An object is attached by a string to the end of a spring. Fang throws the object upwards and starts a stopwatch at t=0t=0t, equals, 0 seconds. The object starts oscillating vertically in a periodic way that can be modeled by a trigonometric function.
The object's average height is -20\text{ cm}−20 cmminus, 20, start text, space, c, m, end text (measured from the top of the spring). It first achieves that average height on the way up at t=0.2t=0.2t, equals, 0, point, 2 seconds, and then again every 222 seconds. The object's maximum and minimum heights are each 5\text{ cm}5 cm5, start text, space, c, m, end text from its average height.
Find the formula of the trigonometric function that models the height HHH of the weight ttt seconds after Fang started the stopwatch. Define the function using radians.
\qquad H(t) =H(t)=H, left parenthesis, t, right parenthesis, equals
What is the height of the object after 0.60.60, point, 6 seconds? Round your answer, if necessary, to two decimal places.

Answer:

I solved the first question. Hope this helped you and can solve other by yourself.

Answer:

Associative property

Step-by-step explanation:

have fun

Given is an A.P. in which -

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = a_2-a_1[/tex]

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 7-2 [/tex]

[tex]\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad = 5[/tex]

nth term of an A.P ,is given by-

[tex]\green{ \underline { \boxed{ \sf{a_n =a+(n-1)d }}}}[/tex]

where

Putting n = 46

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + (46-1)\times 5 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 45\times 5 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 2 + 225 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies \sf a_{46}= 227 \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Therefore, the 46th term is 227

Hence, the [tex]46th[/tex] term is [tex]227[/tex].

What is the sequence?

A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.

Here given sequence is

[tex]2,7, 12,...[/tex]

Here,

[tex]a=2[/tex]

[tex]d=a_2-a_1\\d=7-2\\d=5[/tex]

The general formula of the sequence is

[tex]a_n=a+(n-1)d[/tex]

where,

[tex]a_n=[/tex] nth term

[tex]a[/tex] is the first term

[tex]d[/tex] is the common difference

[tex]n[/tex] is the number of terms

Now substituting the values in general formula is

[tex]a_{46}=2+(46-1)5\\\\a_{46}=2+(45)5\\\\a_{46}=2+225\\\\a_{46}=227\\[/tex]

Hence, the [tex]46th[/tex] term is [tex]227[/tex].

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The area of the ground floor after it has been reduced to the nearest tenth is 10,681,800 square foot.

In order to determine the area of the ground floor after it has been reduced, the area of the floor has to reduced by 6.3%.

Area that was reduced = 6.3% x 11,400,000 = 718,200

New area = 11,400,000 - 718,200 = 10,681,800 square foot

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Step-by-step explanation:

mean = sum of all data points / number of data points

(1.3+1.5+2.2+2.2+2.8)/5 = 10/5 = 2

median is the number where half of the other data points are smaller or equal, and the other half are larger or equal.

median = 2.2

mode is the data point occurring most often = 2.2

range is the difference between largest and smallest data point : 2.8 - 1.3 = 1.5

A geometric sequence has a common ratio.

The formula for the nth term is

[tex]\sf{a_n =ar^{n-1} }[/tex]

where,

Given -

To find -

Solution -

A.T.Q, a = 2 and r = -2

[tex]\rightarrow\sf{a_{12} =2(-2)^{12-1} }[/tex]

[tex]\rightarrow\sf{a_{12 }=2(-2)^{11} }[/tex]

[tex]\rightarrow\sf{a_{12} =2×(-2048) }[/tex]

[tex]\rightarrow\bf{a_{12 }=-4096 }[/tex]

Hence, the 12th term is -4096.

Answer:

Step-by-step explanation:

Area = 1/2 b h

= 1/2 * 4 * 5

= 10 unit^2.

Answer:

you just have to do it yourself

Using the two given solutions and the general absolute value function we will get:

|x + 9|  = 27

The two solutions are:

x = 0 and x = -18.

Remember that the absolute value equation is something like:

|x - a| = b

If we want to have these solutions, then:

|0 - a| = b

|-18 -a| = b

From the first one, we have:

|-a| = b

Replacing that on the second equation we get:

|-18 -a| = |-a|

Notice that if we take a = -9, then we have:

|-18 + 9| = |+9|

|-9| = |+9|

This is true, so a = -9.

Then we find the value of b:

|18 + 9| = b = 27

Then the absolute value equation is:

|x + 9|  = 27

If you want to learn more about absolute value equations, you can read.

