The general equation of the sine function is [tex]\rm y= 2sin(2(x-\pi)[/tex]. The sine and cosine of an acute angle are utilized to find the angle of the triangle.
What is sin function?The sine and cosine of an angle are trigonometric functions. In the context of a right triangle, the sine and cosine of an acute angle are used to find the angle of the triangle.
The standard general equation of a sine function is given as;
[tex]\rm y= AsinB(x-C)+D[/tex]
Where A denotes the amplitude, B is the frequency, D is the vertical shift and C is the phase shift.
The given data in the problem is;
A is the amplitude= 2
B is the frequency=2
D is the vertical shift =0
C is the phase shift.=[tex]\pi[/tex]
The general equation is found as;
[tex]\rm y= 2sin(2(x-\pi)[/tex]
Hence the general equation of the sine function is [tex]\rm y= 2sin(2(x-\pi)[/tex].
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answer and explanation !!
QUICK PLS
Answer:
Step-by-step explanation:
diameter = 6 in
r = 6/2 = 3 in
h = 8 in
[tex]\textbf{Area of cylinder = $2\pi r(r+h)$ }[/tex]
[tex]= 2*3.14*3*(3+8)\\\\= 2*3.14*3*11\\\\= 207.24 \ in^{2}[/tex]
How to find the measure of an interior angle inside a regular polygon
Answer:
Step-by-step explanation:
[tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides
The measure of an interior angle inside a regular polygon is given by;
[tex]\rm S = (n -2) \times 180[/tex].
What is the interior angle?An interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. Or, we can say that the angle measures at the interior part of a polygon are called the interior angle of a polygon.
An Interior Angle is an angle inside a shape.
As per the angle sum theorem, the sum of all the three interior angles of a triangle is 180°.
Multiplying two less than the number of sides times 180° gives us the sum of the interior angles in any polygon.
The measure of an interior angle inside a regular polygon is determined by the following formula;
[tex]\rm S = (n -2) \times 180[/tex]
S = sum of interior angles and n = number of sides of the polygon.
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a parabola has focus of (5 2) and directrix y=0.where is the parabola's vertex
keeping in mind that the vertex will be half-way between the directrix and the focus point, in this case the directrix is below the focus point, meaning is a vertical parabola, Check the picture below.
If triangle DEF is classified as equilateral, which statement must be true?
At least two sides are congruent.
Two sides are perpendicular.
All three sides are congruent.
Two sides are parallel.
Also could you put the answer in the question comment box? I'm out of free answers.
Answer:
Step-by-step explanation:
Answer: All three sides are congruent
The problem is with A. It's true as well. At least 2 of the sides are congruent. The way to eliminate it is to say that does not mean specifically that all three sides are congruent.
I would argue that this is a faulty question, and watch someone squirm as they try to explain to you why a is not the answer. I don't know how to comply with your request. How are the choices designated
A
B
C
or
1
2
3
Answer:
C. All three sides are congruent.
Step-by-step explanation:
A survey asked 100 seventh graders if they have either a cell phone or a tablet. Of the 32 students that have a cell phone, 19 do not have a tablet. Of the 70 students that have a tablet, 57 do not have a cell phone. A total of 11 students stated they do not have a cell phone or a tablet. Some of this information is included in the frequency table.
help please!
Answer:
26
Step-by-step explanation:
Cellphone: 32 - 19 (students without tablet)
Tablet: 70 -57 (students without cellphone)
Both equations remain with only 13 students with both a cellphone and a tablet.
Then 13 + 13 = 26
Can anyone help me with this?
Answer:
-5 ; -3 ; -1.5 ; 0 ; 11 (**Quotient order**) -30/6 ; 21/-7 ; - (-3/-2) ; 0/-20 ; -44/-4 (** Division Problem Order which is the Original Order**)
Step-by-step explanation:
Here are your division problems:
-30/6 ; 0/-20 ; -44/-4 ; 21/-7 ; - (-3/-2)
First, do the -30 divided by 6
The rule when dividing with a negative and positive is you divide normally but have a negative for your answer.
30 divided by 6 is 5 but carry the negative due to the rule.
First one is -5
Next,
This one is simplistic,
It doesn't matter if it is negative anything divided by 0 is 0
Second one is 0
The next one is -44 divided by -4.
The rule when dividing with negative and negative is they cancel out and become a positive answer.
44 divided by 4 is 11
Third is 11
21 divided by -7 is the same as the first one, divide normally and carry negative.
21 divided by 7 is 3 but carry the negative.
