Answer:
126
Step-by-step explanation:
The number of different 4-toppings pizzas can be made with given toppings is 70.
There are 8 different toppings of pizza are given.
What is a combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.
Here, n=8 and r=4
Now, 8C4
= [tex]\frac{8!}{4!(8-4)!} =\frac{8\times7\times6\times5\times4!}{(4\times3\times2\times1)4!}[/tex]
= (8×7×6×5)/(4×3×2×1)
= 7×2×5
= 70
Therefore, the number of different 4-toppings pizzas can be made with given toppings is 70.
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Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) cos(x) sin(2x) sin(x) dx
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]
Find the equations of the lines that pass through the point (4, 5) and are parallel to and perpendicular to the line with equation y + 7x = 5
Parallel: y =
Need help? Click the link to see a video example,
Perpendicular: y =
Answer:
Parallel: y = -7x+33
Perpendicular: y = (⅐)x + 31/7
Step-by-step explanation:
y+7x = 5
Slope of the line is -7.
Slope of any parallel to the line is also -7.
Slope of any perpendicular to the line is ⅐.
plz help me brainlest for whoever answers
Answer:
Circumference = 37.68
Area = 113.04
Step-by-step explanation:
Circumference = π × d
Circumference = 3,14 × 12 feet
Circumference = 37.68
Area = π × r²
Area = 3,14 × 6 × 6
Area = 113.04
(GIVING BRAINLIYEST)
7. what is the volume of these 2 objects
Figure #1
use the smaller part of the figure with the dimensions of 1x2x3 and find the volume of that 1x2x3= 6m
find the area of the bigger part 3x6x3= 54m
54+6= 60m³
Figure #2
smaller part 2x2x7= 28m
bigger part 7x5x3= 105m
105+28= 133ft³
Answer:
v= LxWxH
3x5x2x7x5x7=7350
1x2x4x3x6x3=432
What is the surface area please help I will mark brainliest
Answer:
292.5 square cm
Step-by-step explanation:
13 x 9 / 2 = 58.5 x 5 = 292.5 square cm
Hope that helps!
Which of these represents the equation of a line that passes through the points (-5, -4) and (3, 8)?
A
3
y = x +
7
2
B.
y = {
C
2
3
С
y = ſa +6
y= 3x - 22
D
2
Tom is applying for a visa. He has to pay £1,700 for the visa as well as a 11% charge on the visa price for an on-the-day service. If Tom has 1 year to save, how much money should he save per month to be able to cover his costs? Round your answer to the nearest £10.
Step-by-step explanation:
this is geometric sequence
G1=Go(1+r)^n
G1=1700(1+11%)^1
G1=1700(1+0.1)
G1=1700*0.1
G1=170 per year
G1=170*12 per month
G1=2040
(5x+2)(x2-3x+6)
How do I do this and what’s the answer
Answer:
5x³-13x²+24x+12
Step-by-step explanation:
Start by distributing (5x+2) into (x²-3x+6)
It is easiest to start with 5x.
When distributing 5x, your answer should be: 5x³-15x²+30x.
Then, distribute the 2 just as you did for 5x.
Your answer for that should be: 2x²-6x+12
After that, add the like- terms from both answers together.
5x³-15x²+30x+2x²-6x+12
The final answer is then: 5x³-13x²+24x+12
(4+4)÷22×2
plss someone answer hurry <3
Answer:
first is 4+4=8.........second is 22×2=11 ..........third is 8÷11=0.7272727273 u can do it 0.72
Step-by-step explanation:
hope this help
Answer:
0.72
Step-by-step explanation:
Identify the inequality that represents the following problem. One less than twice a number is no less than five. What is the solution set? 01- 2025 0 20-125 020-15 01-2015
Answer:
2x-1 greater than or equal to 5
Can anyone help with expanding this?
Answer:
log(4) +3 log(x) +7 log(y)
Step-by-step explanation:
Hope it helps!
Answer:
4×6_7482&÷&&÷,geggeve
What is the least common multiple of the two denominators
6/8 , 4/32
please help out, tysm. need this asap. i’m gonna mark brainliest! thanks
Answer:
E and F
Step-by-step explanation:
✔️To eliminate the variable y, we can multiply the first equation, -x + 4y = 1 by 7 and the second equation, 8x - 7y = 42 by 4. This will leave us with the variable x alone to solve for.
✔️Alternatively, we may decide to eliminate the variable x first by multiplying the first equation, -x + 4y = 1 by 8. Both equations would be equivalent, thus when we can easily eliminate the variable x leaving us with variable y to solve for.
Which of the points best represents the location of
5
on the number line?
