Answer:
[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]
Step-by-step explanation:
The equation of the line through the point [tex](x_o,y_o)[/tex] & [tex](x_1,y_1)[/tex] can be represented by:
[tex]y-y_o = m(x - x_o)[/tex]
Making m the subject;
[tex]m = \dfrac{y_1 - y_0}{x_1-x_0}[/tex]
∴
we need to carry out the equation of the line through (0,1) and (1,2)
i.e
y - 1 = m(x - 0)
y - 1 = mx
where;
[tex]m= \dfrac{2-1}{1-0}[/tex]
m = 1
Thus;
y - 1 = (1)x
y - 1 = x ---- (1)
The equation of the line through (1,2) & (4,1) is:
y -2 = m (x - 1)
where;
[tex]m = \dfrac{1-2}{4-1}[/tex]
[tex]m = \dfrac{-1}{3}[/tex]
∴
[tex]y-2 = -\dfrac{1}{3}(x-1)[/tex]
-3(y-2) = x - 1
-3y + 6 = x - 1
x = -3y + 7
Thus: for equation of two lines
x = y - 1
x = -3y + 7
i.e.
y - 1 = -3y + 7
y + 3y = 1 + 7
4y = 8
y = 2
Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7
∴
[tex]\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg) dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ([y^2(-4y+8)] \bigg ) \ dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( -4y^3+8y^2 \bigg ) \ dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{-45+56}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{11}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]
A grocery store sells steak for $6.10 per pound. What would be the cost of 2 lb of steak?
Answer: 12.20
Step-by-step explanation:
because if 6.10 is the amount for one pound, then if u need 2 pounds, then multiply 6.10 with 2.
What is the range of fx) = 3^x
Answer: For the cubic function f(x)=x3 f ( x ) = x 3 , the domain is all real numbers because the horizontal extent of the graph is the whole real number line. The same applies to the vertical extent of the graph, so the domain and range include all real numbers.
Step-by-step explanation:
What is the difference between heat and temperature?
How does a thermometer measure temperature?
When, if at all, does heat transfer stop?
Exit Ticket
What type of heat transfer occurs when eggs fry in a pan?
What type of heat transfer occurs when you roast a marshmallow by holding it over a campfire?
What type of food in which convection helps the cooking process? Explain your answer
When you touch a picnic table, your hand gets warmer. Explain how energy conservation applies to this situation
please answer these i give brainliest
Answer:
heat is hot and tempture is all
6) Choose which postulate proves the triangles congruent.
Answer:
SAS(Side.Angle.Side
Step-by-step explanation:
since x is mid point of pr and qs so px=xr and x is midpoint of qs so qx=sx,
and two lines intercept so angles made on point x are equal.....hence 2 sides and one angle proved so triangles are equal
The postulate that can be used to prove that triangle QXP and triangle SXR are congruent to each other is: SAS Congruence Theorem,
Recall:
Two triangles are congruent by the Side-Angle-Side Congruence Theorem, if two sides and one included angle of one triangle are congruent to two sides and the corresponding included angle in the other triangle.Since X is a midpoint of QS and RP, therefore:
[tex]PX \cong RX\\\\QX \cong SX\\[/tex]
Also,<PXQ = <SXR (vertical angles are congruent)
Thus, triangle QXP and triangle SXR are congruent by SAS.Therefore, the postulate that can be used to prove that triangle QXP and triangle SXR are congruent to each other is: SAS Congruence Theorem,
Learn more here:
https://brainly.com/question/25126660
There was a study done on oxygen consumption of snails as a function of pH, and the result was a degree 4 polynomial whose graph is shown.
Which of the following statements about this function is INCORRECT?
Answer:
A. There is a positive leading coefficient
Step-by-step explanation:
Polynomials can be represented as an equation or graphs.
The incorrect option is: (b) There is a positive leading coefficient.
The polynomial has a degree of 4; this means that the degree of the polynomial is even.
So option (a) The degree of the polynomial is even is true
From the graph, we can see that the function decreases at (7<x<8) and (9<x<10)
This means that, the function decreases at two intervals
So option (d) There are two intervals where the function is decreasing is also true
Also, the function is at maximum at x = 7 and x = 9.
