HELP PLEASE!!!!
The amount of people in the city of Blonton is increasing due to children being born and because people are moving to the area.
~The population is increasing due to births by 13% each year and about 2300 people move to the area in any given year.
~The increase due to people moving to the area is represented by the function M(t) = 2300t.
~The population at any time when taking into account new births is found by P(t) = 375,000(1.013)t where 375000 was the initial population and t stands for the number of years after 1990.
If we added these functions together, what would the sum represent?
Write the product cos(2x)sin(5x) as a sum
Answer:
[tex]\cos(2x)\sin(5x)=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]
Step-by-step explanation:
Given: [tex]\cos(2x)\sin(5x)[/tex]
Formula:
[tex]\sin A+\sin B=2\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})[/tex]
[tex]\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})=\dfrac{\sin A+\sin B}{2}[/tex]
Compare the given expression with formula
[tex]\cos(2x)\sin(5x)=\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})=\dfrac{\sin A+\sin B}{2}[/tex]
Therefore,
[tex]\dfrac{A+B}{2}=5x\Rightarrow A+B=10x[/tex]
[tex]\dfrac{A-B}{2}=2x\Rightarrow A-B=4x[/tex]
Using two system of equation of A and B to solve for A and B
Add both equation to eliminate B
[tex]2A=14x[/tex]
[tex]A=7x[/tex]
Substitute A into A+B=10x
[tex]7x+B=10x[/tex]
[tex]B=3x[/tex]
Substitute A and B into formula
[tex]\cos(2x)\sin(5x)=\sin(\dfrac{7x+3x}{2})\cos(\dfrac{7x-3x}{2})=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]
Hence, Product as sum form [tex]\cos(2x)\sin(5x)=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]
I Need Help ASAP! This is Due in 30 Minutes!
I don't Understand it at all and I need Help
Create a factorable polynomial with a GCF of 7. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
Use basic identities to simplify the expression.
cos θ - cos θ sin2θ
The solution for the expression will be cos Ф - cos Ф.sin² Ф = cos³ Ф.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
The given trigonometric expression will be solved as below,
cos Ф - cos Ф.sin² Ф
We know that, sin² Ф = 1 - cos² Ф
E = cos Ф - cos Ф( 1-cos² Ф)
E = cos Ф - cos Ф - cos³ Ф
E = cos³ Ф
Therefore, the expression is cos Ф - cos Ф.sin² Ф = cos³ Ф.
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In a fast-food restaurant, the ratio of people eating hamburgers to people eating chicken is 4 : 3. There are 84 people in the restaurant. How many people are eating hamburgers and how many are eating chicken? A. 36 people are eating hamburgers; 48 people are eating chicken. B. 12 people are eating hamburgers; 72 people are eating chicken. C. 48 people are eating hamburgers; 36 people are eating chicken. D. 21 people are eating hamburgers; 63 people are eating chicken.
Final answer:
By using the ratio 4:3 and the total number of people (84), we calculate that each part of the ratio represents 12 people. Multiplying 4 parts by 12 gives us 48 people eating hamburgers, and multiplying 3 parts by 12 gives us 36 people eating chicken, making option C correct.
Explanation:
To solve the problem of determining how many people are eating hamburgers and how many are eating chicken given the ratio and the total number of people, we need to divide the total number of people by the sum of the parts of the ratio to find out the value of each part. The ratio given is 4:3, which means for every 4 people eating hamburgers, there are 3 people eating chicken. To find the value of each part of the ratio, we add the parts of the ratio (4 + 3 = 7) and divide the total number of people in the restaurant (84) by this sum.
84 ÷ 7 = 12. This means that each part of the ratio is equivalent to 12 people. Now, we need to multiply the number of each part by the number of people that each part represents. For hamburgers, it's 4 parts, so 4 × 12 = 48 people. For chicken, it's 3 parts, so 3 × 12 = 36 people.
Therefore, the correct answer is C: 48 people are eating hamburgers and 36 people are eating chicken.
He scatter plot shows the number of pages scanned (y) in different number of hours (x) by a scanning machine: which function best represents the data shown in the scatter plot
Watermelon cost $0.39 per pound. Joesphs watermelon costs between $4.00 and $5.00. Which compound inequality correctly represents the possible weights of this watermelon? Round to the nearest tenth.
Answer:
10.26<w<12.82 represents the weight of the watermelon.
Step-by-step explanation:
Watermelon cost $0.39 per pound. Let the weight of Joseph's water melon be w pounds.
Joesph watermelon costs between $4.00 and $5.00.
[tex]\frac{4}{0.39}= 10.26[/tex]
[tex]\frac{5}{0.39}= 12.82[/tex]
Means the melons are between 10.26 and 12.82 pounds.
