Determine a quadratic equation that has solutions of 3 and -4 and includes f(7)=88

Answer:

To solve the quadratic equation 2x^2 + x - 3 = 0 by factoring, we follow these steps:

Step 1: Write the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, the equation is already in standard form: 2x^2 + x - 3 = 0.

Step 2: Factor the quadratic expression on the left-hand side of the equation. We look for two numbers that multiply to give us the constant term (c) and add to give us the coefficient of the linear term (b). In this case, c = -3 and b = 1.

The two numbers that satisfy these conditions are -3 and 1, as -3 * 1 = -3 and -3 + 1 = -2.

Step 3: Use the factored form to set each factor equal to zero and solve for x.

2x^2 + x - 3 = 0

(2x - 3)(x + 1) = 0 (factored form)

Setting each factor equal to zero:

2x - 3 = 0

2x = 3

x = 3/2

x + 1 = 0

x = -1

So the solutions to the equation are x = 3/2 and x = -1.

Answer:

[tex]x = \sqrt{ {16}^{2} + {21}^{2} } = \sqrt{256 + 441} = \sqrt{697} = 26.4[/tex]

The value of the surd form √14 is 3. 74

The square root of a number is a value that, when multiplied by itself, equals the original number.

It is represented by the symbol √ and is a way to find the side length of a square given its area or the length of a diagonal in a right triangle.

From the information given, we have that;

The expression is √14

We can see that the value √14 is a surd which can no longer be simplified into a whole or rational number.

To determine the square root, we use the calculator

√14

3. 7416

In the nearest tenth, we get;

3. 74

Hence, the value is 3. 74

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Answer:

(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

Step-by-step explanation:

To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:

a² = 7 cm²

b² = 17 cm²

c² = 10 cm²

We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.

We can rearrange the equations above to solve for a, b, and c:

a = √7 cm ≈ 2.65 cm

b = √17 cm ≈ 4.12 cm

c = √10 cm ≈ 3.16 cm

Now, we can check whether the Pythagorean theorem holds:

c² = a² + b²

(√10 cm)² = (√7 cm)² + (√17 cm)²

10 cm = 7 cm + 17 cm

This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

The answer of the given question based on the circle is ,  the answer is option (d) 8/3π.

In geometry, an arc is  portion of circumference of a circle. It is  curved line that connects two points on  circle. The length of arc is proportional to the angle that it subtends at the center of the circle.

Since EFB is a straight line and EB is a diameter of the circle, angle EFB subtends the entire circle at F. Therefore, the angle subtended by arc EFD is the difference between the angles subtended by arcs EF and EB.

Arc EF subtends a full circle at F, so its angle is 2π radians. Arc EB subtends a straight angle at F, so its angle is π radians.

Therefore, the angle subtended by arc EFD is:

2π - π = π

The length of arc is given by formula L = rθ, where r is  radius of  circle and θ is  angle (in radians) subtended by  arc at  center of  circle.

In this case, r = 4 and θ = π, so the length of the arc corresponding to angle EFD is:

L = rθ = 4π

Therefore, the answer is (d) 8/3π.

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Answer:

it's the first one. I

n my thinking

Answer:

(a) 1 hat is $15

(b) 1 bag is $12

Step-by-step explanation:

1 hat at $15 + 1 bag at $12 is equal to $27

2 hats at $30 together + 1 bag at $12 is equal to $42

Answer

6

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the area of a triangle, we can use the formula:

Area = (1/2) × base × height

In this case, we have three sides of the triangle given: 5, 3, and 4. To use these to find the area, we need to first determine which side is the base and what the corresponding height is.

We can see that the side with length 5 is opposite the biggest angle, so this is likely the hypotenuse. The other two sides, 3 and 4, must then be the other two legs of a right triangle, with one of them being the base and the other the height.

To determine which is which, we can use the Pythagorean theorem:

c^2 = a^2 + b^2

where c is the hypotenuse and a and b are the other two sides. In this case, we have:

5^2 = 3^2 + 4^2

25 = 9 + 16

So we have confirmed that 3 and 4 are indeed the legs of a right triangle, with 5 as the hypotenuse. We can use the Pythagorean theorem again to find the height:

a^2 + b^2 = c^2

b^2 = c^2 - a^2

b = sqrt(c^2 - a^2)    (taking the positive square root because b is a length)

b = sqrt(5^2 - 3^2)

b = sqrt(16)

b = 4

So the height of the triangle is 4. We can now use the formula to find the area:

Area = (1/2) × base × height

Area = (1/2) × 3 × 4

Area = 6

Therefore, the area of the triangle is 6 square units.