8
A
B
D
+
-2
-1
0
2
C С
OD
OA
B
Answer:
B
Step-by-step explanation:
Answer:
the answer should be B
Step-by-step explanation:
What is the value of 3 in the figure shown below?
E
с
4.2
4.2.
A
20
35°
62°
4.3
4.3
D
B
Answer:
[tex]35degrees[/tex]
Simplify: 299.081+59.26-95.32-365.195
A number squared minus fifteen times the number is equal to 16. Write the equation and give the factors.
[tex]\huge{\mathfrak{\purple{Answer}}}[/tex]
Equation: x² - 15x = 16
Factors: x = -16 and x = 1
[tex]\huge{\mathfrak{\purple{Explanation}}}[/tex]
Given
A number squared minus fifteen times the number is equal to 16.
Equation: x² - 15x = 16
Factors:
x² - 15x - 16 = 0
So,
(x - 16) (x + 1)
=> x - 16 = 0, x + 1 = 0
= x = -16 and x = 1
#HopeItHelps
11 - m = 51 - 6m solve for m
Answer:
m = 9
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Jason wants to eam money by raking leaves. He buys a rake that costs $30.00. He plans to charge $8.00 for each lawn that he rakes Calculate the amount of profit Jason
will make if he rakes 15 lawns?
Answer:
$90 profit
Step-by-step explanation:
2(a+b)=0
A 2a + b
B. 2+a+b
C. 2a + 2b
D. 1a + b
E 1 / + 1 26
......the answer is 2a + 2b
-90 is greater than or equal to -5(k-3)
Answer:
Step-by-step explanation:
equal
If the midpoint of AB Is (5,-4) and the coordinates of Aare (10,-6), then the coordinates of B are
Answer:
Step-by-step explanation:
A(10,6), M(5, -4), B(x,y)
5 = (10+x)/2
x = 0
-4 = (6+y)/2
-8 = 6+y
y = -14
B(0, -14)
The required coordinate of B is given as (0, -2 ).
Given that,
To determine the coordinates of B, If the midpoint of AB Is (5,-4) and the coordinates of A are (10,-6).
What is the midpoint?The midpoint is that point the line whose length from both the ends of the line is equal.
Here,
We have given two coordinates one of the endpoints A of AB and the other is midpoint M i.e. A(10, -6) and M(5, -4).
Definition of midpoint says,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
x₁ = 10, x = 5 , y₁ = -6 , y = -4
now,
5 = [10 + x₂] / 2 ; -4 = [-6 + y₂] / 2
x₂ = 10 - 10 ; y₂ = -8 + 6
x₂ = 0 : y₂ = -2
Thus, the required coordinate of B is given as (0, -2 ).
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(2a -36)
[tex](2a - {36)}^{2} [/tex]
Can somebody plz help me!!
Answer:
yes yes yes yes yes yes yes
Answer:
121π square centimeters
Step-by-step explanation:
We can find the radius of the circle by taking the average of the two diameters provided. (15+7)/2=11. Then we plug that into the area of a circle equation. Area = π[tex]r^{2}[/tex] and that yields the answer.
2. Which expression is equivalent to 5-(-8)?
A (-5) + 8 B 8+5
C 8-5
D 5-8
Answer:
B. 8 + 5
Step-by-step explanation:
5 - (-8)
= 5 + 8
= 8 + 5
Find the volume of this cuboid 5cm
Answer:
125[tex]cm^{3}[/tex]
Step-by-step explanation:
5x5x5= 125
You have 18 pencils.
Seven pencils fit in a pencil case.
How many cases do you need to hold all of your pencils?
Answer:
you need three pencil cases to hold all of your pencil
Answer:
3
Step-by-step explanation:
18 = 7 +7 + 4
Since each box can carry 7 pencils, we need three to hold all of them.
Hope this helps!!
Which function best fits following points?
I need to write fractions as mixed numbers 36/6 20/10 15/8 13/6
36/6 = 6
20/10 = 2
15/8 = 1 7/8
13/6 = 2 1/6
Hope this helped!
Answer:
6, 2, 8 7/8, 2 1/3
Step-by-step explanation:
36/6 represents a division: 36 divided by 6
answer: 6
20/10 also division: 20 divided by 10
answer: 2
15/8 also division (long division...) 15 divided by 8
you will have a remainder (that will become your numerator)
the decimal of that division is 1.875 as a fraction that is a mixed number:
8 AND 875/1000 but!! you are not done yet (that fraction has to be simplified)
If you divide the fractional portion by the greatest common factor (125) you can simplify your fraction to 8 7/8
13/6 is 13 divided by 6 = 2 with a remainder of 2 = 2 2/6 simplified = 2 1/3
Drag the cards to create a number that matches these rules. • The number ends in the tenths place. 50 is the nearest ten when rounding 3. 8 4