Find the exact value, in terms of a, of each of the following. (HINT: Don't let the variable a scare you! The same strategy you used in Problem 2 still works - draw a point on a circle, assign it coordinates, and find the appropriate trig function’s value.)
a. sin (tan^-1(2/a))
b. cot (cos^-1(a))

The volume of the object is 168.96 cubic units. The volume of the object can be found using the formula for volume of a solid with known cross-sections : [tex]V = ∫ A(x)dx[/tex], where [tex]A(x)[/tex] is the area of the cross-section at x.

In this case, the cross-sections are triangles with equal base and height. The area of a triangle is A = 1/2bh, so the area of the cross-section at x is [tex]A(x) = 1/2b^2.[/tex]

The base of the triangle is the distance between the two curves, which is [tex]6−3/8 x^2 - 0 = 6−3/8 x^2.[/tex] So the area of the cross-section is [tex]A(x) = 1/2(6−3/8 x^2)^2.[/tex]

Now we can find the volume by integrating the area function over the x-values of the base region. The base region is bounded by the curve [tex]y=6−3/8 x^2[/tex], so the x-values are the roots of this equation:

[tex]0 = 6−3/8 x^2 3/8 x^2 = 6 x^2 = 16 x = ±4[/tex]

So the volume is:

[tex]V = ∫[−4,4] 1/2(6−3/8 x^2)^2dx = 1/2 ∫[−4,4] (36 - 9/4 x^2 + 9/64 x^4)dx[/tex]
[tex]= 1/2 [(36x - 3/4 x^3 + 9/320 x^5)] from x=-4 to x=4 = 1/2 [(288 - 192 + 72.96) - (-288 + 192 - 72.96)] = 1/2 (576 - 384 + 145.92) = 1/2 (337.92)[/tex]
= 168.96 , So the volume of the object is 168.96 cubic units.

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The amount that x = 153 needs to be to balance the scale. Thus,we would need to drag, One block from A, 5 columns of blocks form B and 3 blocks from C to balance the scale.

a scale is a device used to measure the weight or mass of an object by comparing it to a known reference weight or mass. It works by using the principle of equilibrium, where the weight on one side is balanced by an equivalent weight on the other side. This allows for accurate measurement of the weight or mass of an object.

This is sometimes represented in math as an equation.

We have an equation given in the above image:

221 = x + 68; to find the required blocks to balance the scale, we must find x.

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 68 from both sides:

221 - 68 = x + 68 - 68

153 = x

Therefore, x = 153.

Since each Set "A" is a block of 100 Units, Set "B" is a block of 10 Units, and Set "C" is a Unit, we would need to drag, One block from A, 5 columns of blocks form B and 3 blocks from C to balance the scale.

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Full Question;

The scale shown is not balanced. Drag base ten blocks to the box to show the amount that x needs to be to balance the scale. See the attached image.

The solution is x = 8.

The solution to the equation 2ln(x) = ln(4) + ln(16) should be determined, taking into account any extraneous solutions. The steps to accomplish this are as follows:2ln(x) = ln(4) + ln(16)ln(x^2) = ln(4*16)ln(x^2) = ln(64)By taking the exponential of both sides, this expression can be resolved.x^2 = 64x = ±8Since the natural logarithm is only defined for positive numbers, only the positive value of x is taken into account. Therefore, the solution is x = 8.The process of checking for extraneous solutions involves substituting the answer obtained into the original equation and evaluating it to see whether it is accurate or not.2ln(8) = ln(4) + ln(16)The above equation can be simplified to become: ln(64) = ln(64)The answer is consistent. As a result, the solution is accurate and does not include any extraneous values. The solution is x = 8.

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The slant height of given square pyramid is √45 inch.

A square pyramid is a geometric solid that has a square base and four triangular faces that meet at a common vertex. It belongs to the family of pyramids, which are three-dimensional shapes that have a palled the apex.