The equivalent matrix is [tex]\begin{bmatrix}-6 & -2\\ -6& -8 \\ 5& 5 \\ 1& 19 \\ 7&3 \end{bmatrix}[/tex]

A matrix is a rectangular array of numbers, arranged in rows and columns. Each number in the matrix is called an element, and the number of rows and columns determine the size of the matrix.

Now, to answer your question, the given set of numbers, [-6,-6, 5,1, 7,2, -8, 5,19, 3] can be arranged in a 2x5 matrix or a 5x2 matrix, depending on the order in which you place the numbers. To illustrate:

[tex]\begin{bmatrix}-6 & -6 &5 &1 &7 \\ 2& -8 & 5 & 19& 3\end{bmatrix}[/tex]

or

[tex]\begin{bmatrix}-6 & -2\\ -6& -8 \\ 5& 5 \\ 1& 19 \\ 7&3 \end{bmatrix}[/tex]

Both matrices have the same set of numbers but arranged differently. Hence, it is important to specify the order of the rows and columns to define a matrix uniquely.

In summary, the given set of numbers can be represented as a matrix, which is a rectangular array of numbers arranged in rows and columns. However, to define a matrix uniquely, we must specify the order of the rows and columns. Moreover, matrices can be added, subtracted, and multiplied just like regular numbers.

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Answer:

act back its also known as act or tactics

The rational numbers in the list of options are √4+√16, 2* √4 and √49 • √81

The examples of rational numbers among the given options are:

The other options are not rational numbers:

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Given statement: For log normally distributed returns, the annual geometric average return is always greater than the arithmetic average return.

The given statement is true.

This is because log normal distribution assumes that the rate of return is compounded continuously, which leads to a higher final value of the investment.

For lognormally distributed returns, the geometric average return is greater than the arithmetic average return.

This is because the lognormal distribution has a positive skew, meaning that there are more small positive returns and fewer large negative returns.

This leads to compounding effects over time, which favor the geometric average return.

The geometric average return is calculated by taking the nth root of the product of (1+Ri),

where Ri is the return for the ith period.

The arithmetic average return is calculated by taking the average of the returns over a period.

Therefore, for lognormally distributed returns, the geometric average return is greater than the arithmetic average return.

The geometric average return takes into account the compounding effect, whereas the arithmetic average return does not.

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Answer:

32

Step-by-step explanation:

512 / 4 = 128

128 / 4 = 32

32 / 4 = 8

8 / 4 = 2

Century's final payment will be on May 06 is $4,028.

Total cost of televisions:

51 TVs at $100 each = $5,100

8% discount = $100 x 8% x 10 = $80

5% discount  = $100 x 5% x 10 = $50

5% discount  = $100 x 5% x 31 = $155

Total discount = $80 + $50 + $155 = $285

Cost after discount = $5,100 - $285 = $4,815

Shipping cost: no additional cost

Returned sets:

3 *$100  = $300

ACME will issue a credit to Century for $300

Total cost:

$4,815 + $0 - $300 = $4,515

Partial payment:

$275

Final payment:

Balance after partial payment = $4,515 - $275 = $4,240

5% discount if paid within 10 days after the end of the month = $4,240 x 5% = $212

Final payment on May 06 = $4,240 - $212 = $4,028

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It would take the two pumps working together approximately 240 minutes to remove the water.

To determine how long it would take the two pumps to remove the water working together, we can use the concept of work rates. Specifically, we can determine the work rates of each pump and then add them together to find the combined work rate when both pumps are working together.

Let's start by defining some variables:

Let L be the rate of the larger pump, in units of water volume per minute.

Let S be the rate of the smaller pump, in the same units as L.

Let T be the time it takes for both pumps to remove the water working together, in minutes.

From the problem statement, we know that the larger pump can remove all the water alone in 240 minutes. This means that its work rate is 1/240, since it can remove 1 unit of water volume in 240 minutes. Similarly, the smaller pump has a work rate of 1/400.

When both pumps are working together, their work rates add up. Therefore, we can set up an equation as follows:

L + S = 1/T

Substituting the work rates we found earlier, we get:

1/240 + 1/400 = 1/T

Simplifying this equation, we get:

1/T = 0.0041667

Solving for T, we get:

T = 1/0.0041667 ≈ 240.001 minutes

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The equation of the translated function q(x) in slope-intercept form is q(x) = 2x - 13.

