In 1990 the average family income was about $ 39 , 000 , and in 2010 it was about $ 70 , 768 . Let x = 0 represent 1990, x = 1 represent 1991, and so on. Find values for a and b so that f ( x ) = a x + b models the data A= _____. B=______. What was the average family income in 2005?

Answer:

The area of the surface is 2.72 units

Step-by-step explanation:

The area of a curve y = (x) a ≤x ≤ b rotated about the y axis is given by:

[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]

y = 4 - x²

dy / dx = -2x

(dy/dx)² = (-2x)² = 4x²

Hence:

[tex]s=\int\limits^a_b {2\pi x\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\\\s=\int\limits^0_3 {2\pi x\sqrt{1+4x^2} } \, dx\\\\Let\ u = 1+4x^2\ \\\frac{du}{dx}=8x\\\frac{du}{8x}=dx\\\\Substituting\ value\ of\ u \ and\ dx:\\ \\s=\int\limits^0_3 {2\pi x\sqrt{u} } \, \frac{du}{8x} \\\\s=\frac{\pi }{4} \int\limits^0_3 {\sqrt{u} } \, du\\\\s=\frac{\pi }{4}|\frac{2}{3}u^{3/2}|_0^3\\\\s=\frac{\pi }{4}*\frac{2}{3}(5.196)\\\\s=2.72\ units[/tex]

The area of the surface is 2.72 units

The area of the resulting surface is [tex]37.3437\pi[/tex].

A curve is an object that is similar to a line, but that does not have to be a straight line. A curve may be regarded as a trace left by a moving point.

Given:

[tex]y=4-x^{2}[/tex] , [tex]0 \leq x\leq 3[/tex]

Surface area[tex]=2\pi \int_{a}^{b}x\sqrt{1+\left ( \frac{dx}{dy} \right )^{2}dy}[/tex]

[tex]x=\sqrt{4-y} \ , \ \frac{dx}{dy}=-\frac{1}{2\sqrt{4-y}}[/tex]

when [tex]x=0 \ , \ y=4[/tex]

         [tex]x=3 \ , \ y=-5[/tex]

Area of surface[tex]=2\pi \int_{-5}^{4}\sqrt{4-y}\sqrt{1+\frac{1}{4\left ( y-4 \right )}dy}[/tex]

[tex]=2\pi \int_{-5}^{4}\sqrt{4-y+\frac{4-y}{4\left ( y-4 \right )}dy} \\ =2\pi \int_{-5}^{4}\sqrt{4-y+\frac{1}{4}dy} \\ =\frac{2\pi }{2}\int_{-5}^{4}\sqrt{17-y} \ dy \\ =\pi \int_{-5}^{4}\sqrt{17-y} \ dy[/tex]

Solving with calculator:

[tex]\Rightarrow \pi\left [ \frac{1}{6}\left ( 37\sqrt{37}-1 \right ) \right ][/tex]

[tex]=37.3437\pi[/tex]

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Answer:

180

Step-by-step explanation: 60+60 =120 120+6

Answer:

Step-by-step explanation:

Given the function f(x,y) = ye^x

To evaluate f(2,1), we will substitute x = 2 and y = 1 into the given function to have;

f(2,1) = 1×e^2

f(2,1) = e^2

f(2,1) = 7.3891(to 4dp)

For f(2.5, 1.65), x = 2.5 and y =1.65

f(2.5, 1.65) = 1.65e^2.5

f(2.5, 1.65) = 1.65×12.1825

f(2.5, 1.65) = 15.2281 (to 4dp).

∆z = f(2.5, 1.65) - f(2, 1)

∆z = 15.2281-7.3891

∆z = 7.8390

dz = fxdx + fydy

fx is the differential of the function with respect to x keeping y constant.

