An object is attached to a spring that is stretched and released. The equation d= -8COS(pi/6 t) models the distance, d, of the object in inches above or below the rest position as a function of time, t, in seconds. Approximately when will the object be 6 inches above the rest position? Round to the nearest hundredth, if necessary.
0 seconds
1.38 seconds
4.62 seconds
8 seconds

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )= \dfrac{3}{2} \sqrt{x} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)= \cfrac{- 3}{ {x}^{4} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)= \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

properties to be used here :

[tex]\qquad \tt \rightarrow \:\cfrac{d}{dx}( {x}^{ n } ) = n \sdot{x}^{n - 1} [/tex]

[tex]\large \textsf{Question : 1} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )[/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3}{2} - 1 } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3 - 2}{2} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{1}{2} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} \sqrt{x} [/tex]

[tex]\large \textsf{Question : 2} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - 3} } )[/tex]

[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 3 - 1} } [/tex]

[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 4} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{- 3}{ {x}^{4} } [/tex]

[tex]\large \textsf{Question : 3} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{{x}^{ \frac{1}{2} } } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - \frac{1}{2} } } )[/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ - \frac{1}{2} - 1} } [/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 1 - 2}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 3}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2{x}^{ \frac{ 3}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Law of sines

Explanation:

The law of sines states that the ratios of the sines of angles and their opposite sides are equal for all angles inside a triangle.

Step-by-step explanation:

hope you can understand

Answer: 0.68 or 13.92

Step-by-step explanation:

If the height is 47 meters, then the height, h, is equal to 47.

[tex]47=73t-5t^2\\\\5t^2 - 73t+47=0[/tex]

Using the quadratic formula,

[tex]t=\frac{-(-73) \pm \sqrt{(-73)^{2}-4(5)(47)}}{2(5)}\\\\\\t=\frac{73 \pm \sqrt{4389}}{10}\\\\\\ t=\frac{73+\sqrt{4389}}{10}, \frac{73-\sqrt{4389}}{10}\\\\\boxed{t \approx 0.68, 13.92}[/tex]

Answer:

Step-by-step explanation:

Comment

This is an arithmetic series. It has the following givens.

a = 27     The first term

d = - 2       The difference between one term and the one behind it.

n = quite small

Tn = a + (n - 1)*d

tn = 27 - 2n  + 2

tn = 29 - 2n

Answer:

C

Step-by-step explanation:

The horizontal line, y=2, is solid and shaded above, so it represents

[tex]y \geqslant 2[/tex]

The slanted line, y=x is dashed and shaded below, so it represents y<x.

Answer

Answer is A

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

R × S = 15 could be 5 × 3 = 15, 3 × 5 = 15

                               15 × 1 = 15, 1 × 15 = 15

S ×T =3 From our previous step we can see that S could be 1 or 3 or 5 or 15.

            Given that S×T =3, will make sense that S is 1 or 3

            If S is 1 then T is 3 and if S is 3 then T is 1, so multiplied will give 3.

T×V=7 From previous step we see that T could be 1 or 3.

           Since T×V = 7 it will make sense that T is 1, and therefore V is 7.

T ×V = 7,  S ×T =3, R × S = 15, R × V = ??

1 × 7 = 7,  S ×1 = 3, R × 3 = 15, 5 × 7 = ??

               3 ×1 = 3,  5 × 3 = 15, 5 × 7 = 35

Answer:

1.5kg

Step-by-step explanation:

The mean for the packages on day 1 will be:

= (1 + 8 + 1 + 12 + 1 + 11 + 7 + 6)/8

= 47/8

= 5.875

The mean for day 2 will be:

= (47 + 12)/8

= 59/8

= 7.375

The increase in mean:

= 7.375 - 5.875

= 1.5

Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.

According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.

Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.

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Answer:

A

Step-by-step explanation:

The line is shaded below, so we can eliminate B and D.

Also, the line has negative slope, so this eliminates C.

The inequality of the graph is y ≤ -3x + 3.

The correct option is A.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

The inequality graph has two points on the line (0, 2) and (2, -3).

And the shaded region of the graph is left to the line made by points (0, 2) and (2, -3).

The line passing through the points (0,2) and (2,-3) can be written in a slope-intercept form as:

y = mx + b

where m is the slope and b is the y-intercept.

The slope of the line is given by:

m = (y2 - y1) / (x2 - x1) = (-3 - 2) / (2 - 0) = -5/2

The y-intercept can be found by substituting the coordinates of either point into the equation:

y = mx + b

2 = (-5/2)(0) + b

b = 2

So the equation of the line is:

y = (-5/2)x + 2

The shaded region of the graph is to the left of this line. Since the line has a negative slope, any point below the line will satisfy the inequality y ≤ -3x + 3. Therefore, the correct answer is A.

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The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.

We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:

Plug in the values into the equation of the function

0 = -16t² + 400

Solve for t

0 - 400 = -16t²

-400 = -16t²

-400/-16 = t²

400/16 = t²

√(400/16) = t

20/4 = t

5 = t

t = 5

The number of seconds it takes is: 5 seconds.

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For every meter there are 3.281 feet. The perimeter of the yard is 188ft. Divide 188 by 3.281 and you get 57.3 (rounded to 1dp). Round that up to the nearest meter and you get 58. So, Mr Smith needs 58 meters of fencing for his yard.