The function p(x) = 2(x - 4) can be rewritten in slope-intercept form as:

p(x) = 2x - 8

To translate the graph of p(x) two units to the right and one unit down, we need to make the following adjustments to the equation:

So the equation of the translated function q(x) in slope-intercept form is:

q(x) = 2(x - 2) - 8 - 1

Simplifying, we get:

q(x) = 2x - 13

Therefore, the equation of the translated function q(x) in slope-intercept form is q(x) = 2x - 13.

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The sample points of events A, B, A ∩ B, A ∪ B and A' (complement of A) are given. The probability of event are 1/18, 11/36, 1/18, 7/18 and 17/18 respectively. The probability using additive rule of p(A ∩ B) is 1/36.  Events A and B are not mutually exclusive as they have a non-empty intersection.

Sample points in the events

A: {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}

B: {(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (1, 4), (2, 4), (3, 4), (5, 4), (6, 4)}

A ∩ B: {(4, 3), (3, 4)}

A ∪ B: {(1, 4), (1, 6), (2, 4), (2, 5), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (6, 1), (6, 4)}

A' (complement of A): {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (5, 1), (5, 3), (5, 5), (6, 2), (6, 3), (6, 5), (1, 5), (1, 6), (2, 6), (3, 5), (3, 6), (5, 6), (6, 6)}

The probability of event A is

p(A) = 2/36 = 1/18.

The probability of event B is

p(B) = 11/36.

The probability of event

A ∩ B (i.e., A and B) is p(A ∩ B) = 2/36 = 1/18.

The probability of event

A ∪ B (i.e., A or B) is p(A ∪ B) = 14/36 = 7/18.

The probability of event A' (i.e., not A) is p(A') = 17/18.

By the additive rule, we have p(A ∪ B) = p(A) + p(B) - p(A ∩ B). Therefore, p(A ∩ B) = p(A) + p(B) - p(A ∪ B) = (1/18) + (11/36) - (7/18) = 1/36. This inconsistent with the answer we obtained in above part.

The events A and B are not mutually exclusive because it is possible to roll a 4 and a 3 at the same time, which satisfies both events.

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the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.

How to solve the question?

The given equation is 2x² + x + 4k.

(a) For the equation to have two real solutions, the discriminant b² - 4ac must be positive.

Therefore, for this equation, b² - 4ac > 0

=> 1 - 4(2)(4k) > 0

=> 1 - 32k > 0

=> k < 1/32

Hence, all values of k less than 1/32 will give the equation 2x² + x + 4k two real solutions.

(b) For the equation to have one real solution, the discriminant b² - 4ac must be zero.

Therefore, for this equation, b² - 4ac = 0

=> 1 - 4(2)(4k) = 0

=> 1 - 32k = 0

=> k = 1/32

Hence, only the value of k equal to 1/32 will give the equation 2x² + x + 4k one real solution.

(c) For the equation to have no real solutions, the discriminant b² - 4ac must be negative.

Therefore, for this equation, b² - 4ac < 0

=> 1 - 4(2)(4k) < 0

=> 1 - 32k < 0

=> k > 1/32

Hence, all values of k greater than 1/32 will give the equation 2x² + x + 4k no real solutions.

In conclusion, the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.

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Dodger Stadium: 37,036 more people can attend a Dodger game., Lambeau Field + Georgia Dome: 132,118 fans can be seated altogether in the two parks.

1) Dodger Stadium:

56,000 - 18,964 = 37,036 more people can attend a Dodger game.

2) Alamodome:

35,000 - 20,557 = 14,443 more people can be seated for special events.

3) Lambeau Field + Georgia Dome:

60,890 + 71,228 = 132,118 fans can be seated altogether in the two parks.

4) Arrowhead Pond + Staples Center:

17,174 + 18,118 = 35,292 fans can be held altogether in the two arenas.

5) United Center:

21,500 / 25 = 860 25-seat ticket packages could be sold for one game.

6) Comerica Park:

40,000 / 20 = 2,000 20-seat packages could be sold.

7) Fenway Park - Veterans Stadium:

62,409 - 33,871 = 28,538 more fans can attend a game in Philadelphia.

8) St. Louis Stadium:

66,000 / 8 = 8,250 ticket packages could be sold for one game.

