the discount amount is RS 160.
define discountA discount is a reduction in the price of a product or service that is offered by a seller to a buyer. The discount may be a percentage of the original price or a specific amount of money.
Let the market price of the watch be x.
After allowing a 10% discount, the selling price becomes 0.9x.
Then, adding 15% VAT, the final selling price is:
0.9x + 0.15(0.9x) = 1.035x
We know that the final selling price is RS 1656, so we can set up an equation:
1.035x = 1656
Solving for x, we get:
x = 1600
Therefore, the market price of the watch was RS 1600.
The discount amount is the difference between the market price and the discounted selling price:
Discount amount = Market price - Discounted selling price
= 1600 - 0.9x
= 1600 - 0.9(1600)
= 1600 - 1440
= 160
So the discount amount is RS 160.
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three-fourths of the chocolates in a box are dark chocolate. three-eighths of the dark chocolates are filled with caramel. what fraction of the chocolates in the box are dark chocolate and filled with caramel?
Fraction of the chocolates in the box that are dark chocolate and filled with caramel is 3/32.
To solve this problem, we need to determine what fraction of chocolates in the box are both dark chocolate and filled with caramel. We are given that:
Three-fourths of the chocolates in a box are dark chocolate. Three-eighths of the dark chocolates are filled with caramel. We need to find out the fraction of chocolates that are dark chocolate and filled with caramel. To find out the fraction of chocolates in the box that are dark chocolate, we divide the number of dark chocolates by the total number of chocolates.
This is given by:
3/4 (dark chocolates)
To find the fraction of dark chocolates that are filled with caramel, we multiply the fraction of dark chocolates by the fraction of dark chocolates filled with caramel. This is given by:
3/4 × 3/8 = 9/32
Therefore, the fraction of chocolates in the box that are dark chocolate and filled with caramel is 9/32.
To simplify the fraction 9/32, we can divide the numerator and denominator by their greatest common factor, which is 1:9/32 = 9 ÷ 1 / 32 ÷ 1 = 9/32.
Hence, the answer is 3/32.
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[9,7] is the difference between 2 vectors with components [3,4] and [-6, b] what is b
The value of b is -6
We know that the difference between two vectors with components (a1, a2) and (b1, b2) is given by (b1-a1, b2-a2).
So in this case, we have
[b1 - 3, b2 - 4] = [(-6) - 3, b - 4]
Simplifying the right-hand side gives us
[-9, b - 4]
So we can set the components of the left-hand side equal to the corresponding components of the right-hand side
b1 - 3 = -9
b2 - 4 = b - 4
Solving for b in the first equation gives us
b1 = -9 + 3 = -6
Substituting this into the second equation and simplifying gives us
-6 - 4 = b - 4
-10 = b - 4
b = -10 + 4 = -6
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Is the following equation true or false?
(14.6 ÷ 2) x 3 – 1.9 = 3 x (8 – 4)
True or false
Answer:
False
Step-by-step explanation:
14.6/2 = 7.3
7.3 x 3 = 21.9
21.9 - 1.9 = 20
Other side:
8 - 4 = 4
4 x 3 = 12
20 does not equal 12
therefore false :)
Please help me! This is due at 2:15 PM!!!! WHICH ALREADY PASSED!!! ITS GOING TO BE LATE> A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability? Explain please.
Answer: O: 252
Step-by-step explanation:
Theoretically, all of the letters would've been drawn 250 times as that is the theoretical possibility. The closest number to the theoretical number in this experiment would be 252 which belongs to O
Let x and y both represent rational numbers. Select whether each expression is always, sometimes, or never a
rational number.
x-y
x + y
Always Sometimes Never
The expressions x - y and x = y are sometimes a rational number.
From the question, we have the following parameters that can be used in our computation:
x and y = rational numbers
The difference of two rational numbers is always a rational number, so x - y is sometimes a rational number.
The sum of two rational numbers is always a rational number, so x + y is sometimes a rational number.
Therefore, both expressions are sometimes a rational number.
