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Answer: a glycoprotein that protrudes from the envelope of some viruses (such as a coronavirus) and facilitates entry of the virion into a host cell by binding to a receptor on the surface of a host cell followed by fusion of the viral and host cell membranes

Answer:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{4x-sin(4x)}{16} +c[/tex]

Step-by-step explanation:

Given

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx[/tex]

Required

Evaluate

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx[/tex]

Rewrite as:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {cos(x)\ sin(x)\ sin(2x)} \, dx[/tex]

In trigonometry:

[tex]sin(2x) = 2\ sin(x)\ cos(x)[/tex]

Divide both sides by 2

[tex]\frac{1}{2}sin(2x) = \frac{2\ sin(x)\ cos(x) }{2}[/tex]

[tex]\frac{1}{2}sin(2x) = sin(x)\ cos(x)[/tex]

[tex]\frac{1}{2}sin(2x) = cos(x)\ sin(x)[/tex]

Substitute [tex]\frac{1}{2}sin(2x)[/tex] for [tex]cos(x)\ sin(x)[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {\frac{1}{2}sin(2x)\ sin(2x)} \, dx[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \int\limits {\frac{1}{2}sin^2(2x)} \, dx[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(2x)} \, dx[/tex]

Let [tex]u = 2x[/tex]

Differentiate:

[tex]du = 2 \ dx[/tex]

Make [tex]dx[/tex] the subject

[tex]dx = \frac{1}{2}du[/tex]

Substitute [tex]\frac{1}{2}du[/tex] for [tex]dx[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(2x)} \, \frac{1}{2}du[/tex]

Substitute 2x for u

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}\int\limits {sin^2(u)} \, \frac{1}{2}du[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{2}*\frac{1}{2}\int\limits {sin^2(u)} \, du[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}\int\limits {sin^2(u)} \, du[/tex]

At this point, we apply the reduction formula:

Which is:

[tex]\int\limits {sin^n(u)} \, du = \frac{n-1}{2}\int\limits sin^{n-2}(u)\ du\ - \frac{cos(u)sin^{n-1}(u)}{n}\du[/tex]

Let n = 2; So, we have:

[tex]\int\limits {sin^2(u)} \, du = \frac{2-1}{2}\int\limits sin^{2-2}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

[tex]\int\limits {sin^2(u)} \, du = \frac{2-1}{2}\int\limits sin^{0}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}\int\limits sin^{0}(u)\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

[tex]sin^0(u) = 1[/tex]

So, we have:

[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}\int\limits 1\ du\ - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

Integrate 1 with respect to u

[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}u - \frac{cos(u)sin^{2-1}(u)}{2}\du[/tex]

[tex]\int\limits {sin^2(u)} \, du = \frac{1}{2}u - \frac{cos(u)sin(u)}{2}\du[/tex]

Recall that:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}\int\limits {sin^2(u)} \, du[/tex]

So, we have:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}[ \frac{1}{2}u - \frac{cos(u)sin(u)}{2}\du][/tex]

Open bracket

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{8}u - \frac{cos(u)sin(u)}{8}[/tex]

Recall that:  [tex]u = 2x[/tex] and  [tex]du = 2 \ dx[/tex]      [tex]dx = \frac{1}{2}du[/tex]

So, the expression becomes:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{8}2x - \frac{cos(2x)sin(2x)}{8}[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8}[/tex]

Add constant c

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8} +c[/tex]

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

In trigonometry:

[tex]sin(2\theta) = 2sin(\theta)cos(\theta)[/tex]

Divide both sides by 2

[tex]\frac{1}{2}sin(2\theta) = \frac{2sin(\theta)cos(\theta)}{2}[/tex]

[tex]\frac{1}{2}sin(2\theta) = sin(\theta)cos(\theta)[/tex]

Replace 2x with [tex]\theta[/tex]

[tex]\frac{1}{2}sin(2*2x) = sin(2x)cos(2x)[/tex]

[tex]\frac{1}{2}sin(4x) = sin(2x)cos(2x)[/tex]

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

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{cos(2x)sin(2x)}{8} +c[/tex] becomes

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{sin(4x)}{2*8} +c[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{1}{4}x - \frac{sin(4x)}{16} +c[/tex]

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{x}{4} - \frac{sin(4x)}{16} +c[/tex]

The solution can be further simplified as:

[tex]\int\limits {cos(x)\ sin(2x)\ sin(x)} \, dx = \frac{4x-sin(4x)}{16} +c[/tex]

Answer:

1 1/5 cups of soda.