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Answer:

slope is undefined

ex. a straight vertical line like x = 2 would have an undefined slope

Step-by-step explanation:

formula is

y2-y1 / x2-x1

-13 + 9 / -5 + 5

-4 / 0

slope is undefined

straight vertical line like x = 2 would have an undefined slope

undefined slope is the slope of any vertical line that goes up or down. There is no horizontal movement and hence the denominator is zero while calculating the slope. Thus the slope of the line is undefined.

cuemathcomgeometryundefinedslope

mathbootcampscom

the slope of a line passing through two points with the same x-coordinate, like (-5, -9) and (-5, -13), is undefined because the line is vertical and doesn't have a defined slope.

Slope (m) = (change in y) / (change in x)

In this case, you have two points: (-5, -9) and (-5, -13). The x-coordinates are the same (-5) for both points, which means there is no change in the x-coordinate. Therefore, the denominator in the slope formula becomes zero:

Slope (m) = (change in y) / (0)

When the denominator is zero, division is undefined in mathematics. This corresponds to a vertical line on a graph. A vertical line doesn't have a well-defined slope because it doesn't have a constant rate of change in the x-direction since the x-values don't change. Instead, the vertical line runs parallel to the y-axis.

So, the slope of a line passing through two points with the same x-coordinate, like (-5, -9) and (-5, -13), is undefined because the line is vertical and doesn't have a defined slope.

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Answer:   If you sketch this out, you should be able to convince yourself that if you drew a line parallel to the bases and halfway between them, and a vertical at the end of that line, there would be an extra triangle on the longer base that would just fit into the space at the end of the shorter base, if you cut and pasted it.

You should also be able to convince yourself by what you know about similarity that the length of that parallel halfway line is just halfway between the lengths of the bases (you can add them and divide by two).

So your trapezoid (trapezium, we call ’em this side of the pond) has the same area as a rectangle with an altitude equal to the trapezoid’s and a width equal to the sum of those bases divided by two. And since you know about rectangles, you’re home and dry. I suggest you do the sketch, fill in the numbers, and then you’ve completed a model piece of homework that should earn full marks and the teacher’s approval.

Step-by-step explanation:

Answer:

10.50

Step-by-step explanation:Harold deposited $70 in an account earning 5% interest compounded annually. To the nearest cent, how much interest will he earn in 2 years? Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Answer:

Area=½b×h

Area =½×20×8=80m²

hope it helps!

Answer:

P=67.38

Step-by-step explanation:

All three sides are given. You can use any one of the the three major functions on your calculator to g

Adjacent = PQ = 5

Hypotenuse = PR = 13

Cos(P)  = Adjacent / Hypotenuse

Cos(P) = 5/13

Cos(P) = .3846

Now you need to use the inverse cos to get P

P = cos-1(.3846)

P =67.38

=====================================

Now we'll try the tangent

Tan(P) = opposite / adjacent

Tan(P) = 12/5

Tan(P) =2.4

P = Tan-1(2.4)

P = 67.38

Both functions give the same thing

[tex]\\ \rm\Rrightarrow cosP=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow cosP=\dfrac{5}{13}[/tex]

[tex]\\ \rm\Rrightarrow cosP=0.38[/tex]

[tex]\\ \rm\Rrightarrow P=cos^{-1}(0.38)[/tex]

[tex]\\ \rm\Rrightarrow P=67.67°[/tex]

Hello!

Plug in the value of x:

f(x)=5(x-3)+17

f of x is 5 times the difference of x and 3 plus 17

plug in 2:

f of 2 is 5 times the difference of 2 and 3 plus 17

f(2)=5(2-3)+17

f(2)=5(-1)+17

f(2)=-5+17

f(2)=12

[tex]\huge\boxed{\mathfrak{Answer:{\boxed{\rm{f(2)=12\star\star}}}}}[/tex]

Hope everything's clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

#KeepOnLearning

[tex]\boxed{An~Emotional~Helper!} :-)[/tex]

Answer:

x=4 or x= -2

Step-by-step explanation:

(x-1)(x-1)

x(x-1)-1(x-1)

x^2-x-x+1

x^2-2x+1=9

x^2-2x+1-9=0

x^2-2x-8=0

p= -8

s= -2

1------ -8

2------ -4

x^2+2x-4x-8=0

x(x+2)-4(x+2)

(x+2)(x-4)=0

x+2=0

x-4=0

x= -2

or

x=4

Answer:

cups =15.99994. according to the holy bible.

Step-by-step explanation:

Answer:

c no

jskdha

shdjszdj

see

Answer:

8.2 is your answer.

Step-by-step explanation:

first you would add 22 and 19 together to get 41

then you divide by 5 to get your answer 8.2

22+19=41÷5=8.2

Answer: 147 Degrees

Step-by-step explanation

The size of the final unknown interior angle in a polygon is 147 degrees.

