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
Learn more about the cosine function here:
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please help with number 9!!!
Answer:
2 + sqrt(3)
Step-by-step explanation:
Roots that contain square roots come in pairs
If there is a root that is a- sqrt(b), there is a root that is a+ sqrt(b)
2 -sqrt(3) means there is a root 2 + sqrt(3)
A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower that is 98 meters high. After traveling 83 meters, which statement is most accurate?
Answer:
D). The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
Given that,
Height of the tower = 98 m
Distance traveled by plane = 83 m
The distance of the take-off point from the tower = 42m
This shows that it forms a right-angled triangle with
Base(B) = 42m
Hypotenuse(H) = 83m
To find,
The height of this triangle(x) = ?
Using Pythagoras theorem, we know that,
B^2 + x^2 = H^2
⇒ x^2 = H^2 - B^2
⇒ x^2 = (83)^2 - (42)^2
⇒ x^2 = 6889 - 1764
⇒ x = [tex]\sqrt{6889 - 1764}[/tex]
∵ x = 71.58 m
Thus, the height difference from the position of the plane to the tower = 98 - 71.58
= 26.42 m
Thus, option D i.e. 'the plane's height must be 27m above the tower' is the correct answer.
Which of the following steps were applied to ABC obtain AA'B'C?
12
8
B
6
A
-6
-2
4
6
10
A. Shifted 4 units left and 3 units down
B. Shifted 4 units left and 2 units down
C. Shifted 3 units left and 3 units down
D. Shifted 3 units left and 2 units down
Will give brainliest pls help!!!
Answer: B
Step-by-step explanation:
The transformation that took place to form A'B'C' is Shifted 4 units left and 2 units down.
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, a triangle ABC has undergone a transformation to form A'B'C' we need to identify the steps of transformation
So, considering the point B and B', we see, that, x-coordinate of B is at 5 and that of B' is at 1, that mean there is a shift of 4 units left,
Now, consider the y-coordinate, we see, that B is at 9 and B' is at 7 that gives a downward shifting of 2 units.
Hence, the transformation that took place to form A'B'C' is Shifted 4 units left and 2 units down.
Learn more about transformation click;
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I WILL GIVE BRAINLIEST
Answer:
A
Step-by-step explanation:
(f(-3+h)-f(-3))/h=(5(-3+h)^2-5(-3)^2)/h=(5*(-3+h-3)(-3+h+3))/h=-30*h/h=-30
what is (-5x-3y) - (-x-3z)
Answer:
-4x-3y+3z
Step-by-step explanation:
(-5x-3y)-(-x-3z)
-5x+x-3y+3z
-4x-3y+3z
Find the measure of side C and round to the nearest whole number. Pls help ASAP
Answer:
Step-by-step explanation:
Side a is across from angle A, and side c is the hypotenuse. The trig ratio that utilizes the side opposite and the hypotenuse is the sin of an angle, namely:
[tex]sin(30)=\frac{28}{c}[/tex] and solving that for c:
[tex]c=\frac{28}{sin(30)}[/tex] so
c = 56
what is greatest to least? 39/12 109/36 75/24 10/3 19/6 (btw those are written in faction form)
Answer:
10/3, 39/12, 19/6, 75/24, 109/36
Step-by-step explanation:
Lets simplify:
10/3 = 3 1/3
39/12 = 3 3/12 = 3 1/4
19/6 = 3 1/6
75/24 = 3 3/24 = 3 1/8
109/36 = 3 1/36
What is the measure of
Answer:
34
Step-by-step explanation:
Angle XYZ is an inscribed angle and arc XZ is the arc it intercepts
An inscribed angle is equal to half the measure of its intercepted arc
Hence Angle XYZ = half of arc XZ
If arc XZ = 68 then angle XYZ = half of 68
68/2=34
XYZ = 34
Please help quick! ASAP please!