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The surface area of a cone is given by the formula
S = πl + πr2. Solve the formula for l.
l = S – r2
l = S + r2
l = l equals StartFraction S Over pi minus r squared. – r2
l = l equals StartFraction S Over pi plus r squared. + r2
Answer:
The answer is:
[tex]l=\dfrac{S-\pi r^2}{\pi }[/tex]
Step-by-step explanation:
In order to determine the solution for I, we have to know about the equations.
In any equation there are variables. If we want to determine the value of one of them, we have to free that variable in any side of the equation.
Regarding the surface of a cone, i have attached an image that shows the real formula of the surface of a cone, We can see that in this case:
[tex]l=rI[/tex]
So, we have the next formula and we want to l:
[tex]S=\pi l+\pi r^2[/tex]
[tex]S-\pi r^2=\pi l[/tex]
[tex]\dfrac{S-\pi r^2}{\pi }=l[/tex]
Finally the solution for I is:
[tex]l=\dfrac{S-\pi r^2}{\pi }[/tex]
a vat with 500 gallons of beer contains 4% alcohol (by volume). beer with 6% alcohol is pumped into the vat at a rate of 5 galymin and the mixture is pumped out at the same rate. what is the percentage of alcohol after an hour?
The percentage of alcohol after an hour will be approximately 4.9%.
What is percentage?
A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Let p(t) be the percentage of alcohol at time t.
Where t is in minutes.
Amount of alcohol in vat = Volume of vat x p/100
Rate of change of alcohol in vat = Volume of vat x dp/dt time 1/100
Rate of change of alcohol in vat = 500 x dp/dt x 1/100
Rate of change of alcohol in vat = 5 x dp/dt
Net rate of change of alcohol = (Rate of inflow of alcohol) - (Rate of Outflow of alcohol)
Rate of Inflow of alcohol = 0.06 - 5 = -4.94 gal/min
Rate of outflow of alcohol = p(t)/100 x 5 = 0.05p(t) gal/min
Therefore, the rate of change of alcohol is 0.03 - 0.05 p(t) gal/min
Finally we can write
5 x dp/dt = 0.3 - 0.05 p
Divide both sides by 5
dp/dt = 0.06 - 0.01p
Integrate both sides
[tex]\int {dp} / 0.06 -0.01p = \int dt[/tex]
-100ln (0.06 - 0.01p) = t + C
At t=0, p=4, therefore
-100ln (0.06 - 0.04) = 0 + C
391.2 = C
Substitute the value of C, to get
-100ln (0.06 - 0.01p) = t + 391.2
Substitute t = 60 and solve for p
-100ln (0.06 - 0.01p) = 60 + 391.2
-100ln (0.06 - 0.01p) = 451.2
ln (0.06 - 0.01p) = -4.512
[tex]p = \frac{0.06 - e^{-4.512} }{0.01}[/tex] ≈ 4.9%
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Use a trigonometric ratio to solve for a. found to two decimal places as necessary cas22shapping to whoever gets it right
Answer: a = 16.62
Step-by-step explanation:
sin(37) = 10/a
a = sin(37) / 10
a = 16.62
Answer:
a ≈ 16.62
Step-by-step explanation:
using the sine ratio in the right triangle
sin37° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{a}[/tex] ( multiply both sides by a )
a × sin37° = 10 ( divide both sides by sin37° )
a = [tex]\frac{10}{sin37}[/tex] ≈ 16.62 ( to 2 decimal places )
Kevin has $500 in his savings account and he deposits $25 each week. Janet has $250 in her savings account and she deposits $50 each week.
(a) Write a system of equations that represents the scenario
(b) Solve the system to determine after how many weeks Kevin and Janet will have the same amount of savings. What will that amount be?
Answer:
(a) Let x be the number of weeks and let y be the total amount in their savings accounts. Then, the system of equations that represents the scenario is:
Kevin: y = 25x + 500
Janet: y = 50x + 250
(b) To determine after how many weeks Kevin and Janet will have the same amount of savings, we need to solve the system of equations by setting them equal to each other:
25x + 500 = 50x + 250
Subtracting 25x and 250 from both sides, we get:
250 = 25x
Dividing both sides by 25, we get:
x = 10
Therefore, Kevin and Janet will have the same amount of savings after 10 weeks. To find out what that amount is, we can substitute x = 10 into either equation:
y = 25x + 500
y = 25(10) + 500
y = 750
So after 10 weeks, both Kevin and Janet will have $750 in their savings accounts.
