PLEASE HELP!!! TOTAL 50 POINTS IF GIVEN BRAINLIEST ANSWER!!!

Find the average value of the function f over the given region.
f(x, y) =10x +3y over the triangle with vertices (0, 0), (9, 0), and (0, 2).

Answers

Answer 1

The average value of f(x, y) over the given region (I'll call it T) is

[tex]\dfrac{\displaystyle \iint_T f(x,y) \, dA}{\displaystyle \iint_T dA}[/tex]

In other words, it's the ratio of the integral of f(x, y) over the region to the area of the region.

The set T can be expressed as

[tex]T = \left\{(x,y) \,:\, 0\le x\le9 \text{ and } 0\le y\le -\dfrac29x+x\right\}[/tex]

Since it's a triangle, the denominator is easily computed to be

[tex]\displaystyle \iint_T dA = \frac12 \times 9 \times 2 = 9[/tex]

In the numerator, we have

[tex]\displaystyle \iint_T (10x+3y) \, dA = \int_0^9 \int_0^{-2x/9+2} (10x+3y) \, dy \, dx \\\\ = \int_0^9 \left(\frac32\left(-\frac{2x}9+2\right)^2+10x\left(-\frac{2x}9+2\right)\right) \, dx = 288[/tex]

and hence the average value is 288/9 = 32.


Related Questions

A construction company is building the house shown below. They need to use a scale
of 1 in: 8f (1 inch = 8 feet). They measured the drawing to find that that the height of
the building is 2.5 in.
1.) Explain to the construction workers how they would use this information to
calculate the height of the final building.
2.) What is the height of the final building?
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Answers

Using proportions, we have that:

The height of the building is found using a rule of three.The height is of 20 feet.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The scale is of 1 inch = 8 feet. What is the height for 2.5 inches? The rule of three is given by:

1 inch - 8 feet.

2.5 inches - x feet

Applying cross multiplication, the height in feet of the final building is given by:

x = 8 x 2.5 = 20 feet.

More can be learned about proportions at https://brainly.com/question/24372153

The height of the building is calculated by representing 1 inch as 8 feet. The final building has a height of 20 feet.

What is scaling?

Scaling is the increase or decrease in the height of an object by a scale factor k.

Given that the scale used is:

1 inch = 8 feet. Hence:

Since the height of the building is 2.5 in, hence:

Height of the final building = 2.5 in * 8 ft per 1 in = 20 feet

The height of the final building is 20 feet.

Find out more on scaling at: https://brainly.com/question/25722260

90 is the product of five and Diego’s age use a variable D to represent Diego’s age

Answers

Answer:

Deigo is 18years of age

explaination

[tex]5 \times d = 90 \\ 5 d = 90 \\ 5d \div 5 = 90 \div 5 \\ d = 18[/tex]

this is how to solve it.

Help ASAP.
i need you to please break it down ive tried and just don't understand ​

Answers

Answer:

A) -4

Step-by-step explanation:

Question

[tex]\sf evaluate \ \dfrac{-4+(m+2)}{n} \ \sf when \ m=\dfrac23 \ and \ \sf n=\dfrac13[/tex]

Solution

Substitute the given values of m and n into the original expression:

[tex]\sf \implies \dfrac{-4+(\frac23+2)}{\frac13}[/tex]

Carry out the operation in the brackets first [tex]\sf (\frac23+3)=\frac83[/tex]

[tex]\sf \implies \dfrac{-4+\frac83}{\frac13}[/tex]

Now carry out the operation in the numerator [tex]-4+\frac83=-\frac43[/tex]

[tex]\sf \implies \dfrac{-\frac43}{\frac13}[/tex]

Dividing by a fraction is the same as multiplying by the flipped version of the fraction (flipped = swap the numerator and denominator of the fraction we are dividing by):

[tex]\sf \implies -\dfrac43 \div \dfrac13=-\dfrac43 \times \dfrac31[/tex]

To multiply a fraction, simply multiply the numerators and multiply the denominators:

[tex]\sf \implies -\dfrac43 \times \dfrac31=\dfrac{-4 \times 3}{3 \times 1}=-\dfrac{12}{3}[/tex]

Finally simplify:

[tex]\sf \implies -\dfrac{12}{3}=-4[/tex]

Help help help help help

Answers

Answer:

(-9, -6)

Step-by-step explanation:

I had to only use a pic because no one would be able to understand, worth 100 points IF you get it correct.

