The volume V of the described solid S is 3.48 π and this can be described by performing the integration and using the given data.
How to find the volume of the described solid?Given: The base of S is the region enclosed by the parabola [tex]$y=2-3 \mathrm{x}^2$[/tex] and the x-axis.
Cross-sections perpendicular to the y-axis are squares.
To determine the x-intercept by substituting (y = 0) in the given function.
[tex]$&0=2-3 \mathrm{x}^2 \\[/tex]
[tex]$&x^2=\frac{2}{3} \\[/tex]
[tex]$&x=\pm \sqrt{\frac{2}{3}}[/tex]
The volume of solid S is given by: [tex]$\mathrm{V}=\pi \mathrm{r}^2 \mathrm{~h}$[/tex]
where [tex]$\mathbf{r}=\mathbf{y}\sqrt{x}[/tex] and h = dx.
[tex]$&\mathrm{dV}=\pi\left(2-3 \mathrm{x}^2\right)^2 \mathrm{dx} \\[/tex]
[tex]$&\mathrm{dV}=\pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx}[/tex]
Now, integrate the above expression.
[tex]$&\int \mathrm{dV}=\int_0^{\sqrt{2 / 3}} \pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx} \\[/tex]
[tex]$&\mathrm{V}=\pi\left[\left(9 \frac{\mathrm{x}^5}{5}-\frac{12 \mathrm{x}^3}{3}+4 \mathrm{x}\right)\right]_0^{\sqrt{2 / 3}}[/tex]
Simplify the above expression, we get
[tex]$&\int \mathrm{dV}=\int_0^{\sqrt{2 / 3}} \pi\left(9 \mathrm{x}^4-12 \mathrm{x}^2+4\right) \mathrm{dx} \\[/tex]
[tex]$&\mathrm{V}=\pi\left[\left(9 \frac{\mathrm{x}^5}{5}-\frac{12 \mathrm{x}^3}{3}+4 \mathrm{x}\right)\right]_0^{\sqrt{2 / 3}}[/tex]
Simplify the above expression.
[tex]$$\mathrm{V}=\pi\left[\left(9 \frac{\left(\sqrt{\frac{2}{3}}\right)^5}{5}-\frac{\left(\sqrt{\frac{2}{3}}\right)^3}{3}+4\left(\sqrt{\frac{2}{3}}\right)\right]\right.$$\alpha[/tex]
Now, simplify the above expression by using the arithmetic operations.
V ≈ 3.48 π
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Please awnser fast due tommorow worth 40 pts(I need all of the answered)1 Which of the following could be the graph of the equation y =-2x + 5? How do you know?
Answer: Your image is too blurry to read, but the third graph from the left is correct for y=-2x+5
Step-by-step explanation: This equation is already in the slope-intercept form: y=mx+b. In the slope-intercept form, m=slope of the line and b=intercept. For your equation, the slope is -2 and the y-intercept is where y=5. To graph the line, the -2 slope is down 2 on the y-axis for every +1 on the x-axis. Please see my attached image for the graph.
Two years ago, a car was valued at $24,000. This year, the value of the car is $23,160. What was the percent decrease in the value of the car?
The value of the car is decreased by 3.5%.
A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
The value of the car two years ago was $24,000.
The value of the car this year is $23,160.
The decreased value of the car after two years will be:
= $24,000 - $23,160
= $840
Let y be the percentage by which the value of the car decreased,
y = 840/24000
y = 0.035
y = 3.5/100
y = 3.5%
The value of the car decreased by 3.5 percent in two years.
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brittany is going on vacation and taking her dog pickles along. pickles eats 2 cups of hungry hound dog food each day. brittany wants to know how many days she can feed pickles from a 14-cup bag of hungry hound. which equation can brittany use to find the number of days d she can feed pickles from the bag.
The equation will be 2d = 14 and the number of days d she can feed pickles from the bag is 7 days.
Pickles eat 2 cups of hungry hound dog food each day.
brittany wants to know how many days she can feed pickles from a 14-cup bag of hungry hounds.
We need to find the number of days d she can feed pickles from the bag.
Number of days = d,
So, Every day, Pickles consumes 2 cups of Hungry Hound dog chow.
Pickles then consume cups of Hungry Hound dog chow every day for a few days.
Then,
2*d = 14
[tex]d=\frac{14}{2} = 7[/tex]
Thus, the number of days d she can feed pickles from the bag is 7 days.
