An object moves in simple harmonic motion with period 8 minutes and amplitude 12m. At time =t0 minutes, its displacement d from rest is −12m, and initially it moves in a positive direction.


Give the equation modeling the displacement d as a function of time t

Answer:

B. Domain is left to right so the left point is solid on 2 and the right is solid on 8. The solid point means it can also be equal to.

Answer:

B) {x : 2 \(\leq\) x \(\leq\) 8 }

Step-by-step explanation:

The function of the graph's x values are between 2 and 8, but the dots at the ends of the function are closed, hence the answer is

2 \(\leq\) x \(\leq\) 8

The volume of region bounded by z = x2 y2 and z = 10 - x2 - 2y2 is ∞.

To find the volume of the region bounded by the surfaces z = x^2 y^2 and z = 10 - x^2 - 2y^2, we can use triple integrals in cylindrical coordinates.

First, we need to find the limits of integration.

The surfaces intersect at the boundary where z = x^2 y^2 = 10 - x^2 - 2y^2.

Rearranging the equation gives us x^2 + 2y^2 + x^2 y^2 - 10 = 0.

This can be factored as (x^2 + 1)(y^2 + 2) - 12 = 0.

Thus, we have two curves: x^2 + 1 = 0 and y^2 + 2 = 0.

However, neither curve is possible because we cannot take the square root of a negative number.

Therefore, there is no boundary and the region is unbounded.

To set up the triple integral,

we can use cylindrical coordinates: x = r cos(θ), y = r sinθ), and z = z.

The Jacobian is r, so the volume is given by:

V = ∫∫∫ r dz dr dθ

The limits of integration for r and θ  are 0 to infinity and 0 to 2π, respectively.

The limit for z is from the surface z = x^2 y^2 to z = 10 - x^2 - 2y^2.

However, since there is no boundary, we can integrate from z = 0 to z = infinity.

Thus, we have:

V = ∫∫∫ r dz dr dθ from 0 to infinity for z, 0 to infinity for r, and 0 to 2π for theta.

Evaluating the integral gives us:

V = ∫0^2π ∫0^∞ ∫0^∞ r dz dr dθ = ∞

Therefore, the volume of the region bounded by the surfaces z = x^2 y^2 and z = 10 - x^2 - 2y^2 is infinity.

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H does not satisfy all three properties required for a subspace, we can conclude that H is not a subspace of R2.

The set H is a subspace of R2, we need to check if it satisfies the three properties required for a subspace

1. The zero vector is in H.

2. H is closed under vector addition.

3. H is closed under scalar multiplication.

Now each property

1. The zero vector (0, 0) is in H since it lies on the unit circle.

2. To check closure under vector addition, suppose we have two vectors (x₁, y₁) and (x₂, y₂) in H. If we add them together, (x₁, y₁) + (x₂, y₂), the resulting vector will not necessarily lie on the unit circle. For example, if we add (1, 0) and (-1, 0), the result is (0, 0), which is not on the unit circle. Therefore, H is not closed under vector addition.

3. To check closure under scalar multiplication, suppose we have a scalar c and a vector (x, y) in H. If we multiply them, c × (x, y), the resulting vector will not necessarily lie on the unit circle. For example, if we multiply (1, 0) by 3, the result is (3, 0), which is not on the unit circle. Therefore, H is not closed under scalar multiplication.

Since H does not satisfy all three properties required for a subspace, we can conclude that H is not a subspace of R2.

