# Calculate the moments Mx, My, and the center of mass (x bar, y bar) of a lamina with the given density p=5 and the shape:

f ( x ) = √( 1 - x²), g ( x ) = - 2

= - 50/3

My = p ∫ x * ( f ( x ) ) dx

My = p ∫ x ( √(1+x²)) dx

Substitution: 1 - x² = u, x dx = - du/2

**M x = - 50/3, M y = 0**

M ≈ 5 * 6.3 ≈ 31.2

x = M y / M = 0 / 31.5 = 0

y = M x / M = -50/3 : 31.5 ≈ - 0.529

The center of mass is

**( 0, -0.529 )**

## Related Questions

**Answer: **C) The image is along the same ray as the preimage but is closer to the center of dilation.

(x + p)(x + q)

x^2 + px + 1x +pq

x^2 +

**(p+q)x**+ pq

Hope this answers the question. Have a nice day.

The Factor theorem states that for any polynomial f(x) if f(c)=0 then x-c is a factor of the polynomial f(x).

If any polynomial f(x) is divided by x-a and remainder is 0 that means f(a)= 0 .In other words we can say x-a is a factor of the polynomial f(x).So the statement :If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial is True.

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For f(x)=2x+1 and g(x)=x^2-7, find (f-g)(x)

(f-g)(x)=2x+1-(x^2-7)

(f-g)(x)=2x+1-x^2+7

(f-g)(x)= -x^2+2x+8

What is f(x) = 2x2 + 28x – 5 written in vertex form?

f(x) = 2x^2 + 28x – 5

f(x) = 2(x^2 + 14x) – 5

f(x) = 2(x^2 + 14x + 49) – 5 - 98

**f(x) = 2(x + 7)^2 – 103**

Hope this answers the question. Have a nice day.

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Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

average rate of change is

(f(5) - f(1))/(5 - 1) =

(17 - 5^2 - (17 - 1^2))/4 =

(17 - 25 - 17 + 1)/4 =

So the answer for this problem is

**-6**

I hope my answer helped you. Feel free to ask for more questions.

The **real** answers are **A** and **D**, but not C

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f(x) = P(1 + r)^x

Now we can solve.

Given:

P = 2000

r = -0.06

f(x) = 2000 (1 - 0.06)^x

= 2000 (0.94)^x

2000 (0.94)¹² =

2000 (0.476) =

The answer is

**951.8 square kilometers.**

**The answer is**

BThe vertex of the graph is (5, –37).

B

**The parabola has a minimum.**

C

C

**D**The parabola opens up.

What is the range of the function f(x) = 3x2 + 6x – 9

f(x)=3x^2-6x+1

My solution is:

The domain is all real numbers--there are no restrictions like a square root or variable in the denominator

this is a U shape parabola and you want to find the bottom point, it is at the vertex

x=-b/2a =- (-6) /2 (3) =1

f(1) =3(1)^2 -6(1) +1 =3-6+1 =-2

the minimum is (1, -2)

so the range is all real numbers >= -2

By examining my solution, you could just answer the problem on your own! I hope it helps!

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**Answer:**

D

**Step-by-step explanation:**

She showed that f(n) - f(n - 1) was a constant difference.

The definition of an arithmetic sequence is** the difference between consecutive terms is constant, aka common difference.**

Calculate the length of the circumference of a circle with a diameter of 7 cm

**1) The answer is: [B]: r = 5 .**

**__________________________**

**Explanation:**

**___________**_______________

Given: 7r − 7 = 2r + 18 ; Round your answer to the nearest tenth, if necessary.

____________________________

Since "r" is the only variable given, let us assume we want to solve for "r" (instead of "x").

___________________________

→ Subtract "2r" from EACH SIDE of the equation; and & add "7" to EACH SIDE of the equation:

_____________

→ 7r − 7 − 2r + 7 = 2r + 18 − 2r + 7 ; to get: → 5r = 25 ;

_____________

→ Now, divide EACH SIDE of the equation by "5"; to isolate "r" on one side of the equation; and to solve for "r" :

______________

→ 5r / 5 = 25 / 5 → r = 5 → which is: "Answer choice: [B]".

_________________

**Let us check our answer, by plugging in "5" for "r" in the original equation:**

_________________

→ 7r − 7 = 2r + 18 ; → 7(5) − 7 =? 2(5) + 18? ;

______________________

→ 35 − 7 =? 10 + 18 ?; → 28 =? 28? Yes!

______________________

**2) The answer is: [D]: x = 2 .**

**_____________**

**Explanation:**

_____________

Given: 2x + 12 = 18 − x ; Solve for "x" (round to nearest tenth, if necessary).

_______________

→ Add "x" to EACH SIDE of the equation, & subtract "12" from EACH SIDE of the equation: → 2x + 12 + x − 12 = 18 − x + x − 12 ;

______________

→ To get: 3x = 6 ; → Divide EACH SIDE of the equation by "3";

to isolate "x" on one side of the equation; and to solve for "x":

_____________

→ 3x / 3 = 6 / 3 ; → x = 2 ; which is: "Answer choice: [D]".

______________

**Let us check our answer, by plugging in "2" for "x" in the original equation:**

________________

→ 2x + 12 = 18 − x ; → 2(2) + 12 =? 18 − 2 ?

________________

→ 4 + 12 =? 18 − 2 ? ; → 16 =? 16? Yes!

________________________________

**3) The answer is: [A]: x = -3 .**

**_____________**

**Explanation:**

________________

Given: 8x − 3 = 15x + 18 ; Solve for "x". Round your answer to the nearest tenth, if necessary.

_________________

→ Subtract "8x" from EACH SIDE of the equation, & add "3" to EACH SIDE of the equation:

_______________

→ 8x − 3 − 8x + 3 = 15x + 18 − 8x + 3 ; to get:

_______________

→ 0 = 7x + 21 ; → Subtract "21" from EACH SIDE of the equation;

_______________

→ 0 − 21 = 7x + 21 − 21 ; to get:

_______________

→ -21 = 7x ; Now divide EACH SIDE of the equation by "7";

to isolate "x" on one side of the equation; & to solve for "x":

_______________

→ = -21 / 7 = 7x / 7 ; → -3 = x ; which is "Answer choice: [A]."

**_________________**

**Let us check our answer, by plugging in "-3" for "x" in the original equation:**

________________

→ 8x − 3 = 15x + 18 ; → 8(-3) − 3 =? 15(-3) + 18 ?;

________________________

→ -24 − 3 =? -45 + 18 ? ; → -27 =? -27? Yes!

**___________________________**

**4) The answer is: [C]: y = 11 .**

**_____________**

**Explanation:**

**____________**

Given: 6y − 6 = 4y + 16 ; Solve for "y"; Round to the nearest tenth, if necessary.

____________

(Note: Since "y" is the only variable given; assume we are to solve for "y" instead of "x").

____________

→ Subtract "4y" from EACH SIDE of the equation, & add "6" to EACH SIDE of the equation; → 6y − 6 − 4y + 6 = 4y + 16 − 4y + 6 ; to get:

_______________

→ 2y = 22 ; Now, divide EACH SIDE of the equation by "2"; to isolate "y" one side of the equation; and to solve for "y" ;

_______________

→ 2y / 2 = 22 / 2 ; → y = 11 → which is "Answer choice: [C]".

**_______________________________**

**Let us check our answer, by plugging in "11" for "y" in the original equation:**

**___________________**

→ 6y − 6 = 4y + 16 ; → 6(11) − 6 =? 4(11) + 16 ?

_______________________

→ 66 − 6 =? 44 + 16 ? → 60 =? 60 ? Yes!

**__________________**

**5) The answer is: [B]: x = -11 .**

**_____________________**

**Explanation:**

**_________________**

Given: 3(x − 4) = 5(x + 2) ; Solve for "x". Round to the nearest tenth, if necessary.

**___________**

**→Note the "distributive property of multiplication":**

**_____________**

**a*(b + c) = ab + ac ; and: a*(b − c) = ab − ac ;**

**_______________**

→ Let us expand EACH SIDE of our given equation.

→Start with the "left-hand side":

____________

3(x − 4) = (3*x) − (3*4) = 3x − 12;

______________________________

→Now let us expand the "right-hand side" of the given equation:

____________

→ 5(x + 2) = (5*x) + (5*2) = 5x + 10 ;

______________

→Now, we can rewrite the original equation:

_______________

→ 3(x − 4) = 5(x + 2) ; by substituting the expanded values for EACH SIDE of the question: → 3x − 12 = 5x + 10 ;

__________________

→ Subtract "3x" from EACH SIDE of the equation; and add "12" to EACH SIDE of the equation: → 3x − 12 − 3x + 12 = 5x + 10 − 3x + 12 ; to get:

________________

→ 0 = 2x + 22; → Now subtract "22" from EACH SIDE of the equation:

______________

→ 0 − 22 = 2x + 22 − 22 ; to get: → -22 = 2x ;

__________

→ Divide EACH SIDE of the equation by "2"; to isolate "x" on one side of the equation; & to solve for "x" ;

_____________

→ -22 / 2 = 2x /2 ; → -11 = x ; which is "Answer choice: [B]".

______________

**Let us check our answer, by plugging in "-11" for "x" in the original equation:**

**___________**

→ 3(x − 4) = 5(x + 2) ; → 3(-11 − 4) =? 5(-11 + 2) ? ;

_______________________

→3(-15) =? 5(-9) ? ; → -45 =? -45 ? Yes!

**_____________________________________________**

**Hope these answers and explanations are helpful. Best of luck!**

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Each vertex of the hexagon is translated 8 units left and 7 units down. So, the x-coordinate is 8 units smaller (x - 8), and the y-coordinate is 7 units smaller (y - 7).

Therefore (x, y) → (x - 8, y -7)

Graph passes through the point (-1, 0).

Therefore, x = -1 and y = 0.

This is the only equation which is true for x = -1 and y = 0.

Therefore, the solution is

Calculate the length of the circumference of a circle with a diameter of 4cm

2 π r and r is equal to 2 cm

I.e 12.5 cm

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Find sinx2, cosx2, and tanx2 from the given information.sin(x) = 513, 0° < x < 90°

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**Answer:**

**Option (a) is correct.**

** The radius of circle with equation is 2 units.**

**Step-by-step explanation:**

Given : The equation of circle as

We haave to determine the radiusof th circle whose equation is given as .

Consider the gicen equation

The standard equation of circle with centre (h, k) and radius r is given by

Thus, Comparing the gicen equation h = 7 , k = 10 and r = 2

**Thus, The radius of circle with equation is 2 units.**

What is (x-9)(x-8) simplified?

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Find the center and radius of the circle with equation (x+6)^2y+4)^2=36

Which function is the inverse of f(x) = 2x + 3? f-1(x) = –2x + 3 f-1(x) = 2x + 3

**Answer with Step-by-step explanation:**

Let f(x)=y

⇒ x=

f(x)=2x+3=y

⇒ 2x+3=y

⇒ 2x=y-3

⇒ x=(y-3)/2

⇒

Replacing y by x

⇒

Hence, inverse of the function f(x)=2x+3 is:

Coordinates of K point on original Figure are:

(-2,-3)

once we implement rule on this we get K':

K' ( -2+8,-3+5)

or

K' ( 6,2)

Answer is third option.

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f(x) = one fourth x2 or B

**Answer:**

The answer in the attached figure

**Step-by-step explanation:**

we have

we know that

The y-intercept is the value of the function when the value of x is equal to zero

The x-intercept is the value of x when the value of the function is equal to zero

Using a graphing tool-------> Find the intercepts of the function

see the attached figure

The y-intercept is

The x-intercepts are

therefore

the answer in the attached figure

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