Step-by-step explanation: explained it in the answer
would most people take the following gamble? flip a coin, if heads you win $75, if tails you lose $50. explain your answer.
Answer:
50/50 Chance
Step-by-step explanation:
I'm not sure if you wrote the entire question correctly, but the highest chance you would have of winning would be 100% because the 2 sides * the 50/50 chance they have. So that would make the odds of winning 50%.
At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. What is the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item?
0.13
0.14
0.20
0.22
Let's use conditional probability to solve this problem. We want to find the probability of a customer purchasing a specialty espresso drink and a food item, so we can use the following formula:
P(specialty espresso drink and food) = P(food|specialty espresso drink) * P(specialty espresso drink)
We know that P(specialty espresso drink) = 0.56 and P(food|specialty espresso drink) = 0.35, so we can substitute these values into the formula:
P(specialty espresso drink and food) = 0.35 * 0.56
P(specialty espresso drink and food) = 0.196
Therefore, the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item is 0.196 or approximately 0.20 (rounded to two decimal places).
So, the answer is option C: 0.20.
do seagulls show a preference for where they land? to answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. the biologists chose 200 seagulls at random. each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. in all, 128 seagulls landed on the sand, 61 landed in the mud, and 11 landed on the rocks. carry out a chi-square goodness-of-fit test. what do you conclude?
Based οn the results οf the chi-square gοοdness-οf-fit test, we can cοnclude that seagulls shοw a preference fοr where they land οn the shοre.
What is statistics?Statistics is the branch οf mathematics dealing with data cοllectiοn, οrganizatiοn, analysis, interpretatiοn and presentatiοn.
Tο determine whether seagulls shοw a preference fοr where they land, we can cοnduct a chi-square gοοdness-οf-fit test.
First, we need tο state the null and alternative hypοtheses.
Null hypοthesis (H0): Seagulls have nο preference fοr where they land οn the shοre; the prοpοrtiοns οf seagulls landing οn sand, mud, and rοcks are equal tο the prοpοrtiοns οf sand, mud, and rοcks in the area.
Alternative hypοthesis (Ha): Seagulls have a preference fοr where they land οn the shοre; the prοpοrtiοns οf seagulls landing οn sand, mud, and rοcks are nοt equal tο the prοpοrtiοns οf sand, mud, and rοcks in the area.
We can use the fοllοwing fοrmula tο calculate the chi-square statistic:
χ² = Σ (O − E)2 / E
where χ² is the chi-square statistic, O is the οbserved frequency, E is the expected frequency, and Σ is the sum οf all cells.
The expected frequencies can be calculated as fοllοws:
Expected frequency οf sand = Tοtal number οf seagulls released x Prοpοrtiοn οf sand in the area = 200 * 0.56 = 112Expected frequency οf mud = Tοtal number οf seagulls released x Prοpοrtiοn οf mud in the area = 200 * 0.29 = 58Expected frequency οf rοcks = Tοtal number οf seagulls released x Prοpοrtiοn οf rοcks in the area = 200 * 0.15 = 30We can nοw calculate the chi-square statistic:
χ² = [(128 - 112)2 / 112] + [(61 - 58)2 / 58] + [(11 - 30)2 / 30] = 8.89
Tο determine the degrees οf freedοm fοr the test, we need tο subtract 1 frοm the number οf categοries (3) tο accοunt fοr the fact that the frequencies are nοt independent. Therefοre, the degrees οf freedοm is 2.
Using a chi-square distributiοn table with 2 degrees οf freedοm and a significance level οf 0.05, we find the critical value tο be 5.99.
Since οur calculated chi-square value οf 8.89 is greater than the critical value οf 5.99, we reject the null hypοthesis. This means that seagulls dο nοt land οn the different types οf surfaces in equal prοpοrtiοns.