Since f(x,y) = ye^x

fx = ye^x + 0e^x

fx = ye^x

dx = x2-x1 = 2.5-2

dx = 0.5

fy = e^x

dy = (y2-y1) = 1.65-1

dy = 0.65

Using the point (2, 1) for x and y and substituting the values gotten into dz function:

dz =ye^x(0.5) + e^x(0.65)

If x = 2 and y = 1

dz = 1e^2(0.5) + e^2(0.65)

dz = 7.3891(0.5)+7.3891(0.65)

dz = 7.3891(0.5+0.65)

dz = 7.3891(1.15)

dz = 8.4975

Answer:

111 ft

Step-by-step explanation:

52 x 2 then just add 7

Answer:

$149.96

Step-by-step explanation:

99.99+12.99+36.98=149.96

Total=$149.96

Answer:

82.4

Step-by-step explanation:

Answer:

Use a graphing calc.

Step-by-step explanation:

If graphing by hand, use the vertex as one of the main points and then find other points by plugging in x-values.

Answer:

See be'ow

Step-by-step explanation:

We can use a graphing calculator to plot the points of the parabola.

See the attached file!

Answer:

m = -2

Step-by-step explanation:

For this problem, we will simply solve the equation for m.

19 - 5 ( 2m - 3 ) + 9m = 36

19 - 10m + 15 + 9m = 36

34 - m = 36

-m = 2

m = -2

Hence, for this equation to be true, m must equal negative 2.

Cheers.

Answer:

If you are on Khan Academy doing this, then the answer is 80/100 X 20

Step-by-step explanation:

If the mass of object is 808080 grams and acceleration is 202020 meter per seconds square then the force will be 1632483216 kg [tex]m^{2}[/tex].

A force is an effect that can change the motion of an object. A force can change the position of an object.

Force=mass*acceleration

We have been given mass of the object=808080 grams and acceleration =202020 meters per second.

We have to calculate force in kg per meters square so firstly we have to change mass which is in grams into kilogram=808080/1000=808.080 kg

Force =808.080*202020

=163248321

Force=163248321 kg [tex]m^{2}[/tex]

Hence is mass is 808080 grams and acceleration is 202020 meters per second then force will be 163248321 kg meters square.

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#SPJ2

Answer:

We have a total investment of $20,000 in two different amounts A and B.

Then:

A + B = $20,000.

And we know that the interest of the amount A is 7%, and the interest of the amount B is 10%. (i will assume that both interests are yearly interest)

And after one year, Hank earns $1,640 thanks to those interests, then we have that:

(7%/100%)*A + (10%/100%)*B = $1,640

And we can write this as:

0.07*A + 0.1*B = $1,640

Then we have a system of equations:

A + B = $20,000

0.07*A + 0.1*B = $1,640

To solve this, the first step is isolating one of the variables in one of the equations.

Let's isolate A in the first equation:

A + B = $20,000

A = $20,000 - B.

Now we can replace this in the other equation:

0.07*A + 0.1*B = $1,640

0.07*($20,000 - B) + 0.1*B = $1,640

$1,400 - 0.07*B + 0.1*B = $1,640

0.03*B = $1,640 - $1,400 = $240

B = $240/0.03 = $12,000

Then we have:

A = $20,000 - $12,000 = $8,000

Hank invests $12,000 in the 10% account and $8,000 in the 7% one.

Answer:

[tex] Volume_{Prism} = 165 ft^3 [/tex]

Step-by-step explanation:

Volume of triangular prism is given as base area * height of prism

Base area = area of triangle = ½*base of the traingle*height of the traingle

Base area = 5 ft * 6 ft = 30 ft²

Height of prism = 11 ft

Volume of the prism = [tex] \frac{1}{2}*30*11 [/tex]

[tex] Volume_{Prism} = 15*11 [/tex]

[tex] Volume_{Prism} = 165 ft^3 [/tex]

Answer:

Proved

Step-by-step explanation:

Given

Integers: a, b, c

Required

Show that c is a multiple of a⁶

First, we need to list out the multiples of a³

[tex]a^3 -> a^3, a^6, a^9, a^{12}...[/tex]

Since b is a multiple of a³, then b can be any of the listed multiples

Next, is to list out the multiples of b²

[tex]b^2 -> b^2,b^4,b^6,b^8,b^{10}....[/tex]

Since c is a multiple of b², then c can be any of the listed multiples

To list out the multiples of a⁶, we have to get the common multiples of a³ and b² in terms of a

Substitute a³ for b in

[tex]b^2 -> b^2,b^4,b^6,b^8,b^{10}....[/tex]