With the help of the Pythagoras theorem, we can find out the slant height of pyramid using the formula:

[tex]s^{2} =H^{2} +(\frac{a}{2} )^{2}[/tex]

Here, height of square pyramid is H.

take an equilateral triangle, where a triangle has all sides are equal.

so, the height of the triangle (h) = [tex]\sqrt{a^{2} + (\frac{a}{2}) ^{2} }[/tex] = [tex]\sqrt{6^{2} + (\frac{6}{2}) ^{2} }[/tex] = √45 inch

the height of the square pyramid (H) is:

[tex]H^{2} + (\frac{a}{2}) ^{2} } = h^{2}[/tex]

[tex]H^{2} = (\sqrt{45} )^{2} - (\frac{6}{2}) ^{2} }[/tex]

H = 6 inch

The slant height of pyramid using the formula:

[tex]s^{2} =6^{2} +(\frac{6}{2} )^{2}[/tex] = 36 + 9 = 45

s = √45 inch

Therefore, the slant height of given square pyramid is √45 inch.

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Answer:

25°

Step-by-step explanation:

Triangles have a total count of 180°. Seeing that angle K has a measure of 130°, we know that the other two sides must be equal to 50°. However, if ∠KJL = 50°, then ∠KLJ would be 0°, which is impossible.

Answer:

Step-by-step explanation:

[tex]4.5^{2}[/tex] x [tex]pie[/tex] =63.6[tex]cm^{2}[/tex]

Answer:

20.25pi or about 63.62

Step-by-step explanation:

the formula for area of a circle is pi*r^2.

since the diameter is 9, the radius is half of that, which is 4.5

then, plugging this into our formula, we get 20.25pi. this rounds to 63.62.

Answer:

n=1,-2

L=2,3

m=5,0

Step-by-step explanation:

if that's in point not coordinates

check after me i might be wrong

Answer:

A and E

Step-by-step explanation:

A. 7,358.9 is 7.3589 x 10³

B. 73. 589 is 7.3589 x 10¹

For A which is 10³ to reduce to 10¹, you need to multiply by a fraction

To reduce 3 to 1, you need to deduct 2 (10¹¯³ = 10¯²)

10¹/ 10³ = 10/1000 = 1/100 which can also be written as 0.01

Answer:

Step-by-step explanation:

1. 7pq

2. 9-x^2=(3-x)(3+x)

3. 6z^2
4. i

5. x^2 + xy + 2y^2
6. i:2^3 ii:(x+5)^2 V:(6-7)(6+7) iiii: 4b(b-a) v again: n/a

19:300

Answer:

1x + 4 : 2x = 1 : 2

We can cross-multiply to get:

2(1x + 4) = 1(2x)

2x + 8 = 2x

8 = 2x - 2x

8 = 0

This is not possible, so our assumption that Pete and Mike's scores before today's match were 1x and 3x respectively must be incorrect.

Let's try a different assumption. Let's assume that before today's match, Pete and Mike's scores were 2x and 6x respectively. After today's match, Pete scored 4 goals, so his total score is now 2x + 4. We also know that Pete and Mike's scores were in the ratio of 1:2 after today's match. Therefore, we can write:

2x + 4 : 2(6x) = 1 : 2

We can simplify this to:

2x + 4 : 12x = 1 : 2

We can cross-multiply to get:

2(2x + 4) = 1(12x)

4x + 8 = 12x

8 = 12x - 4x

8 = 8x

x = 1

Therefore, before today's match, Pete and Mike's scores were 2 and 6 respectively. After today's match, Pete's score is 2 + 4 = 6. Since Pete and Mike's scores were in the ratio of 1:2 after today's match, Mike's score must be twice that of Pete's score, which is 2 x 2 = 4.

Therefore, Mike's total score is 6 + 4 = 10. Mike scored a total of 10 goals.

I disregard the null hypothesis & come to the conclusion supports the assertion that the mean classroom sizes for full-time is lower than [tex]33[/tex] pupils but since p-value [tex](0.033)[/tex] falls short of significance threshold [tex]=0.01[/tex].

Depending about where it is in the number, each digit has a different value, which is referred to as value. We estimate it by reducing the place value by the face value of the digit. Worth is the product of will get and face value.

Place value refers to how much a digit is worth in relation to where it is in a number, such as the ones, tens, thousands, and so on. For instance, 5 in 3458 has a placement value of 5 tens, and 50.

X bar [tex]= (36+27+32+36+35+41+28+25+32+27+33+36+30+29+27+28+30+28)/18 = 31.39[/tex]

s [tex]= \sqrt{(((36-31.39)^2 + (27-31.39)^2 + ... + (28-31.39)^2)/17)} = 4.84[/tex]

We can support the university's claim. The P-value is approximately [tex]0.033[/tex]

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0.55 = 55% probability of experiencing neither of the side effects.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

Venn diagrams are diagrams used to visually describe sets, relationships between sets, and operations carried out on them. John Venn (1834–1883) invented the Venn diagram, which makes use of circles (overlapping, intersecting, and non–intersecting) to show the relationship between sets. A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it.