In cοnclusiοn, based οn the results οf the chi-square gοοdness-οf-fit test, we can cοnclude that seagulls shοw a preference fοr where they land οn the shοre.
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A parabola is defined as the set of points the same distance from (6,2) and line y=4. Select all points that are on this parabola
In conclusion there are no points among the given options that are on the parabola.
why it is?
The vertex of the parabola is the midpoint between the point (6, 2) and the line y = 4, which is at (6, 3). Since the focus is below the vertex and the directrix is a horizontal line, the equation of the parabola is of the form:
(x - h)²2 = 4p(y - k)
where (h, k) is the vertex and p is the distance from the vertex to the focus (and from the vertex to the directrix).
Using the vertex and the given point (6, 2), we can find that p = 1. Therefore, the equation of the parabola is:
(x - 6)²2 = 4(y - 3)
Now we can check which of the given points satisfy this equation:
A. (4, 6)
(4 - 6)²2 = 4(6 - 3)
4 = 12 - 12
This point is not on the parabola.
B. (5, 7)
(5 - 6)²2 = 4(7 - 3)
1 = 16
This point is not on the parabola.
C. (6, 5)
(6 - 6)²2 = 4(5 - 3)
0 = 8
This point is not on the parabola.
D. (7, 6)
(7 - 6)²2 = 4(6 - 3)
1 = 12
This point is not on the parabola.
E. (8, 5)
(8 - 6)²2 = 4(5 - 3)
4 = 8
This point is not on the parabola.
Therefore, there are no points among the given options that are on the parabola.
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Complete question:
Which points are on the parabola defined as the set of points the same distance from (6,2) and the line y=4?
HELP SOLVE PLEASEEE ENOUGH POINTSSS
Step-by-step explanation:
$ 540 / 12 mos = $ 45 per month for all of the services
SO H + D + N = 45 and N = 2D
So H + D + 2D = 45
and H+ D = 300/12 = $25 / month
so (H+D) + 2D = 45
25 + 2D = 45
D = 10 dollars per month
then H = 15 dollars per month ( because H+D = 25)
and N = 20 dollars per month ( because N = 2D)
4.
You are given an isosceles trapezoid ABCD with median XY. Complete the following.
AX = 4, CD = __________
If isosceles trapezoid ABCD has a median XY then CD = 8 .
What is trapezoid?
A trapezοid is alsο knοwn as a trapezium is a fοur-sided pοlygοn οr a quadrilateral. It has οne set οf οppοsite sides which are parallel and a set οf nοn-parallel sides. The parallel sides are knοwn as the bases and the nοn-parallel sides are knοwn as the legs οf the trapezοid. A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Given AX = 4
Now, AX = BX as XY is the meridian
i.e.
AB = 2AX
AB = 2(4)
AB = 8
We have given that the trapezoid is an isosceles trapezoid, which means
AB = CD
i.e.
CD = 8
Thus, If isosceles trapezoid ABCD has a median XY then CD = 8.
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Please help me! This is due at 2:15 PM!!!! WHICH ALREADY PASSED!!! ITS GOING TO BE LATE> A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.
Letter Frequency
B 247
I 272
N 238
G 241
O 252
For which letter is the experimental probability closest to the theoretical probability? Explain please.
The experimental probability for the letter B is closest to its theoretical probability.
What is probability?A number between 0 and 1 can be used tο represent prοbability, which is the likelihοοd that a given event will οccur. A prοbability οf 0 denοtes an impοssibility, while a prοbability οf 1 denοtes a certainty that the event will οccur.