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a polygon is a 2d shape with all straight edges. show via induction that the sum of the interior angles of a polygon with n sides is (n −2) ×180◦. don’t include unneeded base cases. hint 1: it is helpful to know that a triangle’s interior angles always sum to 180◦. you may assume this is true for the problem. hint 2: in order to apply your inductive hypothesis to a polygon, you’ll need to think of it in terms of a smaller polygon. how can you make a smaller polygon out of a big one?
Using the process of induction we can prove that the sum of all angles of a polygon is (n −2) ×180°
In geometry, a polygon is a planar shape characterized by a finite number of segmented straight lines linked to form a network of closed polygons (or polygonal circuit). A polygon is defined as either a bounded plane region or a bounding circuit.
Sum of all angles of a triangle is 180°
Sum of all angles of a quadrilateral is 360°
We know that a triangle has 3 sides.
Hence (n −2) ×180 for n=3 given 180
and (n −2) ×180 for n=4 gives 360.
So we can say that the formula holds by the properties of induction.
The portions of a polygonal circuit are known as its margins or sides. A polygon's vertices or corners are the points where two edges meet. The inside of a solid polygon is sometimes referred to as its body. An n-gon appears to be a polygon with n sides, similar to a triangle, which is a 3-gon.
Hence the formula (n −2) ×180◦ holds for induction.
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What is geometric art /geometric abstraction?
Geometric art or geometric abstraction is a form of art based on geometric figures and polygons, like lines, angles, squares, trapezoids, etc.
A cylinder tank has a radius of 7.5 feet and an altitude of 14 feet. If a gallon of paint will cover 130 ft.² of surface how much paint is needed to put two coats of paint on the entire surface of the tank?
A cylinder tank has a radius of 7.5 feet and an altitude of 14 feet. If a gallon of paint will cover 130 ft.² of surface how much paint is needed to put two coats of paint on the entire surface of the tank?
Remember that
The surface area of a cylinder is equal to
[tex]SA=2B+Ph[/tex]where
B is the area of the circular nase
P is the circumference of the circular base
h is the height of the cylinder
so
Find out B
[tex]B=\pi\cdot r^2[/tex]we have
r=7.5 ft
pi=3.14
substitute
[tex]\begin{gathered} B=3.14\cdot(7.5)^2 \\ B=176.625\text{ ft2} \end{gathered}[/tex]Find out the circumference
[tex]\begin{gathered} P=2\pi\cdot r^{} \\ P=2(3.14)\cdot7.5 \\ P=47.1\text{ ft} \end{gathered}[/tex]the value of h=14 ft
therefore
SA=2(176.625)+47.1(14)
SA=1,012.65 ft2
Remember that s needed to put two coats of paint
Multiply the surface area by 2
1,012.65*2=2,025.3 ft2
1 gallon -------> 130 ft2
applying proportion
1/130=x/2,025.3
solve for x
x=2,025.3/130
x=15.6 gal
therefore
the answer is 16 gallonWatch helo video Find the value of f(-3). y = f(x) 9 e 6 4 2 N 6 2 Submit Answer Answer:
when x = -3
f(-3) = 5 5 is the result
Solving Inequalities with One Variable
Show work
2(7 − 2) > 9 + 6
Answer: no solution
Step-by-step explanation:
2× (7-2)>9+6
Calculate the sum or difference
2×5>9+6
Calculate the sum or difference
2 × 5 > 15
2×5>15
Calculate the product or quotient
10 > 15
10 > 15
The solution of the inequality
no solution
How is volume measured for liquids and solids?
Answer: By convention, the volume of liquids and gases is often expressed in units of liters or milliliters, measured with glassware. The dimensions of regularly shaped solids can be measured directly with rulers or calipers, which have linear units, giving volumes in units such as cubic centimeters.
Step-by-step explanation:
Solve the following system of linear equations by graphing:-X+ y = -74x + 4y = 20
1) Let's solve this Linear System, using the method of Elimination/Addition
-x+y=-7 Multi
4x+4y = 20
PLS HELP! THIS HOMEWORK IS DUE TOMORROW
Rhian scored more in the Math test than in the English test because she had a higher percentage
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that: In the Maths test, Rhian scored 14 out of 17, hence:
Mark percentage = (14 / 17) * 100% = 82.35%
In the English test, Rhian scored 31 out of 39, hence:
Mark percentage = (31 / 39) * 100% = 79.49%
Rhian scored more in the Math test.
