What is the integral of the function f(x) = sin 2x?

Answer:

To solve the expression 2 + 7 • (-3)^2, we follow the order of operations, also known as PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we evaluate the exponent: (-3)^2 = 9 (because squaring a number means multiplying it by itself).

Next, we perform multiplication: 7 • 9 = 63.

Finally, we perform addition: 2 + 63 = 65.

So, the value of the expression 2 + 7 • (-3)^2 is 65.

PART A: Linda has $4.41 more than Enrique after one year.

PART B: Enrique has $12.10 more than Linda after the second year.

PART A: After one year, we can calculate the amount of money each person has in their respective accounts.

For Linda's account:

Principal amount = $610

Interest rate = 1.2%

\(Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32\)

\(Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32\)

For Enrique's account:

Principal amount = $590

Interest rate = 3.9%

\(Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91\)

Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91

Comparing the two amounts, after one year Linda has more money.

The difference in the amount is:

$617.32 - $612.91 = $4.41

Therefore, Linda has $4.41 more than Enrique after one year.

PART B: After a second year, we need to calculate the amounts again.

For Linda's account:

Principal amount = $617.32

Interest rate = 1.2%

\(Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41\)

Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73

For Enrique's account:

Principal amount = $612.91

Interest rate = 3.9%

\(Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92\)

Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83

Comparing the two amounts, after the second year Enrique has more money.

The difference in the amount is:

$636.83 - $624.73 = $12.10

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Answer:

1. A

2.C

Step-by-step explanation:

1. 170+170+10+10=360

2. 60x25=1500

1500/100=15

25-15=10

10% OF 10= 1

The answer is 11.

By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

the length of the base AB,

Area = (1/2) * base * height

\(CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\\)

We also know that the area of the triangle is:

\(46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\\)

\(8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\\)

\(AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\\)

Therefore, the length of the base AB is approximately 20.88 centimeters.

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Answer:

x is 5

Step-by-step explanation:

Ok, so

Let me draw the situation here below:

For this problem, we have to use the trigonometric relations.

In this case, it would be useful to use sin(x).

Sin(x) relations the opposite side of the angle and the hipotenuse of the triangle so:

Sin(60) = (7√3) / c

And c = (7√3) / Sin(60)

Remember that sin(60) is a number, whose value is √3/2.

So,

And finally, c = 14 feet

Answer:

StartFraction 10 Over 6 EndFraction divided by 5

Step-by-step explanation:

Answer:

StartFraction 10 Over 6 EndFraction divided by 5

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

That's the answe!!

Answer:

4

Step-by-step explanation:

7 5/6 - 1 1/6 - 2 2/3 =

= 7 5/6 - 1 1/6 - 2 4/6

= (7 + 5/6) - (1 + 1/6) - (2 + 4/6)

= 7 + 5/6 - 1 - 1/6 - 2 - 4/6

= (7 - 1 - 2) + (5/6 - 1/6 - 4/6)

= 4 + 0/6

= 4

Answer:

AB = 38

BC = 4

Step-by-step explanation:

It kinda depends if the image is to scale or not

Answer:8

Step-by-step explanation:

1×8=8

8×8=64

1/8=8/64

The intervals that could be used based on the information will be:

The frequency distribution will be:

Interval Frequency

0-3. 2

4-7. 6

8-11. 4

12-16 8

Lastly, it should be noted that to work out which bar is the tallest, we must compare the frequencies of all the intervals. In our case here, the interval with a frequency of 8, 12-16, has the highest value and therefore its bar will be the tallest in the histogram.

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Answer: 8.4 feet

Step-by-step explanation:

Given: Lumber required for each shelf = \(8\dfrac{3}{4}\ inches\)

For each base side = \(12\dfrac12\ inches\)

For each door stile = \(29\dfrac18\ inches\)

Total lumber required = \((2\times 8\dfrac34 + 2\times12\dfrac12+2\times29\dfrac18)\ \ in.\)

\(=(2\times\dfrac{35}{4}+2\times\dfrac{25}{2}+2\times\dfrac{233}{8})\ in\\\\= (\dfrac{35}{2}+25+\dfrac{233}{4})\ in.\\\\=\dfrac{403}{4}\ in. =\dfrac{403}{4}\times\dfrac1{12}\ feet \ \ \ \ [1 feet = 12 \ in.]\\\\\approx8.4\ feet\)

Hence, we will need 8.4 feet lumber.