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Answer:

13/4

Step-by-step explanation:

We do reciprocal of 1/13 it will be 13/1 after we multiply last answer 13/4

Answer:

3 1/4

Step-by-step explanation:

\( \frac{1}{4} \div \frac{1}{13} \\ \\ = \frac{1}{4} \times \frac{13}{1} \\ \\ = \frac{1 \times 13}{4 \times 1} \\ \\ = \frac{13}{4} \\ \\ = 3 \frac{1}{4} \\ \)

Answer:

180 pesos

Step-by-step explanation:

divide 900 by 5

Answer:

The first input (-3.2, 10.3)..... 2nd input (0.7, 3.6)

Step-by-step explanation:

The first input:             4.3 - 7.5 = -3.2   = the x

    (-3.2, 10.3)                3.5 + 6.8 = 10.3    = the y

The 2nd input:

                             8.2 - 7.5 = 0.7 .  = the x

    (0.7, 3.6)          -3.2 + 6.8 = 3.6   = the y

Mark brainliest if this helped! <3

Step-by-step explanation:

Find 100% of the price:

100 - 15 = 85% (Sale price)

85% = 136

1% = 136 divide 85 = 1.6

100% = 1.6 x 100 = 160

Ans: £160

Answer:

Aonnalin, great name  :)  answer as below

Step-by-step explanation:

They tell us to use slope-intercept form.   This is something you will just have to remember  y = mx+b    

It is confusing b/c there is the other one, the point-slope formula too.  but just remember both and know that the point-slope one is to get to the slope-intercept one.    y-y1 = m(x-x1)  

m= slope

m = (y2-y1) / (x2-x1)

P1= (0,7)  in the form (x1,y1)

P2 =(8,-2) in the form (x2,y2)

m = -2-7 / 8-0

m = -9 / 8

now that we have the slope, just use either point with the point-slope

y-7 = (-9/8)(x-0)

y-7 = -9x/8

y = -9x/8 + 7

y = \(\frac{-9}{8}\) X + 7

slope-intercept form  :)

Answer:

Step-by-step explanation:

tru i took the test

The one critical point at (0, 0).

The critical point (0, 0) is a saddle point, and the critical point (-9, -3) is a relative minimum.

To find the critical points of the given function f(x, y) = x^2 - 6xy - 2y^3, we need to find the points where the partial derivatives with respect to x and y are equal to zero.

Calculate the partial derivative with respect to x (f_x):

f_x = 2x - 6y

Calculate the partial derivative with respect to y (f_y):

f_y = -6x - 6y^2

Set both partial derivatives equal to zero and solve the system of equations:

2x - 6y = 0 ---(1)

-6x - 6y^2 = 0 ---(2)

From equation (1), we can rearrange it to solve for x:

2x = 6y

x = 3y

Substituting x = 3y into equation (2):

-6(3y) - 6y^2 = 0

-18y - 6y^2 = 0

-6y(3 + y) = 0

Now, we have two possible cases:

a) -6y = 0

b) 3 + y = 0

a) -6y = 0

This implies y = 0

Substituting y = 0 into equation (1):

2x - 6(0) = 0

2x = 0

x = 0

So, we have one critical point at (0, 0).

b) 3 + y = 0

This implies y = -3

Substituting y = -3 into equation (1):

2x - 6(-3) = 0

2x + 18 = 0

2x = -18

x = -9

So, we have another critical point at (-9, -3).

Now, to classify each critical point as a relative maximum, relative minimum, or a saddle point, we need to analyze the second-order partial derivatives.

Calculate the second partial derivative with respect to x (f_xx):

f_xx = 2

Calculate the second partial derivative with respect to y (f_yy):

f_yy = -12y

Calculate the mixed partial derivative (f_xy):

f_xy = -6

Now, evaluate the discriminant D = f_xx * f_yy - (f_xy)^2 at each critical point:

For the critical point (0, 0):

D = f_xx * f_yy - (f_xy)^2

= 2 * (-12 * 0) - (-6)^2

= 0 - 36

= -36

For the critical point (-9, -3):

D = f_xx * f_yy - (f_xy)^2

= 2 * (-12 * -3) - (-6)^2

= 72 - 36

= 36

Analyzing the discriminant:

For the critical point (0, 0):

If D < 0, it is a saddle point. In this case, D = -36, so (0, 0) is a saddle point.

For the critical point (-9, -3):

If D > 0 and f_xx > 0, it is a relative minimum. In this case, D = 36 and f_xx = 2, so (-9, -3) is a relative minimum.