9) Miami Dolphins stadium:

75,192 x 8 = 601,536 total fans could attend all 8 regular-season games.

10) Edison Field:

45,050 x 81 = 3,655,050 tickets could be sold for their 81 regular-season games.

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Both events A and B have probabilities of 1/12, and they are independent events since the outcome on one die does not affect the outcome on the other die.

The event A consists of all outcomes in which the number of spots showing on the red die is three or less.

Since the red die has six equally likely outcomes (1, 2, 3, 4, 5, and 6), the probability of A is:

P(A) = the number of outcomes in A / the total number of possible outcomes.

Out of the six possible outcomes on the red die, three of them are three or less: 1, 2, and 3.

Therefore, the number of outcomes in A is three.

Since there are six equally likely outcomes for the green die as well, the total number of possible outcomes is 6 x 6 = 36.

Therefore, we have:

P(A) = 3/36 = 1/12.

The event B consists of all outcomes in which the number of spots showing on the green die is more than three.

There are also three outcomes on the green die that satisfy this condition: 4, 5, and 6.

Thus, we have:

P(B) = 3/36 = 1/12.

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The value of cos(2θ) is 1/2

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

If cos(tetha) = √3/2

this means the adjascent is √ 3 and the hypotenuse is 2

therefore ;

opp = √ 2²- √3)²

= √4-3

= √1

= 1

therefore sin(tetha) = 1/2

cos(2θ) = cos²(tetha) -sin²(tetha)

cos²(tetha) = (√3/2)² = 3/4

sin²(tetha) =( 1/2)² = 1/4

cos(2θ) = 3/4 - 1/4 = 2/4 = 1/2

therefore the value of cos(2θ) is 1/2

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The probability that at least 10 of them support tuition-free college is 0.9838.

To answer this question, we will use the binomial distribution formula. Let p = 0.51 be the proportion of young Americans who support tuition-free college, and let n = 30 be the sample size.

The probability of at least 10 UConn students supporting tuition-free college is equal to the sum of the probabilities of 10 or more, 11 or more, 12 or more, ..., up to 30. We can use the normal approximation to the binomial distribution.

Using the normal approximation, we first calculate the mean and standard deviation of the binomial distribution:
mean = np = 30 * 0.51 = 15.3
standard deviation = sqrt(np(1-p)) = sqrt(30 * 0.51 * 0.49) = 2.46

We then standardize the variable X = number of UConn students who support tuition-free college:
Z = (X - mean) / standard deviation

Now we want to find the probability that X is greater than or equal to 10, which is equivalent to finding the probability that Z is greater than or equal to (10 - 15.3) / 2.46 = -2.14.

Using a standard normal table or calculator, we find that the probability of Z being greater than or equal to -2.14 is approximately 0.9838. Therefore, the probability of at least 10 UConn students supporting tuition-free college is approximately 0.9838.

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There are 60,466,176 different license plates that consist of five symbols, either digits or letters.

To calculate the number of different license plates consisting of five symbols, we need to consider the number of choices for each symbol, which can be either digits (0-9) or letters (A-Z).
Determine the number of choices for each symbol.
There are 10 digits (0-9) and 26 letters (A-Z), so there are a total of 10 + 26 = 36 possible choices for each symbol.
Use the counting principle.
Since there are 5 symbols on the license plate and 36 choices for each symbol, we can use the counting principle to determine the number of different license plates.

The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

Calculate the number of different license plates.
The number of different license plates can be calculated as 36 × 36 × 36 × 36 × 36 = [tex]36^5[/tex] = 60,466,176.

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There are a total of 60,466,176 different license plates consisting of five symbols, either digits or letters. This is because there are 26 letters in the English alphabet and 10 digits, so the total number of symbols is 36.

To calculate the number of different license plates consisting of five symbols, we need to consider that each symbol can be either a digit (0-9) or a letter (A-Z). There are 10 digits and 26 letters, so there are 36 possible choices for each symbol.

To find the total number of different license plates, we use the following steps:

1. Determine the number of possible choices for each symbol (36, as explained above).
2. Since there are five symbols in the license plate, raise the number of choices (36) to the power of 5.
3. Calculate the result.

So, the calculation would be:

36^5 = 60,466,176

There are 60,466,176 different license plates that can be created using five symbols with either digits or letters.