Fourth is -3
Lastly, we need to use the rules once again. the negatives cancel but you still have a negative. This shall be a negative answer.
Here's the twist. 3 can't divide into 2 easily. You need to get a decimal which is fine.
Fifth is -1.5
Now with all of our numbers:
-5, 0, 11, -3, and -1.5 you need to order them from least to greatest.
Rule: The farther you go out with negatives the smaller they are for example like -12.
-5 is first
-3 is second
-1.5 is third
0 is fourth
11 is fifth
-5 ; -3 ; -1.5 ; 0 ; 11 is the quotient order
-30/6 ; 21/-7 ; - (-3/-2) ; 0/-20 ; -44/-4 is the division problem order
Henry is solving the problems 475 x 3. His first step is shown below (400 x ___) + ( 70 x ___ ) + ( 5 x ___ ) What number should Henry write in each of the blanks
Answer:
(400 × 3 ) + (70 × 3) + (5 × 3)
How do I solve the area for the shapes?
Answer:
shaded: 45 units²non-shaded: 36 units²total area: 81 units²Step-by-step explanation:
A "shaded area" problem can be worked by directly computing the area of the shaded shape, or by decomposing the figure in a convenient way. Here the overall square can be decomposed into unshaded triangles and a shaded square. The triangles have dimensions given, but the smaller square does not. Work must necessarily proceed from given dimensions to arrive at the values associated with dimensions not given.
For a problem like this, working the last question first can make it easier.
TotalThe total area is the area of a square 6+3 = 9 units on a side. Its area is ...
Total area = s² = (9 units)² = 81 units²
__
Non-shadedThe area of each of the four non-shaded triangles is ...
A = 1/2bh = 1/2(6 units)(3 units) = 9 units²
There are 4 triangles with that area that are not shaded, so ...
Non-shaded region = 4 × (9 units²) = 36 units²
__
ShadedThe shaded region is that portion of the total area that is not Non-shaded. Its area will be the difference ...
Shaded area = Total area - Non-shaded area
Shaded area = 81 units² -36 units² = 45 units²
what two numbers add up two 40 but multiply to get 100
The two numbers are illustrations of system of equations
The two numbers are 2.7 and 37.3
How to determine the two numbers?Let the numbers be x and y.
So, we have the following equations
x + y = 40
xy = 100
To determine the value of the variables, we simply plot the graph of both equations
From the graph, we have the following result
(x,y) = (2.7, 37.3)
Hence, the two numbers are 2.7 and 37.3
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If ∠A > ∠B, then what is the relation between AC and BC?
Answer:
ab and ac are congruent with each other
Answer:
BC > AC
Step-by-step explanation:
∠A > ∠B (Given)
Side opposite to larger angle is larger and side opposite to smaller angle is smaller.
->AC < BC
or
BC > AC
what's the square root of the area of a square with side 13?
Area :-
[tex]\\ \rm\rightarrowtail side^2[/tex]
[tex]\\ \rm\rightarrowtail 13^2[/tex]
[tex]\\ \rm\rightarrowtail 169[/tex]
Square root:-
√169=133-5 1/3 on a number line
please solve this
with each step
Step-by-step explanation:
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A company that produces cell phones has a cost function of C = 4x^2 - 107x + 4322, where C is the
cost in dollars and c is the number of cell phones produced in thousands). How many units of cell phone
(in thousands) minimizes the cost function?
Based on the cost function, the company that produces cell phones can minimize the cost function at 13.4 cell phones.
What number of cell phones are sold at the minimized cost function?To minimize the cost function, you should differentiate it.
= 4x² - 107x + 4322
dC/dx = 0
8x - 107 = 0
Solving gives:
8x = 107
x = 107 / 8
= 13.4 cell phones
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Given the rhombus ABCD, what is ECB
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A coin is used to simulate the probability of parents having 1 boy and 1 girl if they have a total of two children. A head represents having a girl, and a tail represents having a boy. The coin is flipped twice for each trial. The first flip represents the first child, and the second flip represents the second child. The experiment was performed 12 times, and the results are recorded in the following table.
Trial First Flip Second Flip
1 H H
2 H T
3 T H
4 H T
5 T T
6 H H
7 T H
8 H T
9 H H
10 T T
11 T T
12 H H
Based on the simulation, what is the probability that parents will have 1 boy and 1 girl if they have a total of two children?
Enter your answer as a reduced fraction, like this: 3/14
From the table, it is found that there is a [tex]\frac{5}{12}[/tex] probability that parents will have 1 boy and 1 girl if they have a total of two children.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, out of 12 experiments, 5 resulted in one of each, hence:
[tex]p = \frac{5}{12}[/tex]
There is a [tex]\frac{5}{12}[/tex] probability that parents will have 1 boy and 1 girl if they have a total of two children.
