To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval. Using a graphing utility, we can plot the function and verify the result.
Explanation:To find the area of the region defined by the function y = 6 sin(x) + sin(6x) from x = 0 to x = pi, we need to calculate the definite integral of the function over this interval.
Using a graphing utility, we can plot the function and verify the result. The integral will give us the area under the curve.
A graphing utility like Desmos or Wolfram Alpha can be used to plot the function and find the area under the curve.
simplify
(10)/(5b+4)+(6)/(2b-3)
A.-10b-54/(5b+4)(2b-3)
B. 16/7b+1
C. 16/(5b+4)(2b-3)
D. 50b-6/(5b+4)(2b-3)
I need help finding the slope for AB, BC, CD and DA
A student is running a 10-kilometer race. He runs 1 kilometer every 4 minutes. Select the function that describes his distance from the finish line.
f(x) = - 1 over 4x + 4
f(x) = - 1 over 10x + 4
f(x) = - 1 over 10x + 10
f(x) = - 1 over 4x + 10
Answer:
Option D is correct
[tex]y =-\frac{1}{4}x+10[/tex]
Step-by-step explanation:
Slope intercept form:
The equation of line is given by:
[tex]y=mx+c[/tex] .....[1]
where, m is the rate or slope and c is the y-intercept or initial value.
As per the statement:
Here, y represents the distance in kilometer and x represents the time in minutes.
A student is running a 10-kilometer race
⇒y(0) = b = 10 km
It is also given that he runs 1 kilometer every 4 minutes.
Now, with each passing minute the student is getting closer and closer to the finish line which was 10 kilometers away when the race started. Thus, as the race progresses, the distance between the student and the finish line will decrease.
[tex]m =-\frac{1}{4}[/tex]
Substitute these in [1] we have;
[tex]y = -\frac{1}{4}x+10[/tex]
Therefore, the function that describes his distance from the finish line is, [tex]y = -\frac{1}{4}x+10[/tex]
Jared wrote an equation for the perimeter of an equilateral triangle as 3x = 20. What does x represent in his equation?
Answer:
The length of a side of the triangle.
Step-by-step explanation:
An equilateral triangle has 3 equal sides so the x would be equal to one side of the triangle.
A copy machine makes 44 copies per minute. How many copies does it make in 4 minutes and 30 seconds?
Write the trigonometric expression in terms of sine and cosine, and then simplify.
csc2 x − cot2 x
Solve for x.
x/7 = -3
1,) x = -21
2.) x = -10
3.) x = 4
4.) x = 21
There are 13 fish in an aquarium. seven of the fish are guppies. how many non-guppies are in the aquarium
A giant salmon skier uses skies that are one sixth her height. if she is 174 cm tall how long are her skies?
5,893,402 + 19,392,009 =
Which of the following are properties of the incenter of a triangle? Choose all that apply.
A. The incenter is where all of the bisectors of the angles of the triangle meet.
B. The incenter of an obtuse triangle lies on the outside of the triangle.
C. The incenter is equidistant from each vertex of the triangle.
D. The incenter of a triangle is always inside it.
A & D
A. The incenter is where all of the bisectors of the angles of the triangle meet.
D. The incenter of a triangle is always inside it.
Answer:
A. The incenter is where all of the bisectors of the angles of the triangle meet.
C. The incenter is equidistant from each vertex of the triangle.
D. The incenter of a triangle is always inside it.
Step-by-step explanation:
W hich of the following are you not likely to see on a graph? dependent variable, units, independent variable, prediction ...?
Answer: Fourth option is correct.
Step-by-step explanation:
On graph, we can display dependent variables, units, independent variables , because they can be expressed in numbers easily.
Whereas prediction is not competent every time to get expressed with numerical terms.
Hence, prediction is not likely to see on the graph.
Thus, Fourth option is correct.
Factor completely and then place the factors in the proper location on the grid.
4y2 + 25y + 6
Answer:
factored form of given equation [tex]4y^2+25y+6[/tex] is [tex](4y+1)(y+6)[/tex]
Step-by-step explanation:
Given equation [tex]4y^2+25y+6[/tex]
We have to write the given equation in factors form and then represent the factors on grid.
Consider the given equation [tex]4y^2+25y+6[/tex]
25y can be written as 24y + y , we get
[tex]\Rightarrow 4y^2+24y+y+6[/tex]
Taking 4y common from first two term and 1 common from last two term, we get,
[tex]\Rightarrow 4y(y+6)+1(y+6)[/tex]
[tex]\Rightarrow (4y+1)(y+6)[/tex]
Thus, factored form of given equation [tex]4y^2+25y+6[/tex] is [tex](4y+1)(y+6)[/tex]
On grid it is shown as shown in attachment below.
The difference between five times a number and twelve times the number is –35.
Egypt is 386,700 square miles and wyoming is about 97,818 square miles egypt is about how many times as large as wyoming
Egypt is approximately 4 times as large as Wyoming when comparing their areas.
Explanation:To calculate how many times larger Egypt is compared to Wyoming, we divide the area of Egypt by the area of Wyoming. The area of Egypt is 386,700 square miles, and the area of Wyoming is about 97,818 square miles.
Dividing the area of Egypt by the area of Wyoming gives us: 386,700 / 97,818 ≈ 3.95.
Therefore, Egypt is approximately 4 times as large as Wyoming.
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Please help me
All of the following are equivalent except _____.
2%
0.2
1/50
0.02
m ∠CAD = 0.3(m(GE) - m(CD))
True or False
Answer:
False
You’re welcome ;)
A class of 18 students took a math test. Seven students had an average of 90. The other students had an average of 82.