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Answer: |x + 9| > 0 or |x + 5| < 4

Step-by-step explanation: To begin with, ready to utilize the frame |x - b| > c to speak to the arrangement x < -9:

|x - (-9)| >

Rearranging this gives:

|x + 9| >

Another, we are able utilize the frame |x - b| < c to speak to the arrangement x ≥ -5. Ready to select a esteem of c that's more noteworthy than the remove from -5 to the closest endpoint of the arrangement set (which is -9):

|x - (-5)| < 4

Rearranging this gives:

|x + 5| < 4

Joining these two supreme esteem disparities with an "or" explanation gives:

|x + 9| > or |x + 5| < 4

Rearranging this gives:

x < -9 or -9 < x < -1

We will see that the primary portion of the arrangement set (x < -9) is as of now spoken to within the to begin with supreme esteem imbalance, and the moment portion (x ≥ -5) is spoken to by the moment supreme esteem imbalance.

The measure of angle C is 80°

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It can also be called inscribed quadrilateral.

A theorem if circle geometry states that the opposite angles of a cyclic quadrilateral are supplementary. This means the sum of. opposite angles of a cyclic quadrilateral is 180°

Therefore 3x-59+2x-1 = 180

5x -60 = 180

5x = 180+60

5x = 240

x = 240/5

x = 48

angle A = 2x+4 = 2×48+4

= 100°

therefore angle C = 180-(angle A)

C = 180-100

= 80°

therefore the measure of angle C is 80°

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The point on the number line that represents the amount of liquid each beaker will contain after the liquid has been distributed among the 4 beakers is the option B

(B) Point Bi

A number line is a line that consists of numbers marked at intervals, which indicates quantities, and can be used for numerical operations.

The amount of liquid in the each of the four beakers are;

1/8, 1/8, 6/8, 6/8

The sum of the liquid in the four beakers is therefore;

1/8 + 1/8 + 6/8 + 6/8 = (1 + 1 + 6 + 6)/8 = 14/8

When the same amount of liquid are in each beaker, we get;

The point on the number line corresponding to the point 3.5/8 is the point B, therefore, the correct option is the option B

(B) Option B

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Answer:

b

Step-by-step explanation:

Answer: We can use the trigonometric function tangent to solve this problem. Let x be the horizontal distance from the base of the ladder to the wall. Then we have:

tan(1.60) = x / 8

Multiplying both sides by 8, we get:

x = 8 tan(1.60)

Using a calculator, we find:

x ≈ 8 × 1.518 = 12.14

Therefore, the approximate horizontal distance from the base of the ladder to the wall is 12.14 feet.

Step-by-step explanation:

Thus, the function has a minimum value of -2 at x = -1.

There are "hills and valleys" in functions, or points where their value reaches a minimum or maximum.

Locally, it may not be the lowest or maximum for the entire function.

Stated function:

g(x) = 2x² + 4x

Differentiate the function to find the critical points with respect to x.

g'(x) = 4x + 4  ...eq 1

Put g'(x) = 0

4x + 4 = 0

4(x + 1) = 0

x = - 1 (critical point)

Again Differentiate the function to check for maxima or minima:

g'(x) = 4x + 4

g''(x) = 4

g''(x) > 0 (minimum function)

At x = -1 , the function will be minimum.

Minimum value : Put x = -1 in function.

g(x) = 2(-1)² + 4(-1)

g(x) = 2 - 4

g(x) = -2

Thus, the function has a minimum value of -2 at x = -1.

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The volume of the given cone with a height of 17.3 and a diameter of 10.4 is  489.87 cubic cm

The volume of any cone can easily be determined by the formula (pi*r*r)*(h/3) where pi has the value of 3.14, 'r' is the radius of the cone, and 'h' is the given height of the cone.

Here in the given question, we can see that the height(h) given here is 17.3cm and the diameter is 10.4cm with which we can find the radius because we know the radius is the half of diameter so 'r' will be 5.2cm.

Now just putting the values of 'h' and 'r' in the given formula (pi*r*r)*(h/3)  we get the volume of the cone which is 489.87 cubic cm.

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Answer:

Step-by-step explanation:

here,

height h= 17.3cm

diameter= 10.4cm

therefore, radius r will be 5.2cm

pi= 3.14

solution:

volume v of cone= 1/3*pi*r2*h

= 1/3*3.14*5.2*5.2*17.3 cm3

= 489.7 cm3

explanation:

here, it is given that the height is 17.3cm and the radius is 5.2cm. we know that the formula for finding the volume of a cone is 1/3*pi*r2*h.