Step-by-step explanation:

To solve this you need to change 3 and 2 1/2 into improper fractions so you get 6/2 and 5/2. Then you have to flip 5/2 so it becomes 2/5 and then you just have to cross cancel. Since the 2 from 2/5 can go into the 2 in 6/2 one time, 2/5 changes into 1/5 and 6/2 changes to 6/1. Now you can multiply across so 6 times 1 is 6 and 1 times 5 is 5 so you get 6/5. Now you have to change it into a mixed number which would be 1 1/5.

I hope this helps you :D

Answer:

Step-by-step explanation:

Answer:

50 students

Step-by-step explanation:

hope this helps, have a great day!

Answer: (C

Step-by-step explanation: To evaluate this, solve by raising 7 to the power of 3.

7 x 7 x 7

7 x 7 = 49 x 7 = 343

Therefore, the answer is C.

Answer:

true

Step-by-step explanation:

Answer:

a. [tex]\frac{3}{2}[/tex] b. 48

Step-by-step explanation:

(a) The value of the expression when x = -2 is 1.5.

(b) The value of the expression when x = 3 is 48.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

Given that the expression is 6(2)ˣ.

To evaluate the expression 6(2)ˣ for different values of x, we simply substitute the value of x into the expression and simplify.

(a) When x = -2, we have:

6(2)⁻² = 6(1/4) = 1.5

So the value of the expression when x = -2 is 1.5.

(b) When x = 3, we have:

6(2)³ = 6(8) = 48

So the value of the expression when x = 3 is 48.

To learn more about the function;

brainly.com/question/28303908

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Explanation:

x + 3y = 9

2x + 6y = 12

First you check if the two equations are compatible, that is

if they are parallel, they must not intersect.

Parallel means they have the same slope, given by dy/dx in general, and in the case of linear equations by the ratio of the y coefficient to that of x, that is 3 for the first equation, and 3 for the second. Since these two equations are parallel, they are multiple of each other. Now where these straight lines intersect the axis y = 0, that is the x-axis, is the constant term on the right hand side. Try it

Put y = 0 you get x = 9, for the first equation, and y = 0, x = 6 for the second equation, This is geometrically impossible, and therefore algebraically too. So this problem has no solution

Explanation:

If I'm wrong or That I missed The Question and just missed read it then My Answer Might have been wrong correct me or sumn If Im wrong

(｡づ’▽’｡)づ♡ #CarryOnLearning

Answer:

29

Step-by-step explanation:

(4+[8=4x(2)]x3)+1

(4+[8=8]x3)+1

(4+[8x3])+1

(4+24)+1

28+1

29

Answer:

y = 7x - 8

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Slope m = 7

y-intercept b = -8

Step 2: Write Function

Substitute in parts.

y = 7x - 8

Answer: 32/27

Step-by-step explanation:

x = 8/9

x + 8 /27

[tex]\frac{8}{9} + \frac{8}{27} \\\\\frac{8}{9} * 3 = \frac{24}{27}\\\\\frac{24}{27} + \frac{8}{27}\\\\\frac{24 + 8}{27} \\\\\frac{32}{27}[/tex]

Answer:

Substitute the value of the variable into the equation and simplify.

Exact Form:

32 /27

Step-by-step explanation:

Answer:

9.60 ; - 60.96

Step-by-step explanation:

Given the function :

F(x)=6(x+1) /25, x=0, 1, 2, 3, 4.

x = 0

F(0)=6(0+1)/25 = 6/25 = 0.24

x = 1

F(1)=6(1+1)/25 = 12/25 = 0.48

x = 2

F(2)=6(2+1)/25 = 18/25 = 0.72

x = 3

F(2)=6(3+1)/25 = 24/25 = 0.96

x = 4

F(2)=6(4+1)/25 = 30/25 = 1.2

X ______0 _____ 1 ______ 2 ______ 3 ____ 4

P(x) ___ 0.24 __ 0.48 ___ 0.72 ____ 0.96 __ 1.2

Mean, μ = Σx*p(x) :

(0*0.24) + (1*0.48) + (2*0.72) + (3*0.96) + (4*1.2)

= 9.60

Variance : Σx²*p(x) - μ²

(0^2*0.24) + (1^2*0.48) + (2^2*0.72) + (3^2*0.96) + (4^2*1.2) - 9.6^2

= 31.2 - 92.16

= - 60.96

Answer:

56

Step-by-step explanation:

I assume each person in the group must have 1 pencil AND 1 eraser each.