Therefore, the critical point (0, 0) is a saddle point, and the critical point (-9, -3) is a relative minimum.

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Answer:

3x+7

  3

Step-by-step explanation:

(3x-7) × (3x+7) × ____2x+4_____

         6                     3x∧2-x-14

(3x-7) × (3x+7) × ____2(x+2)_____

         6                 3x∧2 × 6x-7x-14

(3x-7) × (3x+7) × _____x+2_______

         3                  3x × (x+2)-7(x+2)

(3x-7) × (3x+7) × _____ x+2_______

         3                     (x+2) × (3x-7)

3x+7

  3

Hope this helps! :)

Answer:

we have

radius[r]=9ft

height [h]=8ft

now

Volume of cone =1/3×πr²h=1/3×π×9²×8=678.584ft³

The aspect ratio/length of a ping pong table which is 108 inches long and five feet wide is 1.8

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Length = 108 inches, width = 5 ft = 60 in

Aspect ratio = longer dimension / shorter dimension = 108 in / 60 in = 1.8

The aspect ratio/length of a ping pong table which is 108 inches long and five feet wide is 1.8

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There are 62 number of ways in which classes to these students can be assigned. It can be solved by using the fomula of combination.

What is the formula of combination?

Following is the fomula of combination:

\(^nC_r=\frac{n!}{r!(n-r)!}\)

Here, n is the total objects available and r is the number of object need to choose from n objects.

Let six friends are A, B, C, D, E, and manoj.

Consider all 6 friends are in chemistry class. Hence, number of ways in which it can be is,

\(^6C_6\)

Consider 5 friends are in chemistry class. Hence, number of ways in which it can be is,

\(^6C_5\)

Consider 4 friends are in chemistry class. Hence, number of ways in which it can be is,

\(^6C_4\)

Consider 3 friends are in chemistry class. Hence, number of ways in which it can be is,

\(^6C_3\)

Consider 2 friends are in chemistry class. Hence, number of ways in which it can be is,

\(^6C_2\)

Consider 1 friend is in chemistry class. Hence, number of ways in which it can be is,

\(^6C_1\)

Consider no friend is in chemistry class all are in biology class. Hence, number of ways in which it can be is,

\(^6C_0\)

Hence, total number of ways in which classes can be assigned to 6 students is,

\(^6C_6+^6C_5+^6C_4+^6C_3+^6C_2+^6C_1+^6C_0=64\)

Now, the number of ways in which mnoj is alon. There are two ways. Either he will be in the chemistry class or he will be in the physics class.

Hence, subtract 2 from 64 to get the answer.

\(64-2=62\)

Hence, there are 62 number of ways in which classes to these students can be assigned.

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Answer:

C. 7

Step-by-step explanation:

4 * Sum (i = 1 to 3) (1/2)^(i - 1) =

= 4 * [(1/2)^0 + (1/2)^1 + (1/2)^2]

= 4 * [1 + 1/2 + 1/4]

= 4 * [7/4]

= 7

Answer:

7

Step-by-step explanation:

because I'm smart like that

Answer:

the answer is C

Step-by-step explanation:

just divide 42.75 by 9

Answer:    phythagorean therorem??

Step-by-step explanation:  

a^2 + b^2 = c^2

does that help or do you need more help?

Answer:13.5

Step-by-step explanation:

13.5

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

The graph of the inequality is the third one, counting from the top.

Here we have the following inequality:

(1/2)n + 3 < 5

First we need to isolate the variable, we will get:

(1/2)n + 3 < 5

(1/2)n < 5 - 3

(1/2)n < 2

n < 2*2

n < 4

So we will have an open circle at n = 4, and an arrow that goes to the left (because n is smaller than 4).

Then the correct number line is the third one, counting from the top.

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The given statement is true.

Consider linearly independent vectors of \(R_{n}\)

Where n = 2

\(V = \[\begin{array}{ccc}4&\\2\end{array}\right]\)  

\(U = \[\begin{array}{ccc}5&\\6\end{array}\right]\)

Now product of these vectors

UV = 4x5 + 2x6

     = 32

Hence these vectors are not orthogonal.