[tex](a^3)^2 -> (a^3)^2,(a^3)^4,(a^3)^6,(a^3)^8,(a^3)^{10}....[/tex]

[tex]a^6 -> a^6,a^{12},a^{18},a^{24},a^{30}....[/tex]

Recall that c is a multiple of b²

From the above listed multiples, we have a⁶ listed as one of the multiple; Hence, c is a multiple of a⁶

Yes C should be multiple of [tex]a^6[/tex]

Since it is mentioned that b should be the multiple of [tex]a^3[/tex]

So,

[tex]b = a^3R[/tex] here some integer should be R

And, the c should be multiple of [tex]b^2[/tex]

So,

[tex]C = b^2 r[/tex] for some integer r

Now we have to substitute the value of b from the first equation

i.e.

[tex]C = (a^3R)^2r = a^6 (R^2r)[/tex]

Here [tex]R^2r[/tex] is some integer

so,

[tex]C = a^6R'[/tex]

Therefore, we can say that Yes C should be multiple of [tex]a^6[/tex]

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Answer: Choice A) 9

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

Explanation:

We have some variable r that we divide over 3, and then we add on 5. Note the order of operations PEMDAS says to divide first and then add (since D comes before A in PEMDAS).

When we isolate r, we follow PEMDAS in reverse and undo everything. We undo addition by subtracting 5 from both sides

[tex]\frac{r}{3} + 5 \le 8\\\\\frac{r}{3} + 5-5 \le 8-5\\\\\frac{r}{3} \le 3\\\\[/tex]

Then we undo the division happening to r. So we multiply both sides by 3

[tex]\frac{r}{3} \le 3\\\\3*\frac{r}{3} \le 3*3\\\\r \le 9\\\\[/tex]

Since r is less than or equal to 9, this means that r could be 9 or smaller

Only choice A applies.

Don't shade the part A and the part between A and B. Shade the B part only.

Answer:

A coefficient is a number that is in front of a variable. A number that is multiplied by a variable in a variable expression; in an expression such as 3ab, the numerical coefficient of ab is 3. The word constant means unchanging. Since a number’s value never changes, a number with no variable factors is a constant. A constant is a numerical term in an expression. a term that has no variables

Example: 5a+4  The coefficient is 5 and the constant is 4 because it does not have a variable in front of it.

Hope this helps

Answer:

Step-by-step explanation:

d = 200 miles

B rate = x

A Rate = x + 20

Each has traveled two hours

The total distance each travels after two hours is 200 miles (they pass each other).

d = r * t

2*x + 2*(x + 20) = 200      Remove the brackets

2x + 2x + 40 = 200           Combine like terms

4x + 40 = 200                   Subtract 40 from each side

4x = 200 - 40                  

4x = 160                           Divide by 4

x = 160/4

x = 40

There B's rate is 40 miles / hour

A's rate is 40 + 20 = 60 miles / hour

Step-by-step explanation:

Area of a rectangle is base times height.

A = bh

A = (12 in) (2.5 in)

A = 30 in²

Step-by-step explanation:

10 is less than 10.01

10.01-10=0.01

10 is 0.01 less than 10.01

So, 10 is less than 10.01.

Hope it helps you!!

Answer: W(x) = 3.4 L - (25/1000)(L/s)*x

Step-by-step explanation:

The maximum of the jug is 4 L.

now, the jug is 85% filled, then the amount of water in the jug is:

(85%/100%)*4L = 0.85*4L = 3.4L

Now, we pour 25 mL each second, so we could write a linear equation as:

W(x) = 3.4L - (25ml/s)*x

where x is the number of seconds that passed since the beginning,

But we want to write this in Liters, we have that:

1L = 1000mL.

Then 1mL = (1/1000) L

then we can write 25 mL as:

25m L = 25*(1/1000) L = (25/1000) L.

Then we can write the equation as

W(x) = 3.4 L - (25/1000)(L/s)*x

which is the amount of water remaining in the jug after x seconds.

Answer:

531

Start off by subtracting.

Joe = 987 marbles

Donald = 456 marbles.

987 - 456 = 531.

So that is your answer. Hope it helps!