Answer:

$5.50

Step-by-step explanation:

For one water bottle you divide the 55 dollars by 10

55/10= 5.5

Answer:

$5.50

Step-by-step explanation:

We must divide to solve so lets do that now :)

55/10 = 5.50

Each bottle will cost 5 dollars and 50 cents :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

Step-by-step explanation:

This question deals with Slope of a line.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet

Thus, slope =  6/4 = 3/2 ≈ 1.5

For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet

Thus, slope=   10/6 = 5/3 ≈ 1.66

Thus,

Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3

Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

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Answer:

[tex]3x-1[/tex]

Step-by-step explanation:

The formula to find the area of a triangle:

[tex]A = \frac{bh}{2}[/tex]

Here, [tex]A[/tex] is the area, [tex]b[/tex] is the base and [tex]h[/tex] is the height.

However, we are looking for height, so let's rearrange the equation for [tex]h[/tex]:

[tex]A = \frac{bh}{2}\\2A = bh\\h = \frac{2A}{b}[/tex]

Now we know the formula to find the height, let's do so:

[tex]h = \frac{2(18x-6)}{12}\\\\h = \frac{36x-12}{12}\\\\h = 3x - 1[/tex]

Therefore, our final answer is [tex]3x-1[/tex].

The measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the length of AD is 12 units.

It is defined as the law to prove that the two 2-dimensional have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

Triangle ABC ~ EDC

Angle ACD = Angle BCE = 90 degree  (vertically opposite angle)

Angle ACB = Angle DCE = 90 degree  (vertically opposite angle)

BE ║ AD

Angle EBC = Angle CDA = 40 degree  (alternative angles)

Triangle ABC ~ Triangle EDC

Angle ABC = Angle CDE

Angle BAC = Angle DEC

∴ AB ║ DE

Triangle ACD ~ Triangle ECB

Angle EBC = Angle CDA and

Angle BEC = Angle CAD

∴ Triangle ACD ~ Triangle ECB

Angle A + Angle E = 180 degree

∠x + 50 + 50 + ∠x = 180

∠x = 40

Angle CAD = 40 degree

We know,

Angle A = Angle E = Angle B = Angle D = 90 degree

So ABCD is a square

AB = ED = 12

AD = AB  = BE = ED = 12

Thus, the measure of the angle CAD is 40 degrees, the length of ED is 12 units, and the Length of AD is 12 units.

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Answer:

Step-by-step explanation:

The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.

Diagonal = 5 * 2 = 10

P = 2√2 * 10

P = 20√2

Step-by-step explanation:

via the distance formula (based on Pythagoras) I can prove that ABC is a right-angled triangle, and that ADC is fully congruent to ABC.

so, together these 2 triangles (joined at their Hypotenuses, the diagonal AC) build a rectangle.

Answer:

18.18%

Step-by-step explanation:

(65000-55000)/55000×100

By the binomial theorem,

[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]

where

[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]

is the so-called binomial coefficient.

The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have

[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]

but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]

Answer:

(n/m) - p

Step-by-step explanation:

Image attached

Answer:

A

Step-by-step explanation:

First, simplify the numerator:

[tex]\frac{3 }{\sqrt{3} + \sqrt{x} } \\[/tex]

Next, multiply the numerator and denominator by the opposite of the denominator to rationalize the expression.

[tex]\frac{3}{\sqrt{3}+\sqrt{x} }*\frac{\sqrt{3}-\sqrt{x} }{\sqrt{3}-\sqrt{x}}[/tex]

Finally, evaluate the denominator by multiplying them together.

[tex]\frac{3(\sqrt{3}-\sqrt{x})} {(\sqrt{3}+\sqrt{x})(\sqrt{3}-\sqrt{x})}[/tex]

Simplify:

[tex]\frac{3(\sqrt{3}-\sqrt{x})} {3-x}[/tex]

And done! :)

From calculations, we can say that the given tiles will not fit together perfectly.

If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.

Expression for the measure of the interior angle of a polygon,

Interior angle of a polygon = [(n - 2) * 180]/n

Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°

Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°

Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°

To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°

Sum of all interior angles = 108° + 120° + 135° = 363°

Therefore, given tiles will not fit together perfectly.

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The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

As per the law of cosine, the measure of angle x can be written as,

[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]

Hence, the value of x is 117.8°. thus, the correct option is A.

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Answer:

In the circle, the measure of the arc AC is 21°.

Step-by-step explanation:

Concept: We can use the Inscribed Angle theorem to get the measure of AC.

Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.

Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.

So,

3x - 1.5 = 0.5(3x + 9)

6x - 3 = 3x + 9

3x = 12

x = 4

Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,

intercepted arc AC is 21°.

Hence the intercepted arc AC is 21°.

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Answer:

See attached file for answers and explanation.

Step-by-step explanation:

See attached image.

To design a simulation for this situation, one can generate a set of four numbers by using the number generator with numbers 0 to 5 representing those who prefer watching a movie at a theatre and 6 to 9 representing those who do not.

From the information given about the probability, the goal here is to design a simulation for this situation.

In this case, to design a simulation for this situation, one can generate a set of four numbers by using the number generator.

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