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Answer:

1. I believe some solutions could be x= -7, x= -8, x= -9 etc.

Step-by-step explanation:

2. If the inequality was -3x is greater than or equal to 18 then x and also be equal to x=6.

here we can clearly see that the graph intersect both the x-axis and y-axis at points mention below :

{ (3,0),(0,-1),(-3,-2),(-6,-3),(6,1) }

we need to check these points for each equation whether they satisfy or not.

now we consider the first equation--

on putting points (3,0) in equation first

0=3*3-1 (not correct)

now we consider second equation--

on putting points (3,0) in equation second

0=3*3+1 (not correct)

now we consider third equation--

on putting points (3,0) in third equation

0=(1/3*3)-1 results(0=0)(correct)

checking point(0,-1) on third equation

-1=(1/3*0)-1 result(-1= -1)(correct)

checking point(-3,-2) on third equation

-2=1/(3*-3)-1 results(-2= -2)(correct)

checking point(-6,-3) on third equation

-3=1/(3*-6)-1 results(-3= -3)(correct)

checking point(6,1) on third equation

1=1/(3*6)-1 results(1=1)(correct)

now we consider fourth equation-----

checking point(3,0)

0= - 1/3*3+1 result (0=0)(correct)

checking for point (0,-1)

-1=-1/3*0+1 (not correct)

now we can clearly say that only third equation satisfied all the points

so third equation is the function that is graphed as line a.

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The rectangular form of 6{(cos225°) +i(sin225°) }is -3√2-3i√2.The shape that complex numbers typically take is referred to as rectangle form: z = a + bi.

Polar notation depicts a complex number in terms of the lengths of the vector and the angular direction from the starting point. In rectangle notation, a complex number is represented by its vertical and horizontal dimensions. The system is referred to be rectangular because the angles made by the axes at the origin and the measurements at point p are both 90 degrees. As a result, the measurement results in a rectangle with sides Xp and Yp.

To determine  rectangular form, we obtain,

Let Z=6{(cos225°) +i(sin225°)}

Now, cos225°=-cos( 180°+45°)= -cos45°= -\(\frac{1}{√2}\)

sin225°=-\(\frac{1}{√2}\)

S0, 6{(cos225°) +i(sin225°)}= 6 ( -\(\frac{1}{√2}\))+6i(-\(\frac{1}{√2}\))=-3√2-3i√2.

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Answer:

A

Step-by-step explanation:

right on edge

Answer: 0.35

Step-by-step explanation:

3.325 divided by 9.5 = 0.35

Answer:

its b .

Step-by-step explanation:

Answer:

You have to make h the subject using volume of cone formula :

\(v = \frac{1}{3} \times \pi \times {r}^{2} \times h\)

\(3v = \pi {r}^{2} \times h\)

\( \frac{3v}{\pi {r}^{2} } = h\)

\(h = \frac{3v}{\pi {r}^{2} } \)

The square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500 square mils.

To find the square mil area for a 2 inch wide by 1/4 inch thick copper busbar, we need to multiply the width and thickness of the busbar in mils.

1 inch = 1000 mils

So, the width of the busbar in mils = 2 inches x 1000 mils/inch = 2000 mils

And, the thickness of the busbar in mils = 1/4 inch x 1000 mils/inch = 250 mils

Therefore, the square mil area of the copper busbar = width x thickness = 2000 mils x 250 mils = 500,000 square mils.

Hence, the square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500,000 square mils.

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Answer:

Use this image for help and reference

Hopefully this helps:)

THE FORMULAE OF HEMISPHERE : V = 2/3 * π * r³

Step-by-step explanation:

Put the formulae of hemisphere,

V = 2/3 * π * r³

Put the values in the formulae,

= 2/3 × 3.14 × 9³

= 0.6666 × 3.14 × 729

= 2.09312× 729

= 1525.8m³ ans

→ value of π (pie) is 3.14

→ formulae of radius is d/2 = 18/2 = 9 in