Answer:
11.55
Step-by-step explanation:
Which equation is equivalent to -2(2 − 2x) = 4 − 8(1 − x)?
Answer:
x = 0
Step-by-step explanation:
-2(2 − 2x) = 4 − 8(1 − x)
Apply the distributive property:
−2(2 − 2x) = 4 − 8(1 − x)
(−2)(2) + (−2)(−2x) = 4 + (−8)(1) + (−8)(−x)
−4 + 4x = 4 + (−8) + 8x
Combine like terms:
4x − 4 = (8x) + (4+−8)
4x − 4 = 8x + (−4)
4x − 4 = 8x − 4
Subtract 8x from both sides:
4x − 4 − 8x = 8x − 4 − 8x
−4x − 4 = −4
Add 4 to both sides:
−4x − 4 + 4= −4 + 4
−4x = 0
Divide both sides by -4:
-4x/-4 = 0/-4
x = 0
Answer: 0
Step-by-step explanation:
Name the postulate or theorem you can use to prove the triangles congruent
SSS
AAS
ASA
SAS
Answer:
ASA
Step-by-step explanation:
if you understood the other, similar questions now, this one is really, really easy.
we got the confirmation for 2 angles and the side between these angles.
so, angle side angle or ASA
Can someone help me with this question immediately with an explanation??!! Plsss
Answer:
the number of senors is 150
Step-by-step explanation:
call the number of seniors is a
we have number of juniors is 4/3a
number of sophomores is 3/2*4/3*a=2a
number of freshmen is also =2a
sum of all studens in that school = a+4/3a+4a=950
a=150
Brainlest If Correct and i rlly need the help.
Answer:
scale factor= /2
Step-by-step explanation:
The scale factor is 1/2, which is equivalent to 0.5
11. Find out price elasticity of demand from the following table:
Price per unit()=8,10
Quantity Demanded (Units)=200,150
Answer:
Price elasticity of demand = 1
Step-by-step explanation:
Old quantity demanded = 200
New quantity demanded = 150
Old price = 8
New price = 10
Price elasticity of demand = percentage change in quantity demanded / percentage change in price
percentage change in quantity demanded = change in quantity demand / old demand × 100
= 50/200 × 100
= 0.25 × 100
= 25%
percentage change in price = change in price / old price × 100
= 2/8 × 100
= 0.25 × 100
= 25%
Price elasticity of demand = percentage change in quantity demanded / percentage change in price
= 25% / 25%
= 1
Price elasticity of demand = 1
You are making pudding for five friends. The recipe calls for 1/4 cup of sugar per serving. How much sugar do you need?
Answer:
1 1/4 cups I think..
Step-by-step explanation:
1/4 times 4 is 1, plus another 1/4 for the 5th friend is 1 1/4 cups.
Answer:
[tex]\frac{5}{4}[/tex] or [tex]1\frac{1}{4}[/tex] cups
Step-by-step explanation:
This question asks how much total sugar will be needed for 5 servings of 1/4 cup. In other words, this is asking for 1/4 cup to be added together 5 times. However, repeated addition is just multiplication, so this can become a multiplication problem. To do this make both terms a fraction by putting 5 over 1. This looks like: [tex]\frac{5}{1} *\frac{1}{4}[/tex]. Then, simply multiply the numerators together and the denominators together. This equals [tex]\frac{5}{4}[/tex]. If needed this can be put into the mixed fraction of [tex]1\frac{1}{4}[/tex] cups.
please i need your help
Answer:
x is 11
Step-by-step explanation:
[tex]{ \tt{10 + 5 + x = 26}} \\ x = 11[/tex]
What is the volume of a cylinder, in cubic feet, with a height of 3 feet and a base diameter of 18 feet? Round to the nearest tenths place.