Since you have more pencils than erasers, then the limiting factor is the number of erasers. So a group of 56 people will have 1 pencil And 1 eraser and Clare will have 24 pencils left over (assuming Clare has her own pencil and eraser - if not then the group size is 55 assuming Clare is not in the group)

sorry if it's too confusing

Answer:

60³

Step-by-step explanation:

Hi again.

This time we are working with a triangular prism which is a bit trickier than a rectangular prism but it is still pretty easy once you know the formula.

The formula for a triangular prism is :

V = 1/2 x b x h x l

Or in full terms :

Volume = 1/2 x Base x Height x Length

So basically we are going to plug in the base , height, and width like we did before but this time at the end we are going to divide it in half.

So like last time, lets look at what we are given :

Base = 5

Height = 3

Length = 8

And now we put these numbers into the formula :

Volume = 1/2 x Base x Height x Length

Volume = 1/2 x 5 x 3 x 8

Lets save the 1/2 for last and do the others first.

So we can do 5 x 3 and get 15.

Then 15 x 8 and we get 120.

Now the equation is literally :

Volume = 1/2 x 120

(This is the same as 120 / 2 just in multiplication terms)

So lets do this :

120 / 2

=

60

So now we have your answer :

Volume = 60³

(Don't forget the little 3)

Again, I hope this helps!

Any questions or concerns please comment or message me ofc :)

Answer:

17

Step-by-step explanation:

3 multiply by 5 (which is x) = 15+2

The value of function 3x + 2 at x = 5 will be 17.

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is,

⇒ 3x + 2

And, The value of x = 5

Now,

The value of the function 3x + 2 at x = 5 is find as;

The function is,

⇒ 3x + 2

Substitute x = 5 in above equation as;

⇒ 3x + 2

⇒ 3 × 5 + 2

⇒ 15 + 2

⇒ 17

Thus, The value of function 3x + 2 at x = 5 will be 17.

Learn more about the substitution method visit:

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Answer:

6.28

Step-by-step explanation:

C=2πr=2·π·1≈6.28319

Hope this helps ;)

Answer:

11+15x

Step-by-step explanation:

combine 14 - 3 and 8x + 7x = 11 + 15x

Answer:

12/5

Step-by-step explanation:

9 : 3 3/4

9 : 15/4           change to improper fraction

36/4 : 15/4      LCD, 4

36 / 15            compare

12 / 5              reduce

Answer:

1a. 16

1b. 106

Not sure about the rest

Step-by-step explanation:

Answer:

c shows 3

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Has three different terms.

Answer:

y = x+6

Step-by-step explanation:

You can see that (0,6) and (1,7) are points on the line, and the y-intercept of the line is 6.

Use the coordinates of these points to find the slope of the line.

slope = (7-6)/(1-0) = 1

y-intercept = 6

Slope-intercept equation for line of slope 1  that has y-intercept of 6:

y = x+6

Answer:

I hope this helps

Step-by-step explanation:

This is not the same exact question but it shows you the throw down.

A+B+C= 180

so if A=60 and B=70

The sin is= 8

so 60+70= 130

130+c=180

130-180= 50

C=50

given f(x)=(x+5),findf(9)

0C.-196

Answer:

the answer is ribsome

The ribosome serves as the site and carries the enzymes necessary for protein synthesis. They are often takes the shape of small round particles attached in the endoplasmic reticulum.

9514 1404 393

Answer:

  [tex]f(x)=\left\{\begin{array}{ccc}3x+10&\text{for}&x\le -2\\2x-7&\text{for}&x>4\end{array}\right.[/tex]

Step-by-step explanation:

We observe that the left line segment has a rise of 3 for each run of 1. Its slope is ...

  m = rise/run = 3/1 = 3

It goes through point (-2, 4), so its equation can be written ...

  y = m(x -h) +k . . . . line with slope m through (h, k)

  y = 3(x +2) +4 . . . . fill in known values

  y = 3x +10 . . . . . . . simplify — equation of left line

__

The right segment has a rise of 2 for each run of 1. Its slope is ...

  m = 2/1 = 2

Then the equation of the line through point (4, 1) is ...

  y = 2(x -4) +1

  y = 2x -7

__

Taking into account solid and open circles, the equation for the function is ...

  [tex]f(x)=\left\{\begin{array}{ccc}3x+10&\text{for}&x\le -2\\2x-7&\text{for}&x>4\end{array}\right.[/tex]

Answer:

Left 3 down 4 is the correct answer so C

Answer:

B. right 3, down 4

Step-by-step explanation:

Answer:

[tex]y=0.25x-0.5[/tex]

Step-by-step explanation:

Firstly, the slope is [tex]\frac{3}{12} = 0.25[/tex], then you get the expression of the line.