Answer: 13

Step-by-step explanation:

4x+3y=-5 solve x :    

4x = -3y + -5           | -3y

1x = -0.75y + -1.25  | : 4

-3x + 7y = 13 solve x :

-3x + 7y = 13              | -7y

-3x = -7y = 13             | : (-3)

Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333

-0, 75y - 1,25 = 2,333y - 4, 333 solve y:

-0, 75y - 1,25 = 2,333y -4, 333    | -2,333y

-3, 083y - 1,25 = -4,333               | + 1, 25

-3. 083y = -3,088                         | : (-3, 083)

y = 1

Plug y = 1 into the equation 4x + 3y = -5 :

4x + 3 · 1           | Multiply 3 with 1

4x + 3 = -5        | -3

4x = -8              | : 4

x = -2

So the solution is:

y = 1, x = -2

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Answer:

4.5

Step-by-step explanation:

300 times 150 = 4500

4500/1000 ( kilo means 1000 )

4.5

The area of a 2D form is the amount of space within its perimeter. The area of the field in square kilometres is 45,000.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given that the rectangular field is 300meters long and 150 meters wide. Therefore, the area of the field in square kilometres is,

Area = Length x Width

        = 300 meter x 150 meter

        = 45,000 meter²

Hence, the area of the field in square kilometres is 45,000.

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Answer:

11 + x

Step-by-step explanation:

addition uses the communtitve property meaning the numbers can be swaped and still result in the same answer

Step 1; Draw the diagram

Then the adjacent side of the kite are congruent side,

Hence part A is True

The diagonal of a Rhombus bisect each other at a right angle. hence the quadrilateral has its diagonals to be perpendicular to each other.

Hence Part B is True

Answer:0.794

Step-by-step explanation:

Answer:

the answer would be 0.794. but hundredths would be 0.79

hope this helped!

Step-by-step explanation:

Answer:

10 i think thats not really a questuon tho

Answer:

\(T_n = T_{n-1}+3\) where n>1

Step-by-step explanation:

Given

\(19,22,25, ..\)

Required

Determine the recursive formula

The given sequence shows arithmetic progression (AP).

First, we calculate the common difference (d):

\(d = 22 - 19 = 25 - 22\)

\(d = 3\)

The recursive formula of an AP is determined using:

\(T_n = T_{n-1}+d\) where \(n>1\)

Substitute 3 for d

\(T_n = T_{n-1}+3\) where \(n>1\)

Answer:

1 3/4

Step-by-step explanation:

radius is half of diameter

The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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Answer:

The answer is 7 units from vertex T

Answer:

The other pairs are:

\((a)\ (2, \frac{5\pi}{6}) \to\)  \((2, \frac{17\pi}{6})\) and \((-2, \frac{23\pi}{6})\)

\((b)\ (1, -\frac{2\pi}{3}) \to\) \((1, \frac{4\pi}{3})\) and \((-1, \frac{7\pi}{3})\)

\((c)\ (-1, \frac{5\pi}{4}) \to\) \((-1, \frac{3\pi}{4} )\) and \((1, \frac{7\pi}{4})\)

See attachment for plots

Step-by-step explanation:

Given

\((a)\ (2, \frac{5\pi}{6})\)

\((b)\ (1, -\frac{2\pi}{3})\)

\((c)\ (-1, \frac{5\pi}{4})\)

Solving (a): Plot a, b and c

See attachment for plots

Solving (b): Find other pairs for \(r > 0\) and \(r < 0\)

The general rule is that:

The other points can be derived using

\((r, \theta) = (r, \theta + 2n\pi)\)

and

\((r, \theta) = (-r, \theta + (2n + 1)\pi)\)

Let \(n =1\) ---- You can assume any value of n

So, we have:

\((r, \theta) = (r, \theta + 2n\pi)\)

\((r, \theta) = (r, \theta + 2*1*\pi)\)