Answer:
763 feet
Step-by-step explanation:
Volume of cylinder = πr2h
π(18/2)^2 x 3
= 763 feet
Answered by Gauthmath
Maya just bought a refrigerator for $642. She paid $160.40 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
120.40 per payment
Step-by-step explanation:
Subtract the down payment
642 - 160.40
481.60
Divide this by 4
481.60 / 4
120.40
find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]
Convert to p/q form[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]
[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]
please help me need hlp
Answer:
[tex] { - 2x}^{2} - {8x}^{3} + 6x \\ {x }^{2} - {8x}^{3} + 6x[/tex]
Step-by-step explanation:
step one foil methodstep two adding the like termsFor the function f(x)=x+9/7-4x find f^-1(x)
Answer:
Step-by-step explanation:
[tex]f(x)=\frac{x+9}{7-4x} \\put ~f(x)=y\\flip~x~and~y\\f(y)=x\\y=f^{-1}(x)\\y=\frac{x+9}{7-4x} \\flip~x~and~y\\x=\frac{y+9}{7-4y} \\x(7-4y)=y+9\\7x-4xy=y+9\\-4xy-y=9-7x\\or\\4xy+y=7x-9\\y(4x+1)=7x-9\\y=\frac{7x-9}{4x+1} \\or~f^{-1}(x)=\frac{7x-9}{4x+1}[/tex]
HELP!
what is the y-intercept of the function f(x)=5*(1/6)^x
Answer:
The y intercept is (0,5)
Step-by-step explanation:
f(x) = 5 * (1/6)^x
What is the y intercept? Let x = 0
f(0) = 5 * (1/6)^0
f(0) = 5*1 = 0
The y intercept is (0,5)
7) 5(r + 2) = 8 + 57
Step-by-step explanation:
5r + 10 = 65
5r =65 - 10
r = 55/5
r = 11
Answer:
r=11
Step-by-step explanation:
you first have to work with the brackets and then group the like terms
5(r+2)=8+57
5r+10=65
5r/5=65-10
5r/5=55/5
r=11
I hope this helps
help pls I need answer to question (e)
Answer:
I assume you'd already figured out the other questions so you just don't understand the question E
Step-by-step explanation:
The product of the first 2 numbers its stating is -28 and 48, and it's asking if the product (multiply -28 by 48 to get the product) is equal to the HCF and LCM you got in the previous answer.
Which inequality is represented by the graph?
Y>-2/3x+1
Y<-2/3x+1
Y<-3/2x+1
Y>-3/2x+1
Answer:
Last option, y > -3/2x+1
That's the answer you're looking for
Surface area of triangular prism
Answer:
264 Km²
Step-by-step explanation:
cross sectional perimeter of the triangular prism= 9+8+7= 24Km
now,
total surface area= C.S.P × height of the figure
= 24 × 11
= 264 km²
PLease help Qwq it precalc
Answer:
1) x= -7/5
Step-by-step explanation:
−5x-7=0
-5x=7
x=-7/5
Answer:
D
Step-by-step explanation:
To find the zero let y = 0 , that is
- 5x - 7 = 0 ( add 7 to both sides )
- 5x = 7 ( divide both sides by - 5 )
x = [tex]\frac{7}{-5}[/tex] = - [tex]\frac{7}{5}[/tex] → D
Expand the following
(x+2x)(2s-2t)
(m-n)²
(k+9)²
(4a-3b)(c+6d)
please check the attachment for solutions
Select 2 strategies that we can use to subtract 563-192
A. Add 100 + 90 + 2
B. Evaluate (563 - 200) + 8
C. Subtract 571 - 200
Answer:
B and C
Step-by-step explanation:
A = 192
B = (563 - 200) + 8 = 371
C = 571 - 200 = 371
3x – (7x + 2) > 5x + 4
Answer:
x < -2/3Step-by-step explanation:
3x – (7x + 2) > 5x + 4= 3x -7x - 2 > 5x + 4= -4x - 2 > 5x + 4= -4x -5x > 4 + 2 = -9x > 6= x < -2/3[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