Answers

Total left

2-1/4+2/4+1-3/49/4+2/4+7/49+2+7/418/44-2/4

Answer:

[tex]4\:\dfrac{2}{4}[/tex]

Step-by-step explanation:

Add the amounts of each pie left :

[tex]2 \frac{1}{4}+\dfrac{2}{4}+1 \frac{3}{4}[/tex]

Separate the whole numbers and the fractions:

[tex]\implies 2+ \dfrac{1}{4}+\dfrac{2}{4}+1+\dfrac{3}{4}[/tex]

Add the whole numbers and fractions separately:

[tex]\implies 2+1+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}[/tex]

[tex]\implies 3+\dfrac{6}{4}[/tex]

Convert 6/4 into a mixed number:

[tex]\implies 3+1\frac{2}{4}[/tex]

Add the whole numbers:

[tex]\implies 4\frac{2}{4}[/tex]

the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width

Answers

Answer:

Length and width of rectangle is 24 and 8 inches

Step-by-step explanation:

Given:

Length of rectangle is three times the widthPerimeter of rectangle is 64 Inches

To Find:

Length and Width

Solution:

Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:

Perimeter of rectangle = 2(L + B)

→ 64 = 2(3x + x)

→ 64 = 2(4x)

→ 64/2 = 4x

→ 32 = 4x

→ 32/4 = x

→ 8 = x

Hence,

Length of the rectangle = 3x = 3(8) = 24 inches

Width of the rectangle = x = 8 inches

Answer:

Length = 24 inches

Width = 8 inches

Step-by-step explanation :

As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,

Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .

Now, According to the Question :

[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{2 (3 x + x )= 64 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{8x= 64 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{64}{8} }}}}[/tex]

[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar[/tex]

Therefore,

The width of the rectangle is 8 inches .

Now, We are to find the length of the rectangle:

[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}[/tex]

[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}[/tex]

[tex]{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar[/tex]

Therefore,

The length of the rectangle is 24 inches .

Given that V=1,3,4,2 and W= 6,4,7,2 then VW is
Select one:
of
O 4
0 1,3,6,7
O 2
0 2,4

Answers

Answer:

2,4 possibly

Step-by-step explanation:

if its V (intersection) W

then its 2,4

if it has something to do with patterns then i dont know

What is the area of the figure below ?
A. 12
B. 15
C. 18
D. None of these

Answers

Step 1: Find the area of the larger rectangle

Area of a rectangle = base x height

Area = 4 x 3 = 12

Step 2: Find the area of the other rectangle

The tricky part about this one is that we aren't given the length of this rectangle. We do know, however, that the whole base of the figure is 6 and 3 units are taken up by the first rectangle. Therefore, the length of this rectangle is 3.

Area = 2 x 3 = 6

Step 3: Find the area of the figure

Now that we know the area of both rectangles by themselves, all that's left to do is add them up.

6 + 12 = 18

Answer: 18

Hope this helps!

Answer:

18

Step-by-step explanation:

A=bh

A=3x4 A=3x2

12+6=18.

What is g(-2) for g(x) =1/2x^2+2x?
Does anyone know this

Answers

Step-by-step explanation:

please mark me as brainlest

100 Points and Brainly.

Graph The equation: y=(-x)-6

Gibberish for points WILL NOT be tolerated.

Please, if you can, try to make the mark ON the picture I have provided, in red.