This means that:
Option (c) At two pH values, there is a relative maximum value
Hence, the incorrect option is:
(b) There is a positive leading coefficient.
This is so because, the graph decreases at some points on the graph.
This means that, the graph has a negative leading coefficient.
Read more about polynomials at:
https://brainly.com/question/17333460
42 kids bought popcorn at the movie. This was 60% of the kids who attended the movie.
How would you summarize the process to find the number of kids who attended the
movie?
Answer:
Total number of children = 70
Step-by-step explanation:
Given:
Number of kids buy popcorn = 42
Percent of kids buy popcorn = 60% = 0.6
Find:
Total number of children
Computation:
Total number of children = Number of kids buy popcorn / Percent of kids buy popcorn
Total number of children = 42 / 0.6
Total number of children = 70
During the summer, 1.3% of the water in the kiddie pool evaporates every day. If the kiddie pool holds 8,000 gallons of water and is not
refilled for 10 days, how many gallons of water will be in the pool? Round your answer to the nearest gallon enter the amount
Answer:
7019 gallonsStep-by-step explanation:
Initial volume of water = 8000 galDaily reduction = 1.3% Time = 10 daysRequired equation:
8000*(1- 0.013)^10 =8000*0.987^10 =7018.7781 ≈ 7019 rounded to the nearest gallonhelp me.............
Answer:
is there a right angle?
Step-by-step explanation:
2u = u + 43
u = 43?
LOOK AT THE PICTURE TO ANSWER
what is the area of a rectangle with a length of 142 cm and a width of 23 cm?
Answer:
3,266
Step-by-step explanation:
Answer:
3266cm²
Step-by-step explanation:
try it it healps
SOMEONE, PLEASE HELP LITERALLY STRUGGLING!!!!!!
Circle 1 represents students involved with drama after school, circle 2 represents students involved in sports, and circle 3 represents students in academic club activities. What can you conclude about students who fit in region B?
A.
Region B represents the students involved in sports only.
B.
Region B represents the students involved in sports and academic clubs.
C.
Region B represents the students involved in drama and sports.
D.
Region B represents the students not involved in academic clubs.
Please select the best answer from the choices provided
A
B
C
D
Answer:
A
Step-by-step explanation:
Fill in the blank with the correct constant of proportionality. Pounds of Bananas Cost ($) 2, 2.50, 3, 3.75, 5, 6.25, 7, 8.75 The constant of proportionality is
Answer:
it will go up 1 dollar now i had to do it in my head
Step-by-step explanation:
mabey if im wrong sorry
2 Vishal is training for a race. His goal is to run 5.5 miles over three days. The distances he ran each day are shown in the table.
Answer:
Which table?
Step-by-step explanation:
Answer:
I know this is old but here is the answer bc I had this test
Step-by-step explanation:
1. he ran 5.478 in total
2. he ran 0.022 more than his goal.
Vishal ran a total of 5.478 miles. The distance he ran over the three days is greater than his goal by 0.022 miles.
hey , can you help me with this thanks !!
Answer:
16
Step-by-step explanation:
the sides may not seem to help but it dose go to the other side and try to meser it it would be 4. add 8+4+4 or 8+8=16
Answer:
18.6cm (rounded to 3 s.f.)
Step-by-step explanation:
You can actually figure out the two bases of the triangles based on the Pythagoras theorem where the slant length of a 90° triangle is [tex]\sqrt{a^{2} + b^{2} }[/tex] where a is one of the bases and b is the other length that is 90° perpendicular to a.
So this means:
[tex]\sqrt{6^{2} + base^{2} }[/tex] = 8cm
6² + base² = 64cm
36 + base² = 64
base² = 64-36
= 28
base = [tex]\sqrt{28}[/tex]
≈ 5.2915 (5 s.f.)
So the two bases are roughly 5.2915, and the middle base is part of a rectangle, so it has the same length as the rectangle's length, which is 8cm.
Thus, x = 5.2915 + 5.2915 + 8
= 18.6cm (rounded to 3 s.f.)