The "or probability" is given by:

P(A∪B)=P(A)+P(B)-P(A∩B)

P(N)=0.2 , P(D)=0.4 and P(N∩D)=0.15

The "at least one" probability is:

0.2+0.4-0.15=0.45

Hence, the "neither" probability is:

1-0.45=0.55

0.55 = 55% probability of experiencing neither of the side effects.

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The minimum score needed to be in the top 5% on this standardized aptitude test is 7. The distribution of scores on a standardized aptitude test is approximately normal with a mean of and a standard deviation of. What is the minimum score needed to be in the top on this test?

In statistics, we assume that the distribution of scores on a standardized aptitude test is approximately normal with a mean of µ and a standard deviation of σ, where µ and σ are the parameters of the normal distribution. To calculate the minimum score needed to be in the top 5%, we must first determine the z-score corresponding to the top 5%.It is known that the area to the left of z is 0.95, which corresponds to the top 5%.

To find the z-score that corresponds to the 95th percentile, we can use a standard normal distribution table, such as the one found in most statistics textbooks or online. The table gives the z-score that corresponds to the given area to the left of the mean.Using the standard normal distribution table, we find that the z-score corresponding to the top 5% is approximately 1.645. This means that the score needed to be in the top 5% is 1.645 standard deviations above the mean. We can calculate this score using the formula:X = µ + zσwhere X is the score we are trying to find, µ is the mean, z is the z-score corresponding to the top 5%, and σ is the standard deviation. Substituting the values we know into this formula:X = + 1.645 × = + 6.58. Rounding to the nearest integer, we get X = 7.

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Answer:

  Alvarez = Saunders ≠ Jensen

Step-by-step explanation:

You want to know if any or all of the classes collected the same number of canned goods per student when the numbers were ...

The metric "canned goods per student" is computed by dividing the number of canned goods by the number of students. These values might best be compared as decimal numbers.

The attached calculator screen shows this calculation.

The classes of Mr. Alvarez and Mrs. Saunders had equivalent ratios of canned goods per student: 6. Ms. Jensen's class had a ratio of 5.5 canned goods per student, so was not equivalent to the other two.

Answer:

Step-by-step explanation:

We can find out if the ratios of canned goods per student are the same for any or all of the classes by calculating the ratio of canned goods per student for each class.

Therefore, the ratios of canned goods per student are not the same for all the classes. However, Mr. Alvarez's and Mrs. Saunders's classes have equivalent ratios, indicating that each student, on average, collected the same number of canned goods in these two classes. In contrast, Ms. Jensen's class has a different ratio, indicating that, on average, her students collected a different number of canned goods per student compared to the other two classes.

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Reason:

The point X is located at (2,1)

We'll apply the scale factor to quadruple each coordinate to get (8,4)

Then apply the translation rule to shift 3 units left and 1 unit up.

[tex](\text{x},\text{y})\to(\text{x}-3,\text{y}+1)\\\\(8,4)\to(8-3,4+1)\\\\(8,4)\to(5,5)\\\\[/tex]

The answer of the question based on the volume of  prism is given below, the volume of the prism is 48 cubic units.

The Pythagorean Theorem is fundamental theorem in mathematics that relates to three sides of  right-angled triangle. It states that in any right-angled triangle,  square of length of the hypotenuse (the longest side) is equal to sum of  squares of  lengths of other two sides.

we know that the area of the base is given by:

Area of base = (1/2) * base * height

where base = 4 and height = 3 (using the Pythagorean Theorem).

Therefore, Area of base = (1/2) * 4 * 3 = 6 square units.

The height of the prism is given as 8 units.

Hence, the volume of the prism is given by:

Volume = Area of base * height

= 6 * 8

= 48 cubic units.

Therefore, the volume of the prism is 48 cubic units.

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Answer:

4 people

Step-by-step explanation:

We are given that The amount of time it takes p people to paint d doors varies directly with the number of doors inversely with the number of people.

Let constant of proportionality be k

There are 4 people , 10 doors and 2 hours.

