The motion of the hour hand of a clock is a periodic motion that repeats every 12 hours.
The equation that can be used to models the height as a function of time, based on the given options, is presented as follows; [tex]\displaystyle \underline{ H = 0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}[/tex]Reasons:
The given parameters are;
The variation of the height of the tip of the hour hand = 9 feet to 10 feet
At t = 0, the time = 12.00 a.m.
Required: The equation that can be used to model the height as a function of time.
Solution:
The general form of the cosine function is presented as follows;
y = a·cos(b·x - c) + d
The amplitude = a
[tex]\displaystyle a = \mathbf{ \frac{Maximum \ value -Minimum \ value}{2}}[/tex]
Therefore;
[tex]\displaystyle a = \frac{10 -9}{2} = 0.5[/tex]
b = The cycle speed
The period, T, is given as follows;
[tex]\displaystyle T = \mathbf{ \frac{2 \cdot \pi}{b}}[/tex]
The period of a block, T = 12 hours
Therefore;
[tex]\displaystyle b = \frac{2 \cdot \pi}{T}[/tex]
[tex]\displaystyle b = \frac{2 \cdot \pi}{12} = \mathbf{ \frac{ \pi}{6}}[/tex]
[tex]\displaystyle d = \mathbf{ \frac{Maximum \ value +Minimum \ value}{2} = \frac{10 + 9 }{2}} = 9.5[/tex]
At t = 0, H = The highest point = 10 ft.
Which gives;
[tex]\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \times 0 -c\right) + 9.5} = 10[/tex]
[tex]\displaystyle cos \left( -c\right) = \frac{0.5}{0.5} = 1[/tex]
-c = arcos(1) = 0
-c = 0
c = 0
The equation is therefore;
[tex]\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}[/tex]
The above equation is the same as; H = 0.5cosine (StartFraction pi Over 6 EndFraction t) + 9.5
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i need help with this math question
Answer:
D. f(x) = -6x^3 -5x^2 +21x
Step-by-step explanation:
The given zeros mean the function has factors ...
(x -(-7/3))(x -3/2)(x -0)
Multiplying by 6, we can write this as ...
(3x +7)(2x -3)(x) = 6x^3 +5x^2 -21x
And multiplying by -1 gives ...
-6x^3 -5x^2 +21x . . . . . matches choice D
__
Additional comment
The product of factors will be zero when f(x) = 0. This means we can multiply or divide by any convenient factor and the product will remain zero. Effectively, we have multiplied our original factorization by -6 to make the expression match one of the given forms. When we write this final expression as the function f(x), it remains true that the given zeros are zeros (x-intercepts) of f(x).
There are 100 students in the sixth grade. The ratio of boys to girls is 2:3. How many more girls than boys are in the sixth grade?
Answer: I Think you will make 100 time 2 divide 3
Step-by-step explanation:
i'm not sure, have a nice day
Please help me I need help
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b
6 Petra wants to buy an electronic reader that costs $160.75 including tax. She has saved $34.75 SO
far and plans to save an additional $10.50 each week. For how many weeks will Petra need to
save $10.50 to have enough money to buy the electronic reader
Answer:
Petra would need to save for 12 weeks to get 126
126+34.75=160.75
Petra need to save $10.50 to have enough money to buy the electronic reader in 12 weeks.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Petra wants to buy an electronic reader that costs $160.75 including tax. She has saved $34.75.
Here, So far and plans to save an additional $10.50 each week.
Let number of weeks to save $10.50 to have enough money to buy the electronic reader = x
So, We can formulate;
⇒ 10.50x + 34.75 = 160.75
Solve for x;
⇒ 10.50x = 160.75 - 34.75
⇒ 10.50x = 126
⇒ x = 126/10.50
⇒ x = 12
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how many would juile see?
Answer:
12Step-by-step explanation:
4*4*__=48
16*__=48
48/16=3
3*4=12
Answer:
12 boxes on the right side
Step-by-step explanation:
4 going across and 3 rows so 12 boxes
48 divided by 3 is 16 but divided by 4 is 12
since there are 16 boxes at the top its a good inference that there's
only 3 flat rows meaning per every flat there would be 4 boxes and 3 rows
there would be 12 boxes on the right side.