Solve this equation 5x -7 = -12
Answer:
The answer is x = -1
Step-by-step explanation:
Answer:
x=-1
Step-by-step explanation:
5x-7=-12
5x=-5
x=-1
A pet store sells dog treats and the prices are represented
in the graph
X = number of treats
y = cost (in dollars)
Select the true statement.
Select one
Each treat costs $0.50
Each treat costs $3
Each treat costs $2
Each treat costs 51
Answer: 1$
Step-by-step explanation:
When Daria gets to school, the temperature is 5.7°F. The temperature changes
by -9.5°F by the time she goes to bed. What is the temperature when Daria goes
to bed? Show your work.
Answer:
-3.8
Step-by-step explanation:
The temperature when Daria goes to bed was -3.8° F.
What is subtraction?To subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduces or becomes less.
Given that, When Daria gets to school, the temperature is 5.7 °F. The temperature changes by -9.5 °F by the time she goes to bed.
5.7 - 9.8 = -3.8
Hence, The temperature when Daria goes to bed was -3.8° F.
For more references on subtraction, click;
https://brainly.com/question/2346316
#SPJ5
11)
Paul pays the delivery man £180 for working 24 hours.
How much will he pay him for working 40 hours?
£
Answer:
£196
Step-by-step explanation:
1) 180/24=7.5
2) 40-24=16
3) 180+16=196
so he has to pay £196
at the zoo,the ratio of monkeys to gorillas is 5:1
Answer:
thats a statement
Step-by-step explanation:
In which quadrant does the point S(-3, -4) lie?
quadrant I
quadrant II
quadrant III
quadrant IV
It would be quadrant III
Answer:
Quadrant 3
Step-by-step explanation:
Quadrant 3: (-, -)
Pete has 4 packs of gum balls. Each pack has 5 gum balls. If Pete gives the same number of gum balls to 6 friends, how many gum balls will each friend get?
2
3
4
5
Answer:
I would say 3
Step-by-step explanation:
Graph a line through (2,-5) and have a slope of -4
im sorry: In order to solve the inequality -x > 8, which of the following steps must be done?
According to the graph below, what percent of the Simpsons’ annual expenses is Federal taxes? A circle graph titled Simpson's Annual Expenses. Federal taxes, 24 percent; State/local taxes, 10 percent; Housing and household, 23 percent; Food, 6 percent; Medical care, 8 percent; Transportation, 11 percent; Recreation, 3 percent; Clothing, 5 percent; Other, 10 percent. a. 10% b. 14% c. 24% d. 34%
According to the graph, the percentage of the Simpsons’ annual expenses that is Federal taxes is 24%
What is a circle graph?A circle graph also known as pie chart has a shape of a circle and each section are represented in percentages or degrees
From the question, we have:
Federal taxes = 24%State/local taxes = 10%Housing and household = 23%;Food = 6%Medical care = 8%Transportation = 11%Recreation = 3%Clothing = 5%Other = 10%The above means that the percentage of the Simpsons’ annual expenses that is Federal taxes is 24%
Read more about circle graphs at:
https://brainly.com/question/24461724
Answer:
10%
Step-by-step explanation:
Please help me answer!
Answer:
B
..................
Find the value of x in the
following parallelogram:
2x
х
х
2x
Answer:
60°
Step-by-step explanation:
The sum of the angles in any quadrilateral is 360°. In a parallelogram the sum of neighboring angles is 180°. Therefore:
2x + x = 180°
3x = 180°
x = 60°
The value of x is 60.
What is properties of parallelogram?Parallel sides define an object.Congruent opposites are present.Angles at opposites are congruent.Consecutive angles on the same side called supplementary angles.A parallelogram is divided into two congruent triangles by each of its diagonals.A parallelogram's diagonals cut each other in half.Given:
Angles x, x, 2x, 2x.
Using the property of parallelogram, the adjacent angles of parallelogram sum to 180.
x+ 2x= 180
3x= 180
x= 180/3
x= 60
Hence, the value of x is 60.