Since we are given that time varies directly with no. of doors and inversely with no. of people.

[tex]2=k\times\frac{10}{4}[/tex]

[tex]\frac{2\times4}{10}=k[/tex]

[tex]\frac{8}{10}=k[/tex]

[tex]\frac{4}{5}=k[/tex]

Now we are supposed to find that How many people will it take to paint 25 doors in 5 hours.

⇒ [tex]5=k\times\frac{25}{d}[/tex]

⇒ [tex]5=\frac{4}{5} \times\frac{25}{d}[/tex]

⇒ [tex]d=\frac{4}{5} \times\frac{25}{5}[/tex]

⇒ [tex]d=4[/tex]

Hence it will take 4 people to paint 25 doors in 5 hours.

If the profit from T-shirts sales was $1,632, and the vendor pays the rock bands 1/3 of the total profit from T-shirts and sweatshirts sales at every concert, proportionately, the profit from the sweatshirt sales alone is $546.

Proportion describes the equation of two ratios.

In this situation, when we equate the proportion or fraction of the share of profit paid to the band to the actual profit paid, we can find the total profit realized from the concert sales.

The fractional share of the total profit from T-shirts and sweatshirts paid to the rock band = 1/3

The total amount paid to the rock band after the last concert = $726

The profit from T-shirts sales = $1,632

Proportionately, the total profit from the sales of T-shirts and sweatshirts = $2,178 ($726 x 3)

The profit from sweatshirt sales is the difference between the total profits and the profit from T-shirt sales.

= $546 ($2,178 - $1,632)

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For cos(0) to be equal to 0.392, sin(20) must be equal to cos(0 + 30).

We can use the trigonometric identities to simplify the expression cos(0 + 30):

cos(0 + 30) = cos(0)cos(30) - sin(0)sin(30)

Since sin(0) = 0 and cos(30) = √3/2, we have:

cos(0 + 30) = cos(0)√3/2

We can then rearrange this equation to get:

sin(20) = cos(0)√3/2

To solve for cos(0), we can divide both sides by √3/2:

cos(0) = sin(20) / (√3/2)

Using the values of sin(20) ≈ 0.34 and √3/2 ≈ 0.866, we can calculate:

cos(0) ≈ 0.34 / 0.866 ≈ 0.392

Therefore, for cos(0) to be equal to 0.392, sin(20) must be equal to cos(0 + 30).

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Answer:

I think its C

Step-by-step explanation:

Answer:32

Step-by-step explanation:

The train ride duration was 4 hours and 15 minutes.

To find the duration of the train ride, we need to subtract the departure time from the arrival time.

First, let's convert the departure and arrival times to a 24-hour clock format for easier calculation.

6:15 PM in 24-hour clock format is 18:15.

10:30 PM in 24-hour clock format is 22:30.

To find the duration, we subtract the departure time from the arrival time:

22:30 - 18:15 = 4 hours and 15 minutes

Therefore, the train ride duration was 4 hours and 15 minutes.

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Answer:

from the figure

tanx= p/b

or, tanx= 4/9

or, x=arctan(4/9)

or, x=23.49°

Answer:

enjoy your weekend bud , both answers and solutions ares given , if you didn't understand anything lmk with a message and ill be happy to explain

The equation of the quadratic function with four times the maximum width,  with a maximum of 3 and an axis of symmetry of x = -2 is given as follows:

y = -4(x + 2)² - 3.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The width is four times the normal width and the function has a maximum, hence the leading coefficient is given as follows:

a = -4.

Considering the axis of symmetry and the maximum, the parameters h and k are given as follows:

h = -2, k = 3.

Hence the function is defined as follows:

y = -4(x + 2)² - 3.

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Answer:

length of base = 17 cm

Step-by-step explanation:

Area of a triangle A = 1/2 bh where b = base h = height

We are given
b = 2h - 7

A = 102

or
2h = b + 7

h = (b+7) /2

use this in the equation for A

1/2 (b) (b+7)/2 = 102

1/4 x b(b+7) = 102

b(b+7) = 4 x 102

b² + 7 b = 408

b² + 7b - 408 = 0

This is a quadratic equation which can be solved by factoring or using the quadratic formula

We can factor b² + 7b - 408 as follows

Check if b = 17 is correct

With b = 17

h = (b+7) /2

= (17 + 7)/2

= 24/2

= 12

Therefore A = 1/2 x 17 x 12

= 17 x 6

= 102

You can use 3599 red tiles. If you have used 121 blue tiles.