\((r, \theta) = (r, \theta + 2\pi)\)

\((r, \theta) = (-r, \theta + (2n + 1)\pi)\)

\((r, \theta) = (-r, \theta + (2*1 + 1)\pi)\)

\((r, \theta) = (-r, \theta + (2 + 1)\pi)\)

\((r, \theta) = (-r, \theta + 3\pi)\)

\((a)\ (2, \frac{5\pi}{6})\)

\(r = 2\ \ \ \ \theta = \frac{5\pi}{6}\)      

So, the pairs are:

\((r, \theta) = (r, \theta + 2\pi)\)

\((2, \frac{5\pi}{6}) = (2, \frac{5\pi}{6} + 2\pi)\)

Take LCM

\((2, \frac{5\pi}{6}) = (2, \frac{5\pi+12\pi}{6})\)

\((2, \frac{5\pi}{6}) = (2, \frac{17\pi}{6})\)

And

\((r, \theta) = (-r, \theta + 3\pi)\)

\((2, \frac{5\pi}{6}) = (-2, \frac{5\pi}{6} + 3\pi)\)

Take LCM

\((2, \frac{5\pi}{6}) = (-2, \frac{5\pi+18\pi}{6})\)

\((2, \frac{5\pi}{6}) = (-2, \frac{23\pi}{6})\)

The other pairs are:

\((2, \frac{17\pi}{6})\) and \((-2, \frac{23\pi}{6})\)

\((b)\ (1, -\frac{2\pi}{3})\)

\(r = 1\ \ \ \theta = -\frac{2\pi}{3}\)      

So, the pairs are:

\((r, \theta) = (r, \theta + 2\pi)\)

\((1, -\frac{2\pi}{3}) = (1, -\frac{2\pi}{3} + 2\pi)\)

Take LCM

\((1, -\frac{2\pi}{3}) = (1, \frac{-2\pi+6\pi}{3})\)

\((1, -\frac{2\pi}{3}) = (1, \frac{4\pi}{3})\)

And

\((r, \theta) = (-r, \theta + 3\pi)\)

\((1, -\frac{2\pi}{3}) = (-1, -\frac{2\pi}{3} + 3\pi)\)

Take LCM

\((1, -\frac{2\pi}{3}) = (-1, \frac{-2\pi+9\pi}{3})\)

\((1, -\frac{2\pi}{3}) = (-1, \frac{7\pi}{3})\)

The other pairs are:

\((1, \frac{4\pi}{3})\) and \((-1, \frac{7\pi}{3})\)

\((c)\ (-1, \frac{5\pi}{4})\)

\(r = -1 \ \ \ \ \theta = \frac{-5\pi}{4}\)

So, the pairs are

\((r, \theta) = (r, \theta + 2\pi)\)

\((-1, \frac{-5\pi}{4}) = (-1, \frac{-5\pi}{4} + 2\pi)\)

Take LCM

\((-1, \frac{-5\pi}{4}) = (-1, \frac{-5\pi+8\pi}{4} )\)

\((-1, \frac{-5\pi}{4}) = (-1, \frac{3\pi}{4} )\)

And

\((r, \theta) = (-r, \theta + 3\pi)\)

\((-1, \frac{-5\pi}{4}) = (-(-1), \frac{-5\pi}{4}+ 3\pi)\)

Take LCM

\((-1, \frac{-5\pi}{4}) = (1, \frac{-5\pi+12\pi}{4})\)

\((-1, \frac{-5\pi}{4}) = (1, \frac{7\pi}{4})\)

So, the other pairs are:

\((-1, \frac{3\pi}{4} )\) and \((1, \frac{7\pi}{4})\)

Answer:

36

Step-by-step explanation:

(1/2)(3+5)(9)

(1/2)(8)(9)

(4)(9)

36

The median of the two data sets compares as they will be the same.

The medians are the same because the median is the value such that 50% of the data points are higher and 50% are lower. Therefore, the actual value of the highest element doesn't affect the median.

The mean of set B is greater and the standard deviation of B is higher because the highest element is further from the mean. Also, the boxes are the same if the center line is the median since the interquartile range is the same.

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Answer:

I believe it's D. 9-1