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find the area of this circle
Answer:
Formula given : Area = πr²
where r is the radius
the given radius is 5 inches
and pi is 3.14
so 3.14x 5²
3.14 x 25
the area is 78.5 in²
hope it helps, mark as brainliest :D
Answer:
A = 78.54 in²
Step-by-step explanation:
A = πr²
A = π(5²)
A = 25π
A = 78.54 in²
2 = x/6
HELP, WILL MARK BRAINLIEST
Answer:
x= 12
Step-by-step explanation:
12÷6=2
2. Kelley makes her own potting soil mix for planting flowers. She uses 2 scoops of compost with 9 scoops of top soil. If she uses 18 scoops of compost, how many scoops of top soil will she use?
Answer: 81
Step-by-step explanation: If we divide the numbers given to use, (2 factors of compost), you get 9, (do 18 divided by 2). 9 times 9 is 81.
Answer the questions below to find the total surface area of the can.
The total surface area of the can is 61.23 square inches
The total surface area of can S = 2πr(r+h)
where:
h is the height
r is the radius
A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth.
Given
h = 5in
r = 1.5in
S = 2(3.14)(1.5)(1.5 + 5)
S = 6.28(1.5)(6.5)
S = 61.23 square inches
Hence the total surface area of the can is 61.23 square inches
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4x-2y=-40 liner equation
Solving Linear equation 4x-2y= -40 : x = 10 + 0.5y
What is Linear Equation?
A linear equation is a mathematical expression that may be written as x 1+ldots +a n+x n+b=0, where x 1, ldots, and x n are the variables and displaystyle b, a 1, ldots, and a n are the coefficients, which are frequently real integers.
Simplifying
4x + -2y to 40
Solving
4x + -2y = 40
fixing the 'x' variable.
x should be moved to the left of all terms, and the right of all other terms.
To each side of the equation, add "2y."
4x + -2y + 2y = 40 + 2y
combining similar terms
-2y + 2y = 0
4x + 0 = 40 + 2y
4x = 40 + 2y
Multiply each side by "4".
x = 10 + 0.5y
Simplifying
x = 10 + 0.5y
Hence, solving for x the value of x = 10 + 0.5y
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The equation of line L, is y = 5x + 1
The equation of line L, is 2y - 10x + 3 = 0
Show that these two lines are parallel.
Answer:
They are parallel because they both have the same gradient of 5.
Step-by-step explanation:
For lines to be parallel they need to contain the same gradient.
1. therefore we rearrange the second equation to get y the subject so it's in the format of y=mx+c
2. 2y-10x+3=0
- we +10x and -3 on both sides to get y on its own
2y=10x-3
- we divide each side by 2 as we want y not 2y
y=5x-[tex]\frac{3}{2}[/tex]
3. From this we can see that both the equation contains the same gradient (5)
therefore, they are parallel.
Can someone pls help me with this it would Be a blessing
The Telus Plaza South in Edmonton is approximately 134 m tall. Stacy is lying down near the building. The angle formed by the ground and her line of sight from the ground to the top of the building is 67°. Stacy is 316m from the building's foundation to the nearest meter.
What is slight angle?at an angle, leaning to one side, and not straight or erect, according to the Longman Dictionary of Contemporary English The portrait was hung in an unusual position. at a moderate/sharp angle The sign had a small incline to it.A circular mean, also known as an angular mean, is a mean created specifically for angles and other cyclical values like daytimes and fractional parts of real integers. This is essential since many common measures might not be appropriate for values with an angular distribution.A low-angle shot is one that is taken from a camera angle that is low on the vertical axis, pointing upward and anyplace below the eye line.To learn more about slight angles refer to:
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At the mall, Timmy bought a T-shirt and a book for a total of $23. The book cost $12. How much did the T-shirt cost? Let x represent the unknown information. Write an addition equation that models the problem
The equation can be modelled by 23 = 12 + x
How to determine the addition equation?The given parameters are
Cost of book = $12
Total purchase = $23
The total purchase can be calculated by adding the cost of the book and the cost of the T-shirt
This is represented as
Total purchase = Cost of book + Cost of T-Shirt
So, we have
23 = 12 + x
Where x represent the unknown information.
Hence, the addition equation is 23 = 12 + x
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pls help it’s a math question will mark brainliest
Answer: B the lines are neither parallel nor perpendicular.
Step-by-step explanation:
To make this easier we can make both equations into y-intercept statements.
y = 5x - 7
-8y = -x - 6
y = 1/8x + 6/8
By looking at the slopes of both equations (5 and 1/8) we can see that they are neither the same nor opposite reciprocals.