By dividing the number οf balls that cοrrespοnd tο that letter by the tοtal number οf balls, οne can determine the theοretical prοbability οf drawing a letter in a single draw:
P(B) = 15/75 = 0.2
P(l) = 15/75 = 0.2
P(N) = 15/75 = 0.2
P(G) = 15/75 = 0.2
P(O) = 15/75 = 0.2
The experimental probability of drawing a letter is calculated by dividing the number of times that letter was drawn by the total number of draws:
P(B) = 247/1250 = 0.1976
P(I) = 272/1250 = 0.2176
P(N) = 238/1250 = 0.1904
P(G) = 241/1250 = 0.1928
P(Ο) = 252/1250 = 0.2016
To determine which letter's experimental probability is closest to its theoretical probability, we can calculate the difference between the two probabilities for each letter:
|P(B) - 0.2| = |0.1976 - 0.2| = 0.0024
|P(I) - 0.2| = |0.2176 - 0.2| = 0.0176
|P(N) - 0.2| = |0.1904 - 0.2| = 0.0096
|P(G) - 0.2| = |0.1928 - 0.2| = 0.0072
|P(O) - 0.2| = |0.2016 - 0.2| = 0.0016
The letter with the smallest difference is B, with a difference of 0.0024. Therefore, the experimental probability for the letter B is closest to its theoretical probability.
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WHAT EVEN IS THIS! PLEASE HELP
Step-by-step explanation:
It is a trapezoid with bases 9 and 12 ft and height ( dashed line) found using Pythagorean theorem = 4 ft
area = height * average of bases = 4 * (9+12)/2 = 24 ft^2
PLEASE HELP ME!!!!!!!!!!!!!!
This figure is a rectangle with a semicircle on the shorter side.
What is the perimeter of this figure?
Use 3.14 for pi.
A. 20.28 ft
B. 30.28 ft
C. 46.28 ft
D. 74.24 ft
Answer: it should be b
Step-by-step explanation:
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.
Create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours. Show all of your work.
Answer: To create a linear model that represents the amount of fuel on the plane as a function of flight time, we need to use the given information to calculate the fuel burn rate of the airplane in gallons per hour.
Fuel burn rate = Fuel capacity ÷ Range
Fuel burn rate = 63,500 gallons ÷ 14,430 km = 4.4 gallons per km
We need to convert km to miles, as flight time is usually measured in hours and miles. We can use the conversion factor 1 km = 0.621371 miles to convert kilometers to miles.
Range in miles = Range in km ÷ 0.621371
Range in miles = 14,430 km ÷ 0.621371 = 23,594 miles
Fuel burn rate = Fuel capacity ÷ Range in miles
Fuel burn rate = 63,500 gallons ÷ 23,594 miles = 2.69 gallons per mile
Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:
Fuel on plane (in gallons) = Fuel capacity - Fuel burn rate x Flight time (in hours)
F(t) = 63,500 - 2.69t
where F(t) is the amount of fuel on the plane (in gallons) after flying for t hours.
Step-by-step explanation:
Draw triangle LMN with vertices L(2,-2), M(6,-4) and(5,4). Find the coordinates of the vertices after 90degrees rotation about the origin and about each of the point of L,M,and N
The coordinates of the vertices after rotation depend on the point around which rotation is done.
Rotation of a shape around the origin (0,0) means that each point in the shape has to be moved around the origin by a certain angle. This is done by using the equation x'=xcosθ-ysinθ and y'=xsinθ+ycosθ, where x and y are the coordinates of the point before rotation and x' and y' are the coordinates of the point after rotation. In this case, the angle of rotation is 90 degrees. When we rotate triangle LMN by 90 degrees around the origin, the coordinates of the vertices become L'(2,2), M'(-4,6) and N'(4,-5).When we rotate the triangle around any of the points of L, M, or N, the coordinates of the vertices will change accordingly. For example, if we rotate the triangle around point L, the coordinates of the vertices become L'(2,-2), M'(-2,4) and N'(-6,0). Similarly, if we rotate the triangle around point M, the coordinates of the vertices become L'(2,-2), M'(6,-4) and N'(0,6). Lastly, if we rotate the triangle around point N, the coordinates of the vertices become L'(2,-2), M'(4,5) and N'(5,4).
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IK THE PIC IS DARK BUT PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Step-by-step explanation:
For x
From -6 to 2 is 8 units from -6 to -1 is 5/8ths of this
to verify:
for y from 5 to -3 is 8 units 0 is 5/8 of this
5:8
I NEED HELP ON THIS ASAPPP!