Hence, the compound inequality is 10.26<w<12.82 which represents the weight of watermelon.
Two ants race across a table 61 cm long. one travels at 5.13 cm/s and the other at 3.99999 cm/s. when the first one crosses the finish line, how far behind is the second one? answer in units of cm
We use ________ to determine the actual rate of change over intervals.
the dependent variable
the independent variable
absolute value
none of the above
The rule T1, -4 RO, 180°(x, y) is applied to rectangle KLMN. Which rectangle shows the final image??
Answer:
Figure 3.
Step-by-step explanation:
We perform the rotation first. A 180° rotation about the origin maps every point
(x, y)→(-x, -y). This means it negates both the x- and y-coordinates.
The pre-image points are:
K(3, -4); L(3, -1); M(5, -1); N(5, -4). Performing the rotation and negating the coordinates will give us:
K'(-3, 4); L'(-3, 1); M'(-5, 1); N'(-5, 4).
Now we perform the translation. The translation rule is <1, -4>; this means we add 1 to each x-coordinate and subtract 4 from each y-coordinate. This maps to our new points:
K''(-2, 0); L''(-2, -3); M''(-4, -3); N''(-4, 0)
These are the points of figure 3.
can someone help me, i am very confused, i need to find the volume of the figure put i dont know how
please help me and write steps
What is the end point and mid point
Answer:
end point is (-5/3 , 3)
mid-point: (5/6, 3/2)
Step-by-step explanation:
If the price of an item is $34 and the sales tax on it is $1.36, what is the sales-tax rate?
1.36/34 = 0.04
0.04 = 4%
Four is no less than the quotient of a number x and 2.1
A triangle has an area of 180 cm2 and the base that is 20 cm long. what is the height of the triangle answers
Assume that a researcher randomly selects 14 newborn babies and counts the number of girlsâ selected, x. the probabilities corresponding to the 14 possible values of x are summarized in the given table. find the probability of selecting 9 or more girls.
To find the probability of selecting 9 or more girls out of 14 newborn babies, sum the probabilities for selecting 9 to 14 girls from the given table.
Explanation:To find the probability of selecting 9 or more girls out of 14 babies, we need to calculate the sum of the probabilities of selecting 9, 10, 11, 12, 13, and 14 girls. Refer to the given table that summarizes the probabilities for each value of x. Add the probabilities for these values to get the probability of selecting 9 or more girls.
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Labor rate = $7.50 per hour Labor time = 6.5 hours Retail price of parts = $0 Total job cost = $82.00 Overhead rate?
Quintin set a goal to do 15 push-ups each day. By how much would he exceed his goal if he did 17 push-ups in a day?
2
7
19
32
17-15 =2
he would exceed by 2 a day
Find the distance between each pair of points
A cylinder has a height of 2 meters and a diameter that is 5 times the measure of the height. Using 3.14 for pi, which of the following can be used to calculate the volume?
(3.14)(2m)2(10m)
(3.14)(2m)2(5m)
(3.14)(10m)2(2m)
(3.14)(5m)2(2m)
In the triangle below, determine the measure of side a.
Choose the best definition for the following term:substitution
Paul bought 9 total shirts for a total length f $72. Tee shirts cost $10 and long sleeve shirts cost $7. How many of each type shirt did he buy
ten less than twice a number is the same as 7 times the number. find the number
Find the degree of the monomial. 6y2w8
The slopes of perpendicular line segments are 1/2 and d/3 What is the value of d?
d=-6
d=-3/2
d=3/4
d=6
An activity book has 21 pages of crossword puzzles, 18 pages of cryptograms, and 12 pages of mazes. bianca randomly selects a page, completes the activity, and then randomly selects another page to complete. what is the probability that bianca first completes a maze and then completes a crossword puzzle?
Final answer:
The probability that Bianca first completes a maze and then completes a crossword puzzle is approximately 9.8%.
Explanation:
To find the probability that Bianca first completes a maze and then completes a crossword puzzle, we need to calculate the probability of each event occurring and then multiply them together.
The total number of pages in the activity book is 21 + 18 + 12 = 51 pages.
The probability of selecting a maze page first is 12/51, and after completing the maze page, there are now 50 pages remaining in the book, 21 of which are crossword puzzles.
So, the probability of selecting a crossword puzzle page after completing a maze page is 21/50.
To find the probability of both events happening, we multiply the probabilities: (12/51) * (21/50) = 0.098 or 9.8%.
which choice is equal to the repeating decimal below? 0.6
a) 0.666
b) 6/10
c) 0.66666666
A line contains points (−2,−2) and (1,4). Find the distance between the line and the point (6,−1).
If Polly walks across the street to buy a cracker and the people who sell them only have one left and there's a long line out the door... will Polly get a cracker? I'm so confused :/ thanks so much for the help!