1. Simplify 3(2x - y) + 6y.
5x + 7y
6x + 3y
2x + 3y
6x - 7y
Answer:
6x + 3y
Step-by-step explanation:
3(2x - y) + 6y ← distribute parenthesis by 3
= 6x - 3y + 6y ← collect like terms
= 6x + 3y
[tex]\huge\boxed{Hi\: there!}[/tex]
Here, we use the Distributive Property:
[tex]a(b+c)=ab+ac[/tex]
3(2x-y)+6y=6x-3y+6y
Combine like terms:
6x+3y
[tex]\huge\boxed{Therefore,\: our \:equation\: is:6x+3y}[/tex]
[tex]\huge\bf{Good \:luck \:with \:your \: studies! :)\\~Unknown Dreamer}[/tex]
Solve for x. I need help understanding my math.
Answer:
x = 33
Step-by-step explanation:
11 - 4 = 7
You need to make that fraction equal 11
33/3 = 11
I hope this helps!
At the pool, three out of every seven kids are not wearing goggles. Which of the following is the fraction of kids who are not wearing goggles?
A : 4/7
B : 3/7
C : 3/4
D : 4/3
Answer:
B.3/7
Step-by-step explanation:
If you want 10 points answer my question
Plz
Josh went to a restaurant for dinner. The cost of the
meal was $24 with a discount of $2. If the total bill includes
an 8% sales tax and a 14% tip, what is the discount
percent? What was the total bill including the tax and the
tip?
Answer:
17.41 Dollars
Step-by-step explanation:
First, you take the discount, which is 2 dollars, so now the cost without any additional costs is 22 dollars. Next, find 8 percent of 22 by multipling 22*0.08 and then you get 1.76. Subtract that from 22 and 20.24. Then take 14 percent of 20.24 by multiplying it by 0.14, which you get 2.8336. Round that down and you get 2.83. Subtract that from that and you get 17.41.
find the values of x and y ????
show step plz
Answer:
x= 90 degrees
y= 47 degrees
Step-by-step explanation:
Since the two sides of this triangle are equal in lengths, you know that it is an isosceles triangle.
So with this information, you know that the angle at the bottom left is also 47 degrees.
x would be equal to 90 degrees because it is perpendicular to the bottom of the triangle (assuming).
A triangle has 180 degrees, so add up the lengths we have to solve for the missing angle, y.
90+47+y=180
y= 43
[tex]{\huge{\boxed{\mathfrak{Answer\:With\:Explanation}}}[/tex]
First we can say [tex]x=90[/tex]°, since x is located at the right angle part.
Now we can make an equation
[tex]90+47+y=180[/tex]
subtract 137 from sides.
[tex]y=43[/tex]
_________________________________
[tex]{\huge{\boxed{\mathfrak{Answer}}}[/tex]
[tex]x=90[/tex]° [tex]y=43[/tex]°_________________________________
Paul has thirteen coins in his piggy bank. Some of the coins are quarters, some are nickels, and he has a total of $3.55. Which system of equations can be used to determine how many quarters, x, and how many nickels, y, he has?
A.
x + y = 13
0.25x + 0.5y = 3.55
B.
x + y = 13
0.25x + 0.05y = 3.55
C.
x + y = 13
25x + 5y = 3.55
D.
x + y = 3.55
0.25x + 0.05y = 13
Answer:
The answer is B
Convert 34/8 to a decimal using long division
Answer: Using a calculator, if you typed in 34 divided by 8, you'd get 4.25. You could also express 34/8 as a mixed fraction: 4 2/8.
Step-by-step explanation:
Answer:
answer
Step-by-step explanation:
is using a cancalator duh
HELP PLEASE. The product of the roots of the equation ax^2+x-24=0 is equal to -2 2/5. Find the value of a in the equation.
The value of a in the equation is 10
The root of the equation is determined using the equation shown below:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Given the quadratic equation ax^2+x-24=0;
a = ab = 1c = -24The product of the quadratic equation is c/a
Product = c/a
- 2 2/5 = -24/a
-12/5 = -24/a
-12a = 5 * -24
-12a = -120
a = 10
Hence the value of a in the equation is 10
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Compare to ax^2+bx+c
b=1c=-24a=aProduct of roots=c/a
ATQ
[tex]\\ \tt\hookrightarrow \dfrac{c}{a}=-2\dfrac{2}{5}[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{-24}{a}=\dfrac{-12}{5}[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{24}{a}=\dfrac{12}{5}[/tex]
[tex]\\ \tt\hookrightarrow 12a=120[/tex]
[tex]\\ \tt\hookrightarrow a=10[/tex]
What is the domain and range of this graph??