What is the average for the whole class? Round to the nearest whole percent.
A) 80
B) 83
C) 85
D) 87
Answer: C- 85%
Step-by-step explanation:
7x11=630
Remaining Students: 18-7=11
11x82=902
Aveage:
630+902=1532
1532/18=85.1111
To cover A rectangle region of her yard penny needs atleast 170.5 square feet of sod. The length of the region is 15.5 feet. What are the possible widths of the region?
Given that f(x) = 6x 2 and g(x) =2x=4/5 , solve for g(f(1))
Answer:
The answer would be 4.
Step-by-step explanation:
What you have to do here is you have to substitute
So the problem told you the f(x) = 1. So what you want to do is plug that into the function f(x).
So:
f(x) = 6(1)2
= 8
Now we know that f(x) = 8, so what we going to do now is plug f(x) into g(x).
So:
g(f(8)) = 2(8) + 4/5
= 4
The value of g(f(1)) is 4.
Composite function -Composition of functions is the process of plugging one function into another, and simplifying or evaluating the result at a given x-value. Another way to read it is "f circle g of x." It is a process that joins two functions to create a third, unique function.Given ,
f(x) = 6x + 2
g (x) = 2x + 4 /5
To get value of g(f(1)) first we have to solve f(x).
f(x) = 6x + 2 .......................(1)
We simply put x = 1 in equation 1 .
Then, F(1) = 6 × 1 + 2 ⇒ 8
Now , we put value of f(1) in g(f(1)) ,
So, g(f(1)) = [tex]\frac{2x + 4}{5}[/tex]
= [tex]\frac{2 * 8 + 4}{5}[/tex]
= [tex]\frac{16 + 4}{5}[/tex]
= 20/5 ⇒ 4
Therefore, the value of g(f(1)) is 4 .
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How do you fine arccot(-sqrt(3))?
Answer:The answer is be And i’m Strongly positive about this because i just got it right!
Step-by-step explanation:
If f(x) = integral of 1/ (sqrt of t^3 +2)dt, then f'1 = ?
I'll write the equation with teh equation thing also ...?
There are five seniors in a class. For each situation, write how the binomial formula is used to calculate the probability.
a) In how many ways can I choose one senior to represent the group?
b) In how many ways can I choose two seniors to represent the group?
c) In how many ways can I choose three seniors to represent the group?
d) In how many ways can I choose four seniors to represent the group?
e) In how many ways can I choose five seniors to represent the group?
77 decreased by twice of a number
The algebraic expression for '77 decreased by twice of a number' is 77 - 2x, where x is the unknown number.
Explanation:The question '77 decreased by twice of a number' involves creating an algebraic expression. This expression will have the form 77 - 2x, where x represents the unknown number. To decrease 77 by twice a number means to subtract two times that number from 77.
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Select all ratios equivalent to 20:4
4:20, 2:10, 15:3, 1:2
Final answer:
The only ratio equivalent to 20:4 from the given choices is 15:3 because, when simplified, both ratios reduce to 5:1.
Explanation:
To determine which ratios are equivalent to 20:4, we need to find ratios that can be simplified or scaled to form the same relationship. An equivalent ratio maintains the proportion when both terms are multiplied or divided by the same number.
First, the given ratio of 20:4 can be simplified by dividing both terms by 4, which gives us 5:1. Now, we can compare this to the choices provided:
4:20 is not equivalent because when simplified (divided by 4), it gives 1:5, which is the inverse of 5:1.2:10 simplifies to 1:5 (dividing by 2), also not equivalent for the same reason.15:3 simplifies to 5:1 (dividing both terms by 3), which is equivalent to 20:4.1:2 is already in simplest form and is not equivalent to 5:1 or 20:4.Therefore, the only ratio equivalent to 20:4 given in the choices is 15:3.
What is the difference between slope on a table and slope on a graph
The difference between slope on a table and slope on a graph is shown below:
The slope on a table refers to the rate of change between two points represented in a table of values.
It is calculated by finding the ratio of the change in y-values to the change in x-values between two points.
The slope on a table is determined by taking the difference in y-values and dividing it by the difference in x-values.
On the other hand, the slope on a graph refers to the steepness or incline of a line that connects two points on a graph.
It is calculated by the ratio of the vertical change (rise) to the horizontal change (run) between two points on the graph.
While both the slope on a table and the slope on a graph represent the rate of change, they are determined differently.
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A baker bought some flour. He used to 2/5 of the flour to make bread and used the rest to make batches of muffins. If he used 16 pounds of flour making bread and 2/3 pound for each batch of muffins how many batches of muffins did he make
What is the unit rate of 50.4 feet in 14 years?
The lengths of two sides of a triangle are 9 and 15. What can be said about the length of the third side?
It must be geater than or equal to 6 and less than 24.
It must be greater than or equal to 6 and at most 24.
It must be greater than 6 and less than 24.
It must be greater than 6 and at most 24.
Answer:
Your answer is B
As the sum of any 2 lengths of a triangle is always greater than the third length
Step-by-step explanation:
It must be greater than or equal to 6 and at most 24.
Given that
The lengths of the two sides of a triangle are 9 and 15.
We have to determine
What can be said about the length of the third side?
According to the question
The lengths of the two sides of a triangle are 9 and 15.
By the properties of the triangle, the sum of the square of two lengths is equal to the third side length of the triangle.
Always remember that when you add two sides to a triangle, the sum will come out to be higher than the third side’s length.
Hence, It must be greater than or equal to 6 and at most 24.
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A rectangle's length is 4 feet more than its width. If the area of the rectangle is 396 square feet, what is its width, in feet?