Given that,

The other interior angles are 162°, 115°, 120°, 148° and 85°.

We assume that there is an equation (2n - 4) 90.

Here n be 7.

Based on the above information, the calculation is as follows:

= (2n - 4) 90

= ((2) (7) - 4) 90

= 10 (90)

= 900

Now the size of the unknown interior angle is  

= 900-(162+125+148+105+98+115)

= 900 - 753

= 147°

Therefore we can conclude that the size of the final unknown interior angle in a polygon is 147 degrees.

The area of the vase lies between the area [tex]135\ cm^2[/tex] and [tex]155\ cm^2[/tex] will be [tex]153.86\ cm^2[/tex].

As we know that the area of the circle is given by the formula

[tex]A=\pi r^2[/tex]

So now from the question, we will find the radius for both the given areas.

Radius for the first area

[tex]r=\dfrac{A}{\pi} =\dfrac{135}{\pi} =6.56\ cm[/tex]

Radius for the second area

[tex]r=\dfrac{A}{\pi} =\dfrac{155}{\pi} =7.03\ cm[/tex]

Now we can see the range of the radius lies

[tex]6.56\leq r\leq 7.03[/tex]

The radius must be r=7 cm lie between two quantities.

Then the area at r= 7cm will be

[tex]A=\pi r^2[/tex]

[tex]A=\pi\times 7^2=153.86\ cm^2[/tex]

Thus the area for the vase will be [tex]A=153.86\ cm^2[/tex] ar radius r= 7 cm

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Answer:

34.54

Step-by-step explanation:

you do 2 * 3.14 * 5.

to find the area 2pie r the 3.14 comes from the directions, the 2 comes from the circle because the full length of the circle is 10 but you divide by 2 to get 5 and the 5 also comes from the circle and that is the radius.

Answer:

A.  168 units³

Step-by-step explanation:

volume = area of bas × height

volume = (6)(7)/2 × 8

volume = 168 units³

Answer:

  3800 tickets sold

Step-by-step explanation:

We know the number of people seated, and we know the percentage of total ticket sales that represents. So, we can find the total number of tickets sold.

  seated + not-arrived = total sold

  228 + 0.94 × total sold = total sold

  228 = 0.06 × total sold . . . . . . . . . . . . subtract 0.94 × total sold

  228/0.06 = total sold = 3800

There were 3800 tickets sold for the performance.

Answer:

24π inches

Step-by-step explanation:

The area of a circle is denoted by: , where r is the radius. Here, we know that the area is A = , so we can plug this in to find r:

A = [tex]\pi r^{2}[/tex]

[tex]144\pi = \pi r^{2}[/tex]

[tex]r^{2}[/tex] = 144

r = 12

The circumference is denoted by: , where r is the radius. We've found the radius so just plug 12 in for r:

Thus, the circumference is 24π inches.

Hope this helps!

Correct Question :

The area of a circle is 144π in². What is the circumference, in inches? Express your answer in terms of pi.

[tex] \: [/tex]

Step-by-step explanation:

Before finding the circumference of the circle, we have to find the radius of it.

We already know that,

[tex] \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \pi r{}^{2} = \: \: Area_{(circle)}}}}}} \: \: \bigstar \\ \\ [/tex]

So, using this formula we'll find the radius and now we'll substitute the given values :

[tex] \longrightarrow \qquad{ \sf{ \pi \times r{}^{2} = \: 144 \pi }} \\ \\[/tex]

Cancelling π from both sides we get :

[tex]\longrightarrow \qquad{ \sf{ \cancel\pi \times r{}^{2} = \: 144 \cancel\pi }} \\ \\[/tex]

[tex]\longrightarrow \qquad{ \sf{ r{}^{2} = \: 144 }} \\ \\ [/tex]

[tex]\longrightarrow \qquad{ \sf{ r{}^{} = \: \sqrt{144} }} \\ \\ [/tex]

[tex]\longrightarrow \qquad{ \sf{ \pmb{ r{}^{} = \: 12 }}} \\ \\ [/tex]

So,

[tex] \\ [/tex]

Now we'll find the circumference of the circle :

[tex] \\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Circumference_{(circle)} = 2 \pi r}}}}}} \: \: \bigstar \\ \\ [/tex]

Now, we'll substitute the required values in the formula :

[tex] \\ { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times \pi \times 12}}} \: \: \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times 12 \pi }}} \: \: \\ \\ [/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \pmb{ \: \: Circumference_{(circle)} = 24 \pi }}}} \: \: \\ \\ [/tex]

Therefore,

Answer:

Step-by-step explanation: