simplify the following expression
6a^4c+8ac^2-4a^4c-15-10ac^2

Answer: d=7 inches

r=7/2

r=3.5

A=πr²

A=3.14(3.5inch)²

A=3.14×12.25inch²

A=38.465inch²

A≈38.47inch²

Close the path by connecting D to A. Then by Green's theorem, the integral over the closed path ABCDA - which I'll just abbreviate C - is

[tex]\displaystyle \oint_C (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy \\\\ = \iint_{\mathrm{int}(C)}\frac{\partial(4x+y)}{\partial x} - \frac{\partial(\sin(x)+9y)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy[/tex]

(where int(C ) denotes the region interior to the path C )

The remaining double integral is -5 times the area of the trapezoid, which is

[tex]\displaystyle -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy = -\frac52\times(12+4)\times4=-160[/tex]

To get the line integral you want, just subtract the integral taken over the path DA. On this line segment, we have x = 0 and dx = 0, so this integral reduces to

[tex]\displaystyle\int_{DA}y\,\mathrm dy = \int_{12}^0y\,\mathrm dy = -\int_0^{12}y\,\mathrm dy = -72[/tex]

Then

[tex]\displaystyle \int_{ABCD} (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy = -160 - (-72) = \boxed{-88}[/tex]

Your answer is:

A) 0; it represents no correlation between x and y

keep dreaming

Answer:

Number of planes on the runway or waiting to take off is approximately 2

Step-by-step explanation:

Given the data in the question;

On average there are 21 planes taking off per hour

rate of flow = frequency of take off = 21 planes / hr

= 21 planes per 60 minutes

= 0.35 planes/min

Now, we get the throughput time

throughput time = total time for take off =  waiting time on runway + run time on runway

= (4 minutes and 21 seconds) + 27 seconds

= 4.35 minutes + 0.45 minutes

= 4.8 minutes

Now, using Little's law;

Number of planes on the runway or waiting to take off will be;

N = Rate of flow × throughput time

we substitute

N = ( 0.35 planes/min ) × 4.8 min

N = 1.68 planes ≈ 2 planes

Therefore, Number of planes on the runway or waiting to take off is approximately 2

Answer:

E(XY)=1/18

Step-by-step explanation:

x y P(x,y) xy*P(X,Y)

0 0 4/9 0

0 1 2/9 0

1 0 2/9 0

1 1 1/18 1/18

2 0 1/36 0

0 2 1/36 0

1 1/18

from above:

E(XY)=1/18

Answer:

1st row 56 pennies

2nd row 36 pennies

3rd row 14 dimes

4th row 4 quarters

5th row 5 nickels

Step-by-step explanation:

1st row $1.85 + 56 cents = $2.41

2nd row $2.05 + 36 cents = $2.41

3rd row is $1.01 + $1.40 = $2.41

4th row $1.41 + $1.00 = 2.41

5th row $2.16 + 25 cents = $2.41

Answer:

The man would be 40 years old.

Step-by-step explanation:

Blood pressure as function of age:

Is given by the following equation:

[tex]P = 0.006A^2 - 0.02A + 120[/tex]

Find the age of a man whose normal blood pressure measures 129 mmHg.

This is A for which P = 129. So

[tex]129 = 0.006A^2 - 0.02A + 120[/tex]

[tex]0.006A^2 - 0.02A - 9 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

Quadratic equation with [tex]a = 0.006, b = -0.02, C = -9[/tex]. So

[tex]\Delta = (-0.02)^2 - 4(0.006)(-9) = 0.2164[/tex]

[tex]A_{1} = \frac{-(-0.02) + \sqrt{0.2164}}{2*(0.006)} = 40.4[/tex]

[tex]A_{2} = \frac{-(-0.02) - \sqrt{0.2164}}{2*(0.006)} = -37.1[/tex]

Age has to be a positive number, so rounding to the nearest year:

The man would be 40 years old.

Answer:

Small (11.5) is 37 cents per ounce.

Large (27.8) is 36 cents per ounce.

27.8 ounces is the better buy.

Answer:

500000

Step-by-step explanation:

9514 1404 393

Answer:

  3.49

Step-by-step explanation:

The growth factor is one more than the growth rate:

  growth factor = 1 + growth rate

  = 1 + 249% = 1 +2.49

  growth factor = 3.49

Answer:

The minimum number of parallel faces that a prism should have is three pairs

Answer:

The minimum number of parallel faces that a prism should have is three faces

Answer:

angle k is acute.

Step-by-step explanation:

it is less than 90 degrees

Answer:

a., b.

Step-by-step explanation:

Angle K looks like an acute angle with measure between 0 and 90 degrees.

Answer: a., b.

Answer:

7% = .07 = [tex]\frac{7}{100}[/tex]

Step-by-step explanation:

Answer:

closing price of the fast food stock was $997.50

closing price of the toy company stock was $598.50

the price per fast food share was $28.50

Step-by-step explanation:

x = price per share fast food

y = price per share toy company

35x + 63y = 1596

x = y + 19

=>

35(y+19) + 63y = 1596

35y + 665 + 63y = 1596

98y + 665 = 1596

98y = 931

y = $9.50

=>

x = 9.5 + 19 = $28.50

the value of the whole fast food stock was

35x = 35×28.5 = $997.50

the cake if the whole toy company stock was

63y = 63×9.5 = $598.50

Answer:  option C is correct

Step-by-step explanation:[tex]s=( \alpha +\beta +c)/2\\2s=\alpha +\beta +c\\2s-\beta -c=\alpha \\\alpha =2s-\beta -c[/tex]

Answer:

[tex]P(O\ or\ A) = 0.85[/tex]

Step-by-step explanation:

Given

See attachment

Required

[tex]P(O\ or\ A)[/tex]

From the question, we understand that she can only get blood from O or A groups. So, the probability is represented as:

[tex]P(O\ or\ A)[/tex]

This is calculated as:

[tex]P(O\ or\ A) = P(O) + P(A)[/tex]

Using the American row i.e. the blood must come from an American.

We have:

[tex]P(O) = 0.45[/tex]

[tex]P(A) = 0.40[/tex]

So, we have:

[tex]P(O\ or\ A) = 0.45 + 0.40[/tex]

[tex]P(O\ or\ A) = 0.85[/tex]

Answer:

9sin (3)and f,(0)=4,AND f(0)=2

Answer:

[tex]m\angle H = 30^o[/tex]

Step-by-step explanation:

Given

See attachment

Required

Find [tex]m\angle H[/tex]

To calculate [tex]m\angle H[/tex], we make use of:

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

So, we have:

[tex]\cos(H) = \frac{GH}{HI}[/tex]

This gives:

[tex]\cos(H) = \frac{10\sqrt3}{20}[/tex]

[tex]\cos(H) = \frac{\sqrt3}{2}[/tex]

Take arccos of both sides

[tex]m\angle H = cos^{-1}(\frac{\sqrt3}{2})[/tex]

[tex]m\angle H = 30^o[/tex]

Answer:

4x + 3 = 59

x = 14

Step-by-step explanation:

The vertical angles theorem states that when two lines intersect, the angles opposite each other are congruent. One can apply this here by stating the following:

4x + 3 = 59

Solve for (x), use inverse oeprations:

4x + 3= 59

4x = 56

x = 14

Answer:

Relationship : Vertical angle

Step-by-step explanation:

(4x + 3) = 59

4x = 59 - 3

4x = 56

x = 56/4

x = 14

Step-by-step explanation:

The relation between kg and lbs is :

1 kg = 2.2046 lbs

We need to find the values of 1kg/2.2046lbs and 2.2046lbs/1kg.

So,

[tex]\dfrac{1\ kg}{2.2046\ lbs}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

and

[tex]\dfrac{2.2046\ lbs}{1\ kg}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]

Hence, this is the required solution.

Answer:

Both are same as 1.

Step-by-step explanation:

1 kg = 2.2046 lbs

So,

[tex]\frac{1 kg}{2.2046 lbs }=\frac{1 kg }{1 kg} = 1[/tex]

And

[tex]\frac{2.2046 lbs}{1 kg }=\frac{1 kg }{1 kg} = 1[/tex]

Answer:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (15,2.2) and (5,1.6):

[tex]m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}[/tex]

Therefore, the slope of the line is [tex]\frac{\displaystyle 3}{\displaystyle 50}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]

Plug in a given point and solve for b:

[tex]1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b[/tex]

Therefore, the y-intercept is [tex]\frac{\displaystyle 13}{\displaystyle 10}[/tex]. Plug this back into [tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]:

[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]

I hope this helps!

Answer:

x= -5.1

Step-by-step explanation:

The solution  to f(x) = g(x) is where to two graphs intersect

The graphs meet at

about x=2  and x = -5

The best answer listed is  x = -5.1

Answer:

x = −5.1

Step-by-step explanation:

I took the practice test

Answer:

The answer:

I think the choose (1) 1

Answer:

Hence the confidence interval (2.2, 3.52).

Step-by-step explanation:

Hence,

The point estimate = [tex]\bar x_{1} - \bar x_{2}[/tex]

= 7.9 - 5.04

= 2.86

Given CI level is 0.98, hence α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.326

Margin of Error

ME = tc x sp

ME = 2.326 \ 0.2817

ME = 0.6552

CI = ([tex]\bar x_{1} - \bar x_{2}[/tex] - tc x sp , [tex]\bar x_{1} - \bar x_{2}[/tex] + tc x sp)

CI = (7.9 - 5.04 - 2.326 x 0.2817 , 7.9 - 5.04 - 2.326 x 0.2817

CI = (2.2 , 3.52)

Answer:

y - 8 = -2(x + 1)^2

Step-by-step explanation:

The vertex of this parabola is (-1, 8).  It opens downward, so the x^2 term has a negative coefficient.  The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).

Through the vertex form of the equation of a parabola we get:

y - (8) = a(x - (-1)) + 7, or

y - 8 = a(x + 1)^2.  Find coefficient a by substituting the coordinates (-3, 0) in this equation:

0 - 8 = a(-3 + 1)^2, or

-8 = a(-2)^2, or a = -2

The desired equation is

y - 8 = -2(x + 1)^2

Answer:

If you're asking what cosine 3 is it's 0.9999986292247

Step-by-step explanation:

I don't really understand the question

Answer:

Answer is -1

Step-by-step explanation:

i1 = i 

i2 = -1 

i3 = -i

i4 = 1

i0 × i1 × i2 × i3 × i4 = 1 × i  × (- 1) × (- i) × 1 = i2 = - 1

Answer:the answer is -1

Step-by-step explanation:

The given differential equation is

x ² (y' - x ²) + 3xy = cos(x)

Expanding and rearranging terms, we get

x ² y' + 3xy = cos(x) + x ⁴

Multiply both sides by x, which is motivated by the fact that (x ³)' = 3x ².

x ³ y' + 3x ²y = x cos(x) + x ⁵

The left side is the derivative of a product:

(x ³y)' = x cos(x) + x ⁵

Integrate both sides with respect to x :

∫ (x ³y)' dx = ∫ (x cos(x) + x ⁵) dx

x ³y = cos(x) + x sin(x) + 1/6 x ⁶ + C

Solve for y. Since x > 0, we can safely divide both sides by x ³.

y = cos(x)/x ³ + sin(x)/x ² + 1/6 x ³ + C/x³