Answers

function :  y = (-x) - 6

Find x-intercept :

(-x) - 6 = 0(-x) = 6x = -6

Find y-intercept :

y = (-0) - 6 y = -6

mark these two points on both the axis and draw a straight linear graph.

passes coordinates : (0, -6), (-6, 0)

[tex]\\ \rm\rightarrowtail y=-x-6[/tex]

Take some point s

(1,-7)(2,-8)(3,-9)

Graph it

consider the equation 2 x +9 y = -18 A line parallel to the above line would have a slope of_________
A line perpendicular to the above line would have a slope of ________________

Answers

Answer:
A line parallel to the above line would have a slope of -2/9
A line perpendicular to the above line would have a slope of 9/2
Step-by-step explanation:
2x+9y=-18
=>y=-2/9 x-2

Jameson wants to construct a ladder that has 8 rungs. Each rung is
3.2 feet wide. The two sides measure 10.6 feet each. The wood is
sold for $2.25 per linear foot. Find how much the wood to construct
this ladder will cost Jameson. 5.NBT.7

Answers

Answer:

$23.85

Step-by-step explanation:

Linear foot- sold by the lenght.

Therefore you dont worry about the 3.2 feet wide

So now we multiply 10.6 * 2.25

which is...

$23.85


A Cinema has 240 seats. 144 seats were sold
for the current movie. What percent of seats
are empty?

Need help please :)

Answers

Answer:

the answer is 40%

Step-by-step explanation:

240 – 144 = 96

96÷240=0.4=40%

Hope this helps:)....if not then sorry for wasting your time and may God bless you:)

cos(theta)+1 / tan^2(theta) = cos(theta) / sec(theta) - 1

Answers

Hope it helpssss ..best of luck

The equation is:

Answer: the number of labor was :

Answers

Answer:

equation: 1368 = 380 +52xlabor hours: 19

Step-by-step explanation:

The desired equation will relate labor cost, parts cost, and total cost.

A.

The total cost is the sum of the parts cost and the product of labor hours and labor rate. We're told to use x to represent labor hours.

  total cost = part cost + (labor rate)(labor hours)

  1368 = 380 + 52x

__

B.

This equation can be solved in 2 steps:

  988 = 52x . . . . . . . step 1, subtract 380 from both sides

  19 = x . . . . . . . . . . step 2, divide both sides by the coefficient of x

The number of labor hours was 19.

Help help help help

Answers

Step-by-step explanation:

can you tell me what you don't understand about this ?

because it is really simple, once you understand the transformations of equations.

remember, whatever we do to one side. we have to do also to the other side, so that the information in general stays the same.

(7 - 3x)/2 = 8 multiply both sides by 2

7 - 3x = 16 subtract 7 from both sides

-3x = 9 divide both sides by 3

-x = 3 multiply both sides by -1

x = -3

and that's the whole "secret" about solving an equation.

Answer:

x = -3

Step-by-step explanation:

In the question we are given with an equation that is ( 7 - 3x ) / 2 = 8 . And we have asked to find the value of x .

Solution : -

[tex] \longrightarrow \qquad \: \dfrac{7 - 3x}{2} = 8[/tex]

Step 1 : Multiplying both sides by 2 :

[tex] \longrightarrow \qquad \: \dfrac{7 - 3x}{ \cancel{2} }\times \cancel{2 }= 8 \times 2 [/tex]

On further calculations, We get :

[tex] \longrightarrow \qquad \: 7 - 3x = 16[/tex]

Step 2 : Subtracting with 7 on both sides :

[tex] \longrightarrow \qquad \: \cancel{ 7 }- 3x - \cancel{ 7 }= 16 - 7[/tex]

On calculating further, We get :

[tex] \longrightarrow \qquad \: - 3x = 9[/tex]

Step 3 : Dividing with -3 on both sides :

[tex] \longrightarrow \qquad \: \dfrac{ \cancel{ - 3}x}{ \cancel{-3}} = \cancel{\dfrac{9}{ - 3} }[/tex]

On calculating further, We get :

[tex] \longrightarrow \qquad \: \red{\underline{\boxed{\frak{x = - 3}}}}[/tex]

Therefore, value of x is -3 .

Verifying : -

Now , we are verifying our answer by substituting value of x in given equation . So ,

( 7 - 3x ) / 2 = 8

[ 7 - 3 ( -3 ) ] / 2 = 8

( 7 + 9 ) / 2 = 8

16 / 2 = 8

8 = 8

L.H.S = R.H.S

Hence, Verified .