Answer:
i thinks its scalene
Step-by-step explanation:
scalene is under 90 degrees
equal is 90 exact
and obtuse is over 90 but under 180
i need this answer asap with explanation
Answer:
1 , 1.01 , 1.02 , 1.03 , 1.04
Step-by-step explanation:
a sequence with steps of constant size is an arithmetic sequence.
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d has to be found
given a₅ = 1.04 , then
1 + 4d = 1.04 ( subtract 1 from both sides )
4d = 0.04 ( divide both sides by 4 )
d = 0.01
then sequence is
1 , 1.01 , 1.02 , 1.03 , 1.04
what ratio is commonly used as an alternative to 3.14?
The ratio commonly used as an alternative to 3.14 is 22/7 whichj commonly represents the mathematical expression of pi.
This ratio is often used as an approximation for pi (π) which is the mathematical constant representing the ratio of the circumference of a circle to its diameter. While pi is an irrational number and has an infinite number of decimal places, 22/7 is a rational number and can be easily computed.
The value of 22/7 is approximately equal to 3.1428571, which is a fairly accurate approximation for most practical applications. It is often used in situations where a quick estimate is required or where a more accurate value of pi is not necessary.
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A rectangle and triangle are shown below.
The area of the rectangle is equal to the perimeter of the triangle.
Solve for x.
If your answer is a decimal, convert it to 1 d.p.
Answer:
5
Step-by-step explanation:
We know that the area of the rectangle is equal to the perimeter of the triangle
S (rectangle) = (x + 8) × (2x - 1)
P (triangle) = (5x - 1) + (6x + 8) + (8x + 15)
Now we can form an equation:
(x + 8) × (2x - 1) = (5x - 1) + (6x + 8) + (8x + 15)
[tex] {2x}^{2} - x + 16x - 8 = 5x - 1 + 6x + 8 + 8x + 15[/tex]
[tex]2 {x}^{2} - 4x - 30 = 0[/tex]
[tex]d = {b}^{2} - 4 \times a \times c = ({ - 4})^{2} - 4 \times 2 \times ( - 30) = 16 + 240 = 256 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2 \times a} = \frac{4 - 16}{4} = \frac{ - 12}{4} = - 3[/tex]
-3 is a negative number and we cannot use it, since x must be a natural number
[tex]x2 = \frac{ - b + \sqrt{d} }{2 \times a} = \frac{4 + 16}{4} = \frac{20}{4} = 5[/tex]
Reasoning with similarity geometry please help. 40 points
Answer:
ABC and CEF are right triangles | definition of right triangle
ABC and CEF are 30-60-90 triangles | definition of 30-60-90 triangle
ABC is similar to CEF | Angle-Angle-Angle similarity theorem
Simplify the expression-4(-3x - 8) - 34
Answer:
12x-2
Step-by-step explanation:
-4(-3x-8)-34
12x+32-34
12x-2
GEOMETRY: Find the area of the parallelogram. Be sure to include the correct unit in your answer.
The volume of a triangle
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{9\times 7}{63}\\ h=6 \end{cases}\implies V=\cfrac{(63)(6)}{3}\implies V=126~cm^3[/tex]
now, for the slanted cone, we can use Cavalieri's Principle for an slanted cylinder, thus we can say that the slanted cone will have the same volume of a non-slanted cone, now, since this one has a diameter of 6, that means is has a radius of 3.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3} \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3}\implies V=21\pi \implies V\approx 66~cm^3[/tex]
Answer:
64
Step-by-step explanation:
use partial fractions to find the indefinite integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 10x2 7x − 2 x3 x2 dx
The indefinite integral is:
-10 ln|x| + 3 ln|x - 2| + 7 ln|x + 1| + C
First, we factor the denominator of the integrand using partial fractions:
x^3 - x^2 - 2x = (x - 2)(x + 1)x
We then express the integrand as:
10x^2 - 7x + 2 = A/(x - 2) + B/x + C/(x + 1)
Multiplying both sides by the denominator and solving for A, B, and C, we get:
A = -4, B = 10, C = 1
Thus, we can rewrite the integrand as:
-4/(x - 2) + 10/x + 1/(x + 1)
Integrating each term separately and combining the results, we obtain the final expression for the indefinite integral.
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