Answer: D: (-∞, ∞)
R: (-∞, ∞)
Step-by-step explanation:
Since the end points are arrows and have no set stopping point we can assume the answer is all real numbers, also known as infinity
Can someone help help me
Answer:
15π/2 ft
Step-by-step explanation:
Arc length is given by the formula ...
s = rθ . . . . . r = radius; θ = central angle in radians
A 135° arc has a radian measure of (135)(π/180) = 3π/4. The radius of a circle with a 20 ft diameter is (20 ft/2) = 10 ft. So, the arc length is ...
s = (10 ft)(3π/4) = 30π/4 ft = 15π/2 ft
If the Fed's reserve requirement is 5 percent, then what quantity of excess reserves does the Bank of Cheerton now hold?
The quantity of excess reserves that the Bank of Cheerton now hold is $210
From the attached table, the amount generated on the reserve is $4,200
If the Fed's reserve requirement is 5 percent, then the quantity of excess reserves that the Bank hold is given as:
Quantity of excess reserves = 5% of $4,200
Quantity of excess reserves = 0.05 * 4200
Quantity of excess reserves = $210
Hence the quantity of excess reserves that the Bank of Cheerton now holds is $210.
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Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best-predicted crash fatality rate for a year in which there are 425 metric tons of lemon imports. Is the prediction worthwhile?
Lemon Imports Crash Fatality Rate
232 16
268 15.7
361 15.4
472 15.5
535 15
The regression analysis evaluates the amount of relationship that exists
between the variables in the analysis.
The regression equation is; [tex]\underline{\overline y = -0.00255 \cdot \overline x + 16.47268}[/tex]The prediction is worthwhile because it gives an idea of the observed Crash Fatality Rate and it is therefore approximately correct.Reasons:
First part;
The given data is presented as follows;
[tex]\begin{tabular}{|cc|c|}Lemon Imports (x) &&Crash Fatality Rate\\232&&16\\268&&15.7\\361&&15.4\\472&&15.5\\535&&15\end{array}\right][/tex]
The least squares regression equation is; [tex]\overline y = b \cdot \overline x + c[/tex]
Where;
[tex]b = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}[/tex]
[tex]\overline y[/tex] = The mean crash fatality = 15.52
[tex]\overline x[/tex] = The mean lemon import = 373.6
Therefore;
[tex]b = \dfrac{-171.36 }{67093.2 } = -0.00255[/tex]
c = [tex]\overline y[/tex] - b·[tex]\overline x[/tex] = 15.52 - (-0.00255)×373.6 = 16.47268
Therefore;
The regression equation is [tex]\underline{\overline y = -0.00255 \cdot \overline x + 16.47268}[/tex]Second part;
When the imports is 425 metric tons of lemon, we have;
[tex]\overline y[/tex] = -0.00255 × 425 + 16.47268 = 15.38893 ≈ 15.4
Therefore;
When the import is 425 metric tons, the Crash Fatality Rate ≈ 15.4
Given that the predicted value is between the values for 268 and 535, we
have that the prediction is approximately correct or worthwhile
The prediction is worthwhile
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two mountain bikers leave from the same parking lot and head in opposite directions on two different trails. the first rider goes 8km due east, then rides due south for 15km. The second rider goes 8km due west, then changes directions and rides 20 degrees west of due north for 15km. Both riders have been traveling for 23km, but which one is further from the parking lot?
Applying the required rule or theorem, it can be concluded that the second biker is farther from the parking lot. The distance of the bikers to the parking lot are:
i. First biker = 17.0 km
ii. Second biker = 20.22 km
The path of travel of both bikers would form a triangle. Applying the Pythagoras theorem to the path of the first biker would give his distance from the starting point. While applying the cosine rule to the path of second rider would gives his distance to the starting point.
Thus,
a. To determine the distance of the first biker from the parking lot.
Let the required distance be represented by x. Applying the Pythagoras theorem, we have:
[tex]hyp^{2}[/tex] = [tex]adj 1^{2}[/tex] + [tex]adj 2^{2}[/tex]
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex]
= 64 + 225
= 289
x = [tex]\sqrt{289}[/tex]
= 17
x = 17 km
Thus, the first biker is 17.0 km from the starting point.
b. To determine the distance of the second biker from the parking lot.
