

answer is in photo above

Answer:

Suppose that we have a given point (x, y)

If we translate this point N units to the right, then the new coordinates of the point are:

(x + N, y)

Ok, now if we know that the vertices of the trapezoid are:

(1, 2), (3, 1), (3, 5), (1, 4)

And we move the whole figure 4 units to the right, then all the vertices are moved 4 units to the right.

Then the new vertices of the figure will be:

(1 + 4, 2) = (5, 2)

(3 + 4, 1) = (7, 1)

(3 + 4, 5) = (7, 5)

(1 + 4, 4) = (5, 4)

Then the coordinates of the image of the trapezoid (of the new vertices) are:

(5, 2),  (7, 1), (7, 5),  (5, 4)

Answer:

yes...

Step-by-step explanation:

its a congrate triangle

Answer: [tex]750\ ft^2[/tex]

Step-by-step explanation:

Given

Rate of painting 50¢ per square foot

Cost of paint is $100

If the total bill is $475

We can write,

[tex]\Rightarrow 475=100+0.5\times x\quad [x=\text{area in square foot}]\\\Rightarrow 375=0.5x\\\Rightarrow x=750\ ft^2[/tex]

Thus, [tex]750\ ft^2[/tex] must be painted.

Answer:

The irrational number is [tex]\sqrt{\frac{5}{3}}[/tex].

__________________________________

Definition : In mathematics, the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.

Answer:

Step-by-step explanation:

I'm not sure but I think it's A

I'm not sure!!

(pls do not vote ..)

Bye!

Answer:

16 (sixteen) is 6 divided by 3/8.

Answer:

101 - 37 = 64

I hope this is correct

Answer: [tex]11<x<59[/tex]

Step-by-step explanation:

Given

The side of the triangle are [tex]24\ \text{and }35[/tex]

Suppose the third side is [tex]x[/tex]

Also, the sum of the two sides of the triangle is always greater than the third

[tex]\therefore x<24+35\\\Rightarrow x<59\quad \ldots(i)[/tex]

Similarly,

[tex]\Rightarrow x+35>24\\\Rightarrow x>-11[/tex]

Also,

[tex]\Rightarrow x+24>35\\\Rightarrow x>11\quad \ldots(ii)[/tex]

From (i) and (ii) we get

[tex]\Rightarrow 11<x<59[/tex]

Answer:

19

Step-by-step explanation:

Answer:

i think the answer 17

Step-by-step explanation:

area of the parallelogram = 7 × 14

=98 cm²

ok check image file in the image is answers with color code

Answer:

A = πx² - 2πx + π

Step-by-step explanation:

The area of the new cup opening :

We are given the area formula to use :

Area, A = πr²

r = Radius = x-1

Area = π(x - 1)²

A = π(x - 1)(x - 1)

A = π(x² - x - x + 1)

A =π(x² - 2x + 1)

A = πx² - 2πx + π

Answer:

Newton's law of cooling says that:

T(t) = Tₐ + (T₀ - Tₐ)*e^(k*t)

or:

[tex]\frac{dT}{dt} = -k*(T - T_a)[/tex]

in the differential form.

where:

T is the temperature as a function of time

Tₐ  is the ambient temperature, in this case, 70F

T₀ is the initial temperature of the object, in this case, 150F

k is a constant, and we want to find the value of k.

Then our equation is:

T = 70F + (150F - 70F)*e^(k*t)

Now we also know that after a minute, or 60 seconds, the temperature was 135F

then:

135F = 70F + (150F - 70F)*e^(k*60s)

We can solve this for k:

135F = 70F + 80F*e^(k*60s)

135F - 70F = 80F*e^(k*60s)

65F =  80F*e^(k*60s)

(65/80) = e^(k*60s)

Now we can apply the Ln(x) function to both sides to get:

Ln(65/80) = Ln(e^(k*60s))

Ln(65/80) = k*60s

Ln(65/80)/60s = k = -0.0035 s^-1

Then the differential equation is:

[tex]\frac{dT}{dt} = -0.0035 s^-1*(T - 70F)[/tex]

Answer:

pls give me brainliest plzzzzz

Answer:

A.

Step-by-step explanation:

When x = -3 g(x) = + 2 and this is the maximum value of g(x).

All other values of x give a value of g(x) < 2.

The range is (-∞, 2]