Therefore , our answer is valid .

#Keep Learning

Event A has a 90% chance of occurring. Event B has a 20% chance of occurring. The correlation (i.e. whether they tend to occur together, or separately, or are unrelated) between the events is unknown.

What is the maximum probability that both event A and event B will occur?

What is the minimum probability that both event A and event B will occur?

Answers

The maximum probability that both event A and event B will occur is 18%.

How to compute the probability?

From the information, Event A has a 90% chance of occurring. Event B has a 20% chance of occurring. Therefore, the maximum probability will be:

= 90% × 20%

= 18%

The minimum probability that both event A and event B will occur will be:

= (90% + 20%) - 1

= 1.10 - 1

= 10%

Learn more about probability on:

https://brainly.com/question/24756209

pls help...

What is the mode for the set of data?

Answers

Answer:

9

[tex]\rule{70mm}{2pt}[/tex]

Step-by-step explanation:

In statistics, the mode is the value that is repeatedly occurring or you can say that has higher frequency in a given set of numbers or values. For instance in (1, 2, 5, 6, 2, 3) mode is 2 because it has appeared in the given set twice.

As in the given problem, the cross represents the number of a particular number, indicating whether the given number is repeated or not. And if repeated, how many times?

→ 5, 6, 10 = 1 (number of repetition; each)

→ 7, 8 = 2 (number of repetition; each)

9 = 3 (number of repetition)

Therefore, the mode for the given set of data is 9.

Question
The sum of four times a number and two is 14. Find the number.

Answers

Answer:3

Step-by-step explanation:let the number be x

4x+2=14

4x=14-2

4x=12

divide both sides by 4

4x/4=12/4

x=3

Tony saw 6 birds in a tree. 1/6 of them flew away. How many were left?

Answers

Answer:

5 birds flew away

Step-by-step explanation:

1/6x6=1

( 1 bird flew away)

so, 6-1=5

Answer:

[tex]\huge\boxed{\bf\:5\:\:birds}[/tex]

Step-by-step explanation:

Number of birds Tony saw = 6Fraction that flew away = ⅙

Number of birds that flew away = ?

Number of birds that flew away = Number of birds × Fraction that leftNumber of birds that flew away = 6 × ⅙Number of birds that flew away = 1

Number of birds remaining = ?

Number of birds remaining = Total number of birds - Number of birds that flew awayNumber of birds remaining = 6 - 1Number of birds remaining = 5

[tex]\rule{150pt}{2pt}[/tex]

Write the linear inequality shown in the graph. The gray area represents the shaded region.

x > –3
y ≥ –3
y > –3
x ≥ –3

Answers

Answer:

y > –3

Step-by-step explanation:

by looking at the graph we notice that the (shaded/gray) area which we are focusing on covers all the values of x ,on the other hand it only covers the values of y which they are Greater than -3

Remark : y > -3 not y ≥ -3 because the line that separates the shaded region and the other one is a broken line.

Answer:

y > –3

Step-by-step explanation:

For the function f(x)=−7x2+8x−8, find f(4).

Answers

Answer:

- 88

Step-by-step explanation:

[tex]f(x ) = - 7 {x}^{2} + 8x - 8 \\ plug \: x = 4 \\ \\ \implies \: f(4 ) = - 7 {(4)}^{2} + 8(4) - 8 \\\\ \implies \: f(4 ) = - 7 \times 16 + 32 - 8 \\\\ \implies \: f(4 ) = - 112+ 32 - 8 \\ \\ \implies \: f(4 ) = - 120+ 32 \\\\ \implies \: f(4 ) = - 88 \\[/tex]

Q13
A man has a flight at 19:15 on Thursday. He must arrive at the airport 2 hours before this time to
check in.
He needs to know what time he should leave home.
He will park his car at the airport car park and it will take 15 minutes to get to the check in counter.
The distance from his house to the airport is 90 miles.
He will drive at an average of 60miles per hour.