Let the required distance be represented by x. So that applying the cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex] - 2(15*8) Cos (180 - 20)
= 64 + 225 - 240 Cos 160
= 289 - 240 * -0.5
[tex]x^{2}[/tex] = 289 + 120
= 409
x = [tex]\sqrt{409}[/tex]
= 20.2237
x = 20.22 km
Thus, the second biker is 20.22 km from the starting point.
Therefore, the second biker is farther from the parking lot.
A sketch of the path of travel for the two bikers is attached for more clarifications.
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Use the original price and the markdown to find the retail price.
Original price: $130; Markdown: 28%
Answer:
The retail price would be $93.6
Step-by-step explanation:
This is because you can divide 130 by 100 to find 1% of such, and you'll get 1.3. Then, multiply 1.3 by 72, which makes 72% of the original price, to come find your answer, $93.6. Hope this helps!
what does it mean when the will says tomorrow it's ashes will be scattered to the four winds in the westing game
Answer:
In the document, Westing names the sixteen heirs present as his “nieces and nephews” and says that tomorrow his ashes “will be scattered to the four winds.” He then asserts that his life has been taken by one of his heirs, and he promises that the heir who finds something will receive the inheritance
Step-by-step explanation:
Westing names the sixteen heirs present as his “nieces and nephews” and says that tomorrow his ashes “will be scattered to the four winds.” He then asserts that his life has been taken by one of his heirs, and he promises that the heir who finds something will receive the inheritance.
What are the main events in The Westing Game?The main events in the Westing Game include moving into Sunset Towers, the Halloween dare, the reading of Samuel Westing's will, and the pairing of teams. Finally, the solving of clues and ultimately solving the puzzle.
Who Wins The Westing Game?Several years after that, Turtle stays with Sandy/Westing (as Eastman) while he really dies. She finally wins the prize and goes to play chess with her niece Alice.
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What is the value of 2^2n ?
Answer:
2^2n = 4n
hope it helps you :)
Answer:
4n
Step-by-step explanation:
2^2n = 4n
hope u liked this answer :)
Suppose you want to have $600,000 for retirement in 20 years. Your account earns 9% interest. How much would you need to deposit in the account each month?
HELP please it’s due in a hour
Answer:
5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.
Step-by-step explanation:
First find the length of the 2 missing sides. Remember that the picture is WAY out of proportion, so the sides won't be what they look like.
Since the left side is 4 and the right side is 8 cm, the missing left side is 4 cm.
Since the top side is 5 and the bottom side is 10 cm, the missing top piece is 5 cm.
So the sides starting at the bottom right and going clockwise are 10, 4, 5, 4, 5, 8 cm. Multiply each of these * 0.5 and call them meters.
5 m, 2 m, 2.5 m, 2 m, 2.5 m, 4 m.
the sum of two numbers x and y is 18 and their difference is 14. how is that written as an equation
Answer:
16 and 2
Step-by-step explanation:
16+2=18
16-2=14
Solve 7,030 ÷ 3 using the division algorithm ?????????????????
Answer: 2,343.3333 repeating, or just 2,343 1/3
Step-by-step explanation:
If you divide, your answer comes out to be 2,343.3333 repeating or 2,343 1/3.
Write the equation of the line that passes through the points (-7,7) and (-6,-5)
Answer:
y= -12x - 77
Step-by-step explanation:
HOPE THIS HELPS
Hey y’all please help me ASAP.
Answer:
the top right box
Step-by-step explanation:
Answer:
-g-8≥9
Step-by-step explanation:
Just ask.
Hope this helps. :)
3х + 9 = 2х + 5
is it no solutions, all real numbers, or does x equal something?
Answer:
x = -4Step-by-step explanation:
Given Equation:3x + 9 = 2x + 5Question:Whether x has one solution or infinite solutions or no solutions?Solution:=> 3x + 9 = 2x + 5
(On shifting like terms to one side we get)=> 3x - 2x = 5 - 9
(On subtracting)=> x = - 4
Result:Hence, x has only one solution that is, x = -4 (Ans)
Topic : Linear equations in one variable
Given :
3х + 9 = 2х + 5Solution :
[tex]\qquad \sf \: { \dashrightarrow 3x + 9 = 2x + 5}[/tex]
Transposing variables on one side and constant terms on the other side, we get :
[tex]\qquad \sf \: { \dashrightarrow 3x - 2x = 5 - 9}[/tex]
[tex]\qquad \sf \: { \dashrightarrow x = - 4}[/tex]
Hence, the x is equal to something which is (– 4)ill give a braineist if answered... CORRECTLY