Learn more about properties of parallelogram here:
https://brainly.com/question/26651476
#SPJ2
What is 4(2 + a) = 24
a=
Answer:
2/5
Step-by-step explanation:
Rearrange terms:
4(2 + a) = 24a
4(a + 2) = 24a
Distrbute:
4(a + 2) = 24a
4a + 8 = 24a
Subtract 8 from both sides of the equation:
4a + 8 = 24a
4a + 8-8 = 24a-8
Simplify:
4a = 24a - 8
Subtract 24a from both sides of the equation:
4a = 24a - 8
4a - 24a = 24a - 8 - 24a
Combine like terms:
-20a = -8
Divide both sides of the equation by the same term:
-20a = -8
-20a/-20 = -8/-20
Simplify:
Cancel terms that are in both the numerator and denominator
Divide the numbers
a = 2/5
I hope that helps! :D
By 27leejaeyDeanna Jones opened a video rental store this year with 400 tapes. She plans to buy 150 new tapes each year from now on. Deanna expects to have 1300 tapes available during her fifth year in business. At her current purchasing rate, will she reach her goal? Explain.
A. No, she will have only 1150 tapes.
B. Yes, she will have exactly 1300 tapes.
C. Yes, she will have over 1300 tapes.
HURRY NEED SOON PLEASE
Student #1:
6(x - 0.5) > 3
6x - 3 > 3
6x > 0
x > 0
Solved the inequality incorrectly but graphed their solution correctly.
Solved the inequality correctly and graphed their solution correctly.
Solved the inequality correctly but graphed their solution incorrectly.
Solved the inequality incorrectly and graphed their solution incorrectly.
Answer:
D, both incorrect
Step-by-step explanation:
Answer:
Student #1:
6(x - 0.5) > 3
6x - 3 > 3
6x > 0
x > 0
2) Solved the inequality correctly and graphed their solution correctly.**PLEASE HELP**
Find the equation, f(x)=a(x-h)^2+k, for a parabola that passes through the point (0,0) and has a (-3,-6) as its vertex. What is the standard form of the equation?
A.) The vertex form of the equation is f(x)= - 2/3(x+3)^2-6. The standard form of the equation is f(x)=2/3x^2+4x.
B.) The vertex form of the equation is f(x)=2/3(x+3)^2-6. The standard form of the equation is f(x)+-2/3x^2-4x.
C.) The vertex form of the equation is f(x)= - 2/3(x-3)^2-6. The standard form of the equation is f(x)=2/3x^2-4x.
D.) The vertex of the equation is f(x)=2/3(x+3)^2-6. The standard form of the equation is f(x)=2/3x^2+4x.
Answer:
D) The vertex of the equation is [tex]f(x) = \frac{2}{3}\cdot (x+3)^{2}-6[/tex]. The standard form of the equation is [tex]f(x) = \frac{2}{3}\cdot x^{2}+4\cdot x[/tex].
Step-by-step explanation:
Let [tex]A(x,y) = (0,0)[/tex] and [tex]V(x,y) = (-3, -6)[/tex] (vertex).
If we know that [tex]x = 0[/tex], [tex]y = 0[/tex], [tex]h = -3[/tex] and [tex]k = -6[/tex], then the standard equation results in:
[tex]a\cdot (0+3)^{2}-6 = 0[/tex]
And the value of [tex]a[/tex] is:
[tex]9\cdot a - 6 = 0[/tex]
[tex]a = \frac{2}{3}[/tex]
And the vertex form of the equation is [tex]f(x) = \frac{2}{3}\cdot (x+3)^{2}-6[/tex].
Lastly, the standard form of the equation is found by algebraic means:
[tex]f(x) = \frac{2}{3}\cdot (x^{2}+6\cdot x +9)-6[/tex]
[tex]f(x) = \frac{2}{3}\cdot x^{2}+4\cdot x[/tex]
The standard form of the equation is [tex]f(x) = \frac{2}{3}\cdot x^{2}+4\cdot x[/tex].
In consequence, the right answer is D.
- 4(6 + 5g) equivalent expressions
Answer:
the awnser is 4g because if you multiply the -4 by 6 and 5 g you get the equation: -24+-20g.. subtract -24 from -20 you will get 4g