Answers

Answer: around 6 or 5 o clock

Step-by-step explanation: hope this helps

In the game of​ roulette, a player can place a ​$7 bet on the number 5 and have a 1/38 probability of winning. If the metal ball lands on ​, the player gets to keep the ​$7 paid to play the game and the player is awarded an additional ​$245. ​ Otherwise, the player is awarded nothing and the casino takes the​ player's ​$7. What is the expected value of the game to the​ player? If you played the game 1000​ times, how much would you expect to​ lose? Question content area bottom Part 1 The expected value is ​$ -0.37. the player would expect to lose about ​$

Answers

Answer:

973.68 times

Step-by-step explanation:

Since you would expect to win 1 in 38, the amount of times you will win in 1000 times is 1000 / 38 which is 26.32. therefore you would expect to lose 1000 - 26.32 times which is 973.68

What is the area?
2 yd
8 yd
5 yd

Answers

Answer:

28

Step-by-step explanation:

I assume the polygon is a trapezoid with parallel bases of 2 yd and 5 yd, and an altitude of 8 yd.

area of trapezoid = (base1 + base2)h/2

area = (2 yd + 5 yd)(8 yd)/2

area = 28 yd²

An object is thrown upward from the top of 96​-foot building with an initial velocity of 80 feet per second. The height h of the object after t seconds is given by the quadratic equation h=16t^2+80t+96. When will the object hit the​ ground?

Answers

The function of the object height is an illustration of a projectile motion

The object will never hit the ground

How to determine when the object hits the ground?

The function is given as:

h=16t^2+80t+96.

When the object hits the ground, h = 0

So, we have:

16t^2+80t+96 = 0

Divide through by 16

t^2+5t+6 = 0

Expand

t^2 + 3t + 2t + 6 = 0

Factorize

t(t + 3) + 2(t + 3) = 0

Factor out t + 3

(t + 2)(t + 3) = 0

Solve for t

t = -2 or t = -3

The time (t) cannot be negative.

Hence, the object will never hit the ground

Read more about projectile motion at:

https://brainly.com/question/1130127

Answer:

6

Step-by-step explanation:

did this question in savvas

The fuel gauge shows how much fuel is left in a 10 gallon tank. How far can you drive if the car's average fuel consumption is 40 miles per gallon?

Answers

Answer:

ok so we have 10 gallons left and we get 40 miles per gallon so this is just multiplycaiton

10*40=400

so you can get 400 more miles

Hope This Helps!!!

The measure of an angle is 74.4°. What is the measure of its complementary angle?

Answers

Answer:

15.6

Step-by-step explanation:

complementary angles sum up to 90

90-74.4=15.6

therefore the measure of it's complementary angle is 15.6

PLSSS HEELPPP A line passes through (3, -2) and (6, 2).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.

a. y+2= 4/3(x+3); -4x+ 3y= -18
b. y+2= 4/3(x-3); -4x+3y= -18
c. y-2= 4/3(x-3); -4x+3y= 18
d. y-3= 4/3(x+2); -4x+3y= 17

Answers

Answer:

b)

Step-by-step explanation:

Question (a)

[tex]\sf let \ (x_1,y_1)=(3,-2)\\\\\sf let \ (x_2,y_2)=(6,2)[/tex]

[tex]\sf slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{2-(-2)}{6-3}=\dfrac43[/tex]

Point-slope formula: [tex]\sf y-y_1=m(x-x_1)[/tex]

Substituting m and point (3, -2) into the formula:

[tex]\sf y-(-2)=\dfrac43(x-3)[/tex]

[tex]\sf y+2=\dfrac43(x-3)[/tex]

Question (b)

Rewrite in standard form:

[tex]\sf y+2=\dfrac43x-4[/tex]

[tex]\sf \implies y=\dfrac43x-6[/tex]

[tex]\sf \implies 3y=4x-18[/tex]

[tex]\sf \implies -4x+3y=-18[/tex]

Kim is 15 years old. Her father is 4 times as old as her now. In how many years time their total age be 115 years.

Answers

Answer:

100 later kim will be 115

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