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The volume of the solid whose base is the semicircle y = √(16 - x²), where -4 < x < 4 and whose cross section perpendicular axis are squares is 256/3 unit³

To obtain the volume of a 3D shape, the cross-section area is discovered and then integrated across a predetermined limit. This technique is known as the cross-sectional method of volume fining. The area of the square base is determined in the given problem, and it is then integrated to determine the overall volume.

To find the volume we will first find the cross-sectional area and then integrate it with respect to x from -4 to 4.

Thus the volume is given as follows:

y = √(16 - x²)

V = ₋₄∫⁴ (√(16 - x²))² dx

V = ₋₄∫⁴ (16 - x²) dx

V = [16x - x³/3]₋₄⁴

V = (64 - 64/3 + 64 -64/3)

V = 256/3 unit³

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Answer:5.6

Step-by-step explanation: When you divide by 10's the amount of 0's in the power of ten is how much you move the decimal point over to the right and in this case, is 1 time so 56/10=5.6

The result after dividing the number 56 by 10 is 5.6.

Given a number 56.

This is divided by 10.

Here, therefore, dividend is 56 and the divisor is 10.

If the divisor of any division problem is either 10 or any powers of 10, then there is an easy method to know the value of the quotient.

The quotient is the same number as the dividend by shifting the decimal point to left that times as the number of zeroes in the divisor.

So using this,

Here, divisor is 10. There is only 1 zero.

So from 56, decimal point is once shifted to the left.

Hence the quotient is 5.6.

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ANSWER

EXPLANATION

We want to find the location of 1 3/9.

The space between each successive whole number is divided into 9 smaller divisions.

The

The answer choice which is a function among the given answer choices is; Choice B as they are all correct.

From conventional mathematics, a function from a set x to a set y assigns to each element of X exactly one element of Y.

The set of values x is called the domain of the function and the set of values y is called the codomain/range of the function.

Functions basically represents the idealization of how a varying quantity depends on another quantity.

It therefore follows from the paragraph above that all of the answer choices are functions.

Therefore, the answer choice which is a function among the given answer choices is; Choice B as they are all correct.

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Each silver bead costs $0.50, and each green bead costs $1.

Let's assume the cost of each silver bead is 's' dollars, and the cost of each green bead is 'g' dollars.

According to the given information, the necklace requires 25 silver beads and 15 green beads, and the bracelet requires 10 silver beads and 5 green beads.

The total cost of the necklace beads is $27.50, and the total cost of the bracelet beads is $10.

Using this information, we can set up the following system of equations:

25s + 15g = 27.50 (Equation 1)

10s + 5g = 10 (Equation 2)

We can solve this system of equations using any appropriate method, such as substitution or elimination.

Let's use the elimination method to solve the system:

Multiplying Equation 2 by 3, we get:

30s + 15g = 30 (Equation 3)

Subtracting Equation 3 from Equation 1:

25s + 15g - (30s + 15g) = 27.50 - 30

-5s = -2.50

s = 0.50

Now, substituting the value of s into Equation 2:

10(0.50) + 5g = 10

5 + 5g = 10

5g = 5

g = 1

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Answer:

48

Step-by-step explanation:

4/10 x 120 = (120/10) x 4 = 12 x 4 = 48

another way:

4//10 x 120/1 = 480/10 = 48

If my answer is incorrect, pls correct me!

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Then 62.5% of the campers at the Wild Outdoors camp this morning will be horseback riding

To find the percentage of campers that will be horseback riding, we need to first add the ratio together to get the total number of parts. In this case, the ratio of horseback riding to canoeing is 5:3, so there are 5 + 3 = 8 parts in total.

To find the percentage of campers that will be horseback riding, we divide the number of parts for horseback riding by the total number of parts, then multiply by 100 to get the percentage.

So, 5 parts out of 8 parts are for horseback riding. This is equivalent to 5/8 or 0.625 as a decimal. To find the percentage, we multiply by 100, which gives us 62.5%.