To begin, find out how many total tiles are in the square by squaring the number of tiles along one side. Then subtract the number of tiles in the two diagonals of the square, which are all blue, to get the number of red tiles. Let us try to solve the problem. Given that the tiles are square and congruent, they must have identical dimensions. Let us assume that the length of one side of the square tile is x.

Therefore, the length of each side of the square can be determined by dividing the number of tiles by the length of the side of the square. The total number of tiles in the square can be calculated by squaring the number of tiles along one side. Consider the following equation: Let x be the length of each side of the square tile.

Then, the total number of tiles that make up the square can be determined using the following equation:

Total number of tiles in square = [tex]x^2[/tex]

We know that all the tiles are congruent squares, except those that are blue, which are located on the two diagonals. This means that there are 2 diagonals of blue tiles, and the remaining tiles are red. To determine the number of blue tiles in the two diagonals, use the following formula:

Length of diagonal = √2 x side length

Since the diagonals pass through opposite corners of the square, they must be equal in length. The total number of blue tiles, 121, is equal to twice the number of blue tiles in one diagonal. Use the following formula to determine the number of blue tiles in one diagonal: 121 / 2 = 60.5 The answer is rounded up to 61.

Using the Pythagorean Theorem, the length of the diagonal of each blue tile can be calculated. The following equation can be used: Side of square = x

Length of diagonal of one blue tile = x√2

The number of blue tiles in one diagonal is the length of the diagonal divided by the length of the diagonal of one blue tile. This can be expressed as a formula:x / (x√2) = number of blue tiles in one diagonal

Simplify the formula:

x / (x√2) = number of blue tiles in one diagonal

Multiply both sides by √2 and simplify:(√2 / 2) = number of blue tiles in one diagonal

This indicates that each diagonal has a total of 61 blue tiles. Because the two diagonals have a total of 122 blue tiles, the number of red tiles is equal to the total number of tiles minus the total number of blue tiles. The following equation can be used to calculate the number of red tiles:([tex]x^2[/tex]) - 122 = number of red tiles

Substitute 61 for x: [tex](61)^2[/tex] - 122 = 3721 - 122 = 3599.

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Answer:

160

Step-by-step explanation:

area of trapezoid = 1/2 (base 1+base 2) x height.

24+8=32

32x10=320

320x1/2=160.

160.

The rate of the selling price of each egg is 6%

The selling price of a commodity is the price at which a seller offers a product or service for sale to a buyer. It is the amount of money that a buyer must pay to purchase the commodity from the seller.

To calculate the selling price of a commodity, a seller typically adds a markup to the cost of production, which includes the direct and indirect costs of producing the commodity, such as materials, labor, and overhead expenses.

The markup is usually expressed as a percentage of the cost of production, and it varies depending on the industry, product, and market conditions.

If 200 eggs were bought for Rs10 each, then all egg costs Rs2000.

20 broken eggs, remaining 180 eggs.

Based on these conditions, we can formulate an equation:

10 × (8% + 1) ÷ (200 - 20)

Simplify;

[tex]=\dfrac{10\times 1.08}{180}[/tex]

Eliminate the common factor;

[tex]=\dfrac{1.08}{18}[/tex]

[tex]=\dfrac{108}{1800}[/tex]

Calculate the product or quotient;

[tex]=\dfrac{6}{100}[/tex]

Rewrite the rate of the selling price as a percentage = 6%

Therefore, we can conclude that the rate of the selling price as a percentage is 6%.

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The equation of the line perpendicular to y = -4x - 2 and passing through (-12, 2) is y = 1/4x + 5.

Given that a line passes through (-12, 2) and is perpendicular to y = -4x - 2. We have to find the equation of this line. To find the equation of the line perpendicular to the given line, we need to know the slope of the line we want to find. The slope of the given line is -4. Since the lines are perpendicular, the slope of the line we want to find will be the negative reciprocal of -4, which is 1/4.

Thus, the equation of the line passing through (-12, 2) and is perpendicular to y = -4x - 2 is:y - 2 = 1/4(x + 12)Simplify by distributing the 1/4:y - 2 = 1/4x + 3

Add 2 to both sides: y = 1/4x + 5

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