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How many distinct subsets of the set $s=\{1,8,9,39,52,91\}$ have three-digit sums?
The number of distinct subset of the set is an illustration of combination
There are 34 distinct subset of the set that have three digit sums
How to determine the number of distinct subsets?The set is given as:
S = {1,8,9,39,52,91}
Group the elements
S = {(1,8),9,39,52,91}
So, we have:
S ={s1,s2,s3,s4,s5}
To have a three-digit sum, the sum of the selected elements must be 100 or above.
The number of ways the above set can be selected is:
[tex]n_1 = 4 * [^3C_1 + ^3C_2 + ^3C_3] + 1[/tex]
Evaluate
[tex]n_1 = 4 * [3 + 3 + 1] + 1[/tex]
[tex]n_1 = 29[/tex]
The set can be further rearranged as:
S = {(52,39),9,(8,1)}
i.e.
S = {b1,b2,b3}.
The number of ways the above set can be selected such that the sum is 100 or above is:
[tex]n_2 = 2 * [^2C_1] + 1[/tex]
Evaluate
[tex]n_2 = 2 * 2 + 1[/tex]
[tex]n_2 = 5[/tex]
So, the total number of ways is:
[tex]n = n_1 +n_2[/tex]
This gives
[tex]n = 29 +5[/tex]
[tex]n = 34[/tex]
Hence, there are 34 distinct subset of the see that have three digit sums
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There are 34 distinct subsets of the see that have three-digit sums.
What are distinct subsets of the set?When we know that S is a subset of T, we place the circle representing S inside the circle representing T.
The set is given as:
S = {1,8,9,39,52,91}
Group the elements
S = {(1,8),9,39,52,91}
S ={s1,s2,s3,s4,s5}
To have a three-digit sum, the sum of the selected elements must be 100 or above.
The number of ways the above set can be selected is:
[tex]\rm n_1=4\times (^3C_1+^3C_2+^3C_3)+1\\\\n_1=4(3+3+1)+1\\\\n_1=4 \times 7+1\\\\n_1=28+1\\\\n_1=29[/tex]
The set can be further rearranged as:
S = {(52,39),9,(8,1)}
S = {b1,b2,b3}.
The number of ways the above set can be selected such that the sum is 100 or above is:
[tex]\rm n_2=2\times ^2C_1+1\\\\n_2= 2\times 2+1\\\\n_2=4+1\\\\n_2=5[/tex]
The distinct subsets of the set are;
[tex]\rm n_1+n_2=29+5 =34[/tex]
Hence, there are 34 distinct subsets of the see that have three-digit sums.
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What is 164 divided by 5.40
Answer:
30.37
Step-by-step explanation:
164÷5.40164×100/54016400/540give 30.37Answer:
[tex]164 \div 5.40 ={\ 30.3704{}}[/tex]
The answer is 30.3704
Find ℒ{f(t)} by first using a trigonometric identity. (write your answer as a function of s. ) f(t) = cos2(t)
The Laplace transform of f(t) = cos² t is equal to the following expression: [tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex].
How to determine the Laplace transform of a non-simple trigonometric expression
In this we need to rewrite the given function in terms of sines and cosines, whose Laplace transforms are well known. There is the following trigonometric formula:
[tex]\cos ^{2} t = \frac{1-\cos 2t}{2}[/tex] (1)
Now we proceed to apply the Laplace transforms:
[tex]\mathcal {L} \{f(t)\} = \frac{1}{2}\cdot \mathcal {L} \left\{1 \right\}-\frac{1}{2}\cdot \mathcal {L}\left\{\cos 2t\right\}[/tex]
[tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex]
The Laplace transform of f(t) = cos² t is equal to the following expression: [tex]\mathcal {L} \{\cos^{2} t\} = \frac{1}{2\cdot s} - \frac{s}{2\cdot (s^{2}+2)}[/tex]. [tex]\blacksquare[/tex]
Remark
The statement is poorly formatted, the correct form is shown below:
Find [tex]\mathcal {L}\{f(t)\}[/tex] by first using a trigonometric expression. (Write your answer as a function of s). f(t) = cos² t
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convert 36 inches to feet there are 12 inches in a foot
HELP ASAP PLEASE>:)
Answer:
3 feet
Step-by-step explanation:
PLEASE HELP ill like!!!!!! Its 20 points
Answer:
1. Degree= 6, trinomial
2. degree= 4, binomial
Step-by-step explanation:
1. The largest exponent is 6 making it the degree and there are three terms because (m^5n^2), (mn^2), (n^6).
2. Since (9a^2bc^2) has the more than 1 exponent, you add them and the degree is 4. There are two terms because (2a^3b), (9a^2bc^2).