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The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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Answer:

Q.2 \(4\sqrt2\) units

Q.3 \(10\sqrt2\) units

Step-by-step explanation:

Given that points:

C(-1, 3) and D (-5, 7)

E(0, -5) and F(10, -15)

To find:

Q.2. Distance between C and D

Q.3. Distance between E and F

Solution:

First of all, let us solve the question marked as number 2 in the attached image.

C(-1, 3) and D (-5, 7)

\(x_2 = -5\\x_1 = -1\\y_2 = 7\\y_1 = 3\)

To find the distance 'd' between the points, we can use distance formula:

\(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(d = \sqrt{(-5-(-1))^2+(7-3)^2}\\\Rightarrow d = \sqrt{(-4)^2+(4)^2}\\\Rightarrow d =\sqrt{16+16}\\\Rightarrow d =\sqrt{32} = 4\sqrt2\ units\)

First of all, let us solve the question marked as number 3 in the attached image.

E(0, -5) and F(10, -15)

\(x_2 = 10\\x_1 = 0\\y_2 = -15\\y_1 = -5\)

To find the distance 'd' between the points, we can use distance formula:

\(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(d = \sqrt{(10-0)^2+(-15-(-5))^2}\\\Rightarrow d = \sqrt{10^2+(-10)^2}\\\Rightarrow d =\sqrt{100+100}\\\Rightarrow d =\sqrt{200} = 10\sqrt2\ units\)

Please find attached image for the answers filled in the boxes.

Answer:

The area of square will increase with a scale factor of 25

Step-by-step explanation:

Scale factors are used in geometrical drawings and problems to solve the problems involving large quantities.

We know that

\(A = s^2\)

Here A is area of square and s is side.

It is given that the side length is increases by a scale factor of 5

Which means the new side is 5s

So the new area will be:

\(A' = (5s)^2\\A' = 25s^2\\A' = 25A\)

The new area is 25 times of the original area before applying scale factor.

Hence,

The area of square will increase with a scale factor of 25

Answer: I don’t understand the question??

Step-by-step explanation: Can you say the question again like the same way the homework does

The amount received from loans as a number in millions is 242,700 million rand.

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

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Answer:

5:6 is larger

Step-by-step explanation:

6:9 = 6/9 = 2/3 = 0.6666...

5:6 = 5/6 = 0.8333...

5:6 is larger

Answer:

5:6

Hope this helps! :)

2 ways to get to 1/2

Way 1:

Use the 1/4 scoop 2 times

1/4 + 1/4 =2/4

2/4 simplified is 1/2

Way 2:

Use the 1/8 scoop 4 titmes

1/8+1/8+1/8+1/8=4/8

4/8 simplified is 1/2

Hope this helps!

Answer:

---------------

Let the numbers be s and l.

We are given that:

Set up equations:

Eliminate l:

Solve for s:

Find l:

Answer:

It would take 1 more mile if he took route Street A and then Street B rather than just Street C.

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

We use the Pythagorean Theorem to find the length of Street C:

2² + 1.5² = c²

c = √6.25

c = 2.5

Now we find how much longer route A and B is compared to C:

3.5 - (2 + 1.5) = 3.5 - 2.5 = 1

To calculate his total expenditure in 14 months, we need to first calculate his monthly expenses. The man will save Rs 105,000 in 14 months.

Monthly expenses are the costs incurred on a monthly basis. This may include basic living costs, such as rent and utility bills, as well as discretionary spending on entertainment, food, and other expenses.

The man's total income in 14 months will be Rs 168,000 (Rs 12,000 x 14).

To calculate his total expenditure in 14 months, we need to first calculate his monthly expenses.

1/8 of his income in food is Rs 1,500 (12,000/8).

1/5 of his income in clothing is Rs 2,400 (12,000/5).

Education cost is 1/20 of his income which is Rs 600.