Answer:

agree with previos answer

Step-by-step explanation:

Answer:

393.5$

Step-by-step explanation:

$18,000 -- car price

Total sum (105%) = [tex]\frac{18000}{100}[/tex]* 105%

Hence

[tex]\frac{18000/100*105}{48}[/tex] = 393.5$

Answer:

x=2.2 this is nice question

Answer:

a democracy

I hope this helps!

Answer:

16

Step-by-step explanation:

Take the total number of sandwiches and multiply the fraction that were ham

56 * 2/7

56/7 *2

8 *2

16

16 sandwiches were ham

Answer:

[See Below]

Step-by-step explanation:

Here are some pictures to help you.

The quadratic formula is shown below.

The beauty of the quadratic formula is that as long as your quadraticis in the form ax² + bx + c = 0, where a, b, and c are integers, you can go straight to the answer by simply plugging your values for a, b, and c into the quadratic formula.

It's a good idea to memorize it.

Believe me it's worth it, you'll be using it all the time.

Answer:

the calculated value of R would be incorrect and it would be greater than the actual value

Step-by-step explanation:

From the general gas equation,

We have a mole of gas as

PV =nRT

We will have to make R the subject of the formula

So we divide through by nT

R = PV/nT

So we have an inverse proportion between R and absolute temperature.

So when we record a lower temperature than what the actual temperature should be, R is going to be affected such that the wrongly calculated value of R would be more than the actual value.

Answer:

54,795

Step-by-step explanation:

Answer:

7.1

Step-by-step explanation:

Using the distance formula

d = sqrt (  (x2-x1)^2 + ( y2-y1)^2)

    sqrt (  (-5-2)^2 + ( -3- -2)^2)

    sqrt(   ( -7)^2  + ( -3 +2)^2)

   sqrt(   ( 49  + 1)

   sqrt( 50)

  7.071067812

To the nearest tenth

7.1

Answer:

7.1 units

Step-by-step explanation:

We can use the distance formula to find the distance between these two points.

The distance formula is:

[tex]\sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex].

x1 is 2, x2 is -5, y1 is -2, and y2 is -3, so we can plug these values into the equation.

[tex]\sqrt {\left( {2 - (-5) } \right)^2 + \left( {-2 - (-3) } \right)^2 }\\\\\sqrt {7^2 + 1^2}\\\\\sqrt{49+1}\\\\\sqrt{50}\approx7.1[/tex]

Hope this helped!

Answer:

A. -4

Step-by-step explanation:

Given the function f(x) = x + 3 for x ≤ -1 and 2x - c for x > -1, for the function to be continuous, the right hand limit of the function must be equal to its left hand limit.

For the left hand limit;

The function at the left hand occurs at x<-1

f-(x) = x+3

f-(-1) = -1+3

f-(-1) = 2

For the right hand limit, the function occurs at x>-1

f+(x) = 2x-c

f+(-1) = 2(-1)-c

f+(-1) = -2-c

For the function f(x) to be continuous on the entire real line at x = -1, then

f-(-1) = f+(-1)

On equating both sides:

2 = -2-c

Add 2 to both sides

2+2 = -2-c+2

4 =-c

Multiply both sides by minus.

-(-c) = -4

c = -4

Hence the value of c so that f(x) is continuous on the entire real line is -4

The value of 'c' is -4 and this can be determined by using the concept of continuous function and arithmetic operations.

Given :

f(x) is continuous on the entire real line when c f(x) = x + 3 for [tex]x \leq -1[/tex], 2x - c for x > -1.

Remember for a continuous function, the left-hand limit is equal to the right-hand limit. So, determine the left-hand and right-hand limit.

The left-hand limit is calculated as:

f(-1) = (-1) + 3

f(-1) = 2    --- (1)

The right-hand limit is calculated as:

f(-1) = 2(-1) - c

f(-1) = -2 - c   --- (2)

Now, equate both the expression (1) and (2).

2 = -2 - c

c = -4

For more information, refer to the link given below:

https://brainly.com/question/1111011

Please find attached

Answer:

equation : 2x+9-5y=0

Step-by-step explanation:

x and y cut axes at -4.5 and 1.4 respectively

given

when x=0

9-5y=0

y=1.4

When y=0

2x+9=0

x=-4.5