An equilateral triangle with side length 7 cm is shown in the diagram, work out the area of the triangle.
Give your answer rounded to 1 DP.
Whose procedure is correct? keisha’s procedure is correct. david’s procedure is correct. both procedures are correct. neither procedure is correct.
Both procedures are correct. Because the end answer and the step-by-step explanation are right.
What is the procedure?It is a step-by-step explanation of the equations. The procedure is important
It explains the sequence of actions and specifies what has to be done at each stage, frequently specifying when and by whom the procedure should be conducted.
The end answer for Keisha's solution is;
[tex]\rm cos \theta =[/tex]± [tex]\frac{15}{17}[/tex]
The end answer for David's solution is;
[tex]\rm cos \theta =[/tex]± [tex]\frac{15}{17}[/tex]
Hence both procedures are correct. Because the end answer and the step-by-step explanation are right.
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Answer:
C: Both procedures are correct
Step-by-step explanation:
on edge :)
Find the length of PF
Answer: 6
Step-by-step explanation:
Please help! will give brainlest!
Answer:
1
Step-by-step explanation:
[tex] \tan \bigg( \frac{5\pi}{4} \bigg) \\ \\ = \tan \bigg( \pi + \frac{\pi}{4} \bigg) \\ \\ = \tan \bigg(\frac{\pi}{4} \bigg) \\ \\ = 1[/tex]
[tex]\tan \left(\dfrac{5 \pi}4 \right)\\\\\\=\tan \left(2 \cdot \dfrac{\pi}2 + \dfrac \pi4\right)\\\\\\=\tan \left(\dfrac{\pi}4 \right)\\\\\\=1[/tex]
forgot can you explain the answer
Answer:
18 is 30% of 60
Step-by-step explanation:
Try to line up percents % and the actual numbers they represent.
number : precent
60 is 100%
18 is x %
cross multiply
x·60 = 100·18
divide both sides by 60 to isolate x
x = ((100·18)/60
x = 30
geomerty!!! HELP PLEASE
Answer:
The Scale Factor is 5.3
Step-by-step explanation:
Here's the reason why:
You are trying to make the rectangle much larger.
The 14yd by 6yd is trying to get to the 74.2yd by 31.8yd.
We need to remember the importance of length and width.
If 14 yards is our length then 74.2 yards is our length on the enlarged rectangle.
You must do 74.2/14 because we need to work backwords.
**You can't find something to multiply 14 by to get to 74.2 unless you do division.**
74.2/14 is 5.3
Now do the same with the width.
31.8/6
That is 5.3 as well.
Therefore the scale factor is 5.3
The Roberts family uses a container shaped like a cylinder to recycle aluminum cans. It has a height of 4 feet and a diameter of 1.5 feet. The container is full.
The Volume of the container is: 28.3 ft3
How much do the contents weigh if the average weight of aluminum cans is 37 ounces per cubic foot?
The volume of the container is the amount of can in it
The contents weigh 1047.1 ounces
How to determine the weight of the container?The given parameters are:
Volume = 28.3 cubic feet
Average weight of can = 37 ounces per cubic foot
So, the weight of the container would be:
Weight = Volume * Average weight of can
Substitute known values
Weight = 28.3 cubic feet * 37 ounces per cubic foot
Evaluate the product
Weight = 1047.1 ounces
Hence, the contents weigh 1047.1 ounces
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Help can somone help please.
Answer:
0.7
Step-by-step explanation:
5(9n-6)
5×9n-5×6
45n-30
45n/45 -30/45
or 45n÷45-30÷45
n= 0.6666
0.7
hope dis helps!!!!!
in a school of 330 students, 85 of them are in a drama club, 200 of them are in a sports team and 60 of them do both
find the probability that the student isn't in a sports or drama club
Answer:
105/330 = 21/66 = 7/22
7/22 is the answer I think
Step-by-step explanation:
n(U) = 330
n(A) = 85
n(B) = 200
n(A n B) = 60
Now,
n(A U B) = n(A) + n(B) - n(A n B)
or, n(A U B) = 85 + 200 - 60
or, n(A U B) = 285 - 60 = 225
Now,
n(A U B) compliment = n(U) - n(A U B)
n(A U B) compliment = 330 - 225
so, n(A U B) compliment = 105
Now,
probability = 105/330