Total expenditure in 14 months

= (Rs 1,500 + Rs 2,400 + Rs 600) x 14

= Rs 63,000.

Therefore, the man's total savings in 14 months will be

Rs 168,000 - Rs 63,000

= Rs 105,000.

He will save Rs 105,000 in 14 months.

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Question:

A man earns Rs 12000 in a month. He spends 1/8 of his income in food; 1/5 in clothing and 1/20 in education. How much does he save in 14 month?​

Answer:

6

Step-by-step explanation:

The two triangles are similar which means the the two length is parallel

.°., the Length of the smaller triangle=6

Part a

Setting \(x=6\), \(y=7.9(1.02)^6 \approx \boxed{8.9}\)

Part b

Setting \(x=14\), \(y=7.9(1.02)^{14} \approx \boxed{10.4}\)

Answer:

Step-by-step explanation:

5

Answer:

Step-by-step explanation:

48-5+ 2x -7 -54 ABE 39. - x=2. 66 - 12 = 54. BC, 15. AB=5 =BC. 6x = 66. - They are. XH. Not. 2) Find the coordinates of the midpoint of the segment with the given endpoints. ... j) Concurrency of Perpendicular Bisectors of a Triangle Theorem: ... Find AE. 40. Find AD. 76. 76. Sy + 20. Find BC. 54. Find AC. 80. Find CD. 76.

We are given:

There were 7 chocolate bars, evenly shared between 4 friends

Number of Bars one person will get:

Number of bars one person will get = Number of Bars / Number of Friends

Number of Bars = 7 / 4

but since this number does NOT match any of the given options, we will convert it to a mixed fraction

The number of bars one person will get will be \(1\frac{3}{4}\), written as a mixed fraction.

Therefore, the correct answer is option D

Answer:

4 friends =7 chocolate

1 friend =7/4 chocolate =1 3/4 part of chocolate.

Answer:

B. If there is no pattern, the model is probably reasonable.

Answer: See explanation

Step-by-step explanation:

a. What was the amount of interest paid by Debbie?

Interest is calculated as:

= PRT

= (16500 × 9% × 1)

= 16500 × 0.09 × 1

= $1485

Debbie paid $1485 as interest.

b. What was the interest rate paid by Jan?

Interest = PRT/100

6450 = (107500 × R × 1) / 100

6450 × 100 = 107500R

645000 = 107500R

R = 645000 / 107500

R = 6.0

The interest rate is 6.0%

The measure of the bearings from B are 310 degrees, 245 degrees and 137 degrees

To determine the bearings from B, we make use of the following guidelines

Using the above as a guide, we have the following:

Hence, the values of the bearings are 310 degrees, 245 degrees and 137 degrees

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Answer:

Step-by-step explanation:

First, let us substitute x and y values: -7 = -2(-5) + 4

Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).

Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:

14 + b = -7

by simplifying, we can conclude that b = -21

Finally, we can plug in the b-value into our original equation:

y = -2x + 4 - 21

After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).

The mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg

Let's denote the mass of one art book by "a" and the mass of one biology book by "b".

From the given information, we have two equations:

6a + 4b = 7.2 (equation 1)

2a + 3b = 3.4 (equation 2)

We can solve for "a" and "b" by using any method of solving linear equations, such as substitution or elimination.

Here, we'll use elimination method. Multiplying equation 2 by 3 and subtracting it from equation 1 multiplied by 2, we get:

12a + 8b - (6a + 9b) = 14.4 - 10.2

6a - b = 4.2 (equation 3)

Multiplying equation 2 by 2, we get:

4a + 6b = 6.8 (equation 4)

Multiplying equation 3 by 6, we get:

36a - 6b = 25.2 (equation 5)

Adding equations 4 and 5, we get:

40a = 32

a = 0.8 kg

Substituting this value of "a" in equation 2, we get:

2(0.8) + 3b = 3.4

1.6 + 3b = 3.4

3b = 1.8

b = 0.6 kg

Therefore, the mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg.

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