Stefan sells jin a bicycle for $113 and a helmet for $19. The total cost for jin is 110% of what stefan spent originally to buy the bike and helmet. How much did stefan spend originally? How much money did he make by selling the bicycle and helmet to jin?
Stefan spent originally to buy a bike $95 and $15 to buy a helmet and he made $17.27 by selling the bicycle and $1.73 by selling the helmet to Jin.
The selling cost for Stefan bicycle = $113 and
the selling cost of a helmet = $19.
The total cost for Jin is 110% of the money spent by Stefan
Let us assume purchasing cost of a bicycle = $x.
Purchasing cost of a helmet = $y.
For bicycle
110% of x is $113
=> 1.10 × x = 113
Dividing both sides by 1.10, we get
x=$102.72.
Stefan spent for his bicycle = 102.72
For helmet.
110% of y is $19.
=> 1.10 × y = 19.
Dividing both sides by 1.10, we get
y = $17.27
Stefan spent for his helmet = 17.27
money made by selling the bicycle is $113 - 102.72 = $10.72
money made by selling the helmet is $19 - 17.27 = $1.73.
Therefore, Stefan spent originally to buy a bike $95 and $15 to buy a helmet and he made $17.27 by selling the bicycle and $1.73 by selling the helmet to Jin.
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4. Cindy has $2.50 to spend on milk and
candy. The milk costs $0.70. Her favourite
candies cost $0.12 each.
a) Write an equation that models the
number of candies that Cindy can afford.
b) Solve the equation.
A customer wanted to purchase a video game and realized that they were short $5. 32 to be able to pay. Which value is the opposite of being short $5. 32?
−$10. 64
−$5. 32
$5. 32
$10. 64
Anna shipped a small package from north carolina to Virginia for $1.15 her package weighed 5 ounces write and solve an equation to determine the shipping cost per ounce
Given:
Total shipping cost = $1.15
Weight of package = 5 ounces
The equation to determine the hipping cost per ounce is:
[tex]\begin{gathered} \text{Shipping cost per ounce = }\frac{Total\text{ shipping cost}}{\text{Weight of package}} \\ \\ \text{Shipping cost per ounce = }\frac{1.15\text{ }}{5\text{ }} \end{gathered}[/tex][tex]\text{Shipping cost per ounce = }\frac{1.15\text{ }}{5\text{ }}\text{ = \$0.23}[/tex]Shipping cost per ounce = $0.23
ANSWER:
[tex]\frac{1.15\text{ }}{5\text{ }}\text{ = \$0.23}[/tex]PLEASE HELP ME QUICKK
It is given that a = 30°. It is also shown that C is a right angle, thus c = 90°. The interior angles of a triangle always add up to 180°. So:
a + b + c = 180
30 + 90 + b = 180
b + 120 = 180
b + 120 - 120 = 180 - 120
b = 60°
helppppppp A construction company takes 1/4 hours to remove 1/4 metric tons of dirt from a construction site.
What is the unit rate in metric tons per hour?
Write your answer in simplest form. i need this urgentlyyyyyy
The unit rate in metric tons per hour is 1 metric ton per hour.
The unit rate will be calculated by simply performing the division of amount of dirt by amount of time.
Keep the values in formula to find the value of the unit rate in metric tons per hour.
Unit rate = 1/4÷1/4
Performing division on Right Hand Side of the equation to find the value of the unit rate in metric tons per hour.
Unit rate = 1 metric ton per hour
Thus, the unit rate to remove dirt from construction site is 1 metric ton per hour.
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4. An object will most effectively absorb the
sun's rays if it is
(A) polished, and dark in color.
(B) polished, and light in color.
(C) rough, and light in color.
(D) rough, and dark in color.
Which of the following is a solution of the equation 9 - 2x = -1?
-4
5
4
-5
Answer:
It's 5
Step-by-step explanation:
A cone and a cylinder both have a radius of 3 inches and a height of 7 inches. If you wanted to adjust the cone's radius so that both solids have the same volume, what should the cone's radius be?
Answer:
radius = 5.196 ins. to nearest thousandth.
Step-by-step explanation:
Volume of the cylinder = π (3)^2 7
= 63π in^3.
Volume of the cone = 1/3 π r^2 7 where r is the new radius of the cone
So, 63π = 7/3 π r^2
r^2 = 63 / 7/3
= (63*3)/7
= 27
r = 5.196 in.
Simplify open parentheses x to the 2 fifths power close parentheses to the 5 sixths power
Answer:
x 1/3
Step-by-step explanation:
