With the aid of an illustrative example, discuss the relationship between the area of a region and the definite integral. *​

Answer:

The height of first tree is

[ 5.5+18tan(50 degrees) ] ft. This is approximately 26.95 ft.

Angle of elevation from Jimmy's eyes to top of tree is arctan([20+18tan(50 degrees)] /18). This is approximately 66.53 degrees.

Step-by-step explanation:

It would help you to draw a picture for both of these.

You have a person whose height is 5.5 ft and from there horizontal gaze they see a bird from a 50 degree angle of elevation. He is standing 18ft ftom the tree.

So we will first want to find the distance from his eyesight level to the top of the tree. We can do this using the tangent ratio since we have the opposite and adjacent measurements.

Let the distance from eyesight level to the top of the tree be r.

tan(50)=r/18

Multiply both sides by 18:

18tan(50)=r

Now the height of the tree is

[5.5+18tan(50 degrees)] ft.

Now if he is the middle of two trees, then he 18 ft from the 2nd tree.

Since he says the height is 20ft taller than the first tree then it's height is

[20+5.5+18tan(50 degrees)] ft.

Now since we want to find his angle of elevation to the top of the 2nd tree we need to take out his height given us the distance from his eyesight level to the top of the tree which is

[20+18tan(50 degrees)] ft..

So again we are using the tangent ratio.

Let this angle if elevation be P.

tan(P)=[20+18tan(50 degrees)] /18

Take arctan() of both sides:

P=arctan([20+18tan(50 degrees)] /18)

Answer:

x ≥ -30

Step-by-step explanation:

The equation is 3 - x / 2 ≤ 18.

First, subtract 3 on both sides:

- x / 2 ≤ 15.

Multiply by -2 on both sides and swap the less than or equal to sign:

x ≥ -30

Hope this helps!

Answer:

4 + x×9 >= 22

Step-by-step explanation:

that is the word by word "translation".

Answer:

[tex]x=\frac{4\sqrt{3}}{3}[/tex]

Step-by-step explanation:

From the figure attached,

ΔABC is an equilateral triangle.

Therefore, by the property of the equilateral triangle,

Measure of each angle = 60°

By applying tangent rule in the right triangle ADC,

[tex]\text{tan}(60^{\circ})=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

[tex]\sqrt{3}=\frac{4}{x}[/tex]

[tex]x=\frac{4}{\sqrt{3}}[/tex]

[tex]x=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3} }[/tex]

[tex]x=\frac{4\sqrt{3}}{3}[/tex]

I think its B because it is always B

Answer:

9(5+8)

Step-by-step explanation:

Answer:

r = 3 ft

Step-by-step explanation:

Area = 9π

So, πr²=9π where r is the radius

so, r²=9

or, r=√9

or, r=3, since r can't be negative

Answered by GAUTHMATH

Answer:

Dotplot, because a small number of scores are reported individually.

Step-by-step explanation:

Given the data :

Score (points) _______ 1 _ 2 _ 3 _ 4 _ 5

Number of Students __ 1 _ 2 _ 4 __3_ 2

Both the dot plot and histogram are used to represent graphical representation of data. The histogram uses bars ot represent data values or frequency of data organized or presented as ranges. This means histograms are usually ideal for grouped data which maintain a specified amount of interval between each class Or group. The Dotplot on the other hand handles individual data values using dots that represent the frequency of each. Since the data above are reported as individual data values, then the Dotplot is an ideal choice.

Answer:

small dot plot bb

Step-by-step explanation:

xoxo

Answer:

gradient = - [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (3, 1) ← 2 points on the line

m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex]

Answer:

Number of cookies each friend gets = 14 cookies

Step-by-step explanation:

Total cookies available for the party = 98

Number of friends invited = 7

how many did each freind get

Number of cookies each friend gets = Total cookies available for the party / Number of friends invited

= 98/7

= 14 cookies

Number of cookies each friend gets = 14 cookies

Answer: P (3 or odd) = 1/2

Step-by-step explanation:

Concept:  

Here, we need to know the idea of probability.  

Probability is a measure of the likelihood of an event to occur.  

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

The numbers on a dice: 1, 2, 3, 4, 5, 6

Total numbers = 6

Number of 3 = 1

Number of Odd = 3

[Since 3 is one of the odd numbers and they are overlapping, so we should subtract 1 from the number of favorable outcomes]

P (3 or odd) = Favorable / Total (refer to the attachment)

P (3 or odd) = [(1 + 3) - 1] / 6

P (3 or odd) = (4 - 1) / 6

P (3 or odd) = 3 / 6

P (3 or odd) = 1/2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

I say it's the fourth option

Answer:

The inverse is 1/4x

Step-by-step explanation:

y = 4x

To find the inverse, exchange x and y

x = 4y

Solve for y

1/4 x = 4y/4

1/4x = y

The inverse is 1/4x = y

Answer:

y = x/4

Step-by-step explanation:

y = 4x

x = 4y

y = x/4

Answer:

6(b + 5) = 4

Step-by-step explanation:

To start of we know that by saying six time the sum of a number and five. The problem wants us to put b + 5 in parenthesis to establish that the 6 is being distributed to both the b and the 5. Now that we have the first part, all we have to do is write that this expression is equal to four.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

-quadratic / parabolic

- y intercept = 0

- x intercepts at 0 and 6

- highest value = 9

- graph is increasing between 0 and 6

Step-by-step explanation:

Step-by-step explanation:

8 . 9 + 3x = 6

3x =6 - 9

3x = -3

x =. -1

9 . 9 (x - 1) - 4( 7 - x ) ≤ 10x - ( 2x +1 ) -6

9x -9 - 28 - 4x ≤ 10x - 2x + 1 - 6

C. L. T.

9x - 4x - 10x + 2x ≤ 1 - 6 + 28 + 9

- 3x ≥ 32

x ≥ - 32/3

x ≥ 10⅔

10 b/ 22 =. 16/ 88

cross multiply

88b = 352

b = 4

11. x- 10 / x+2 = 1/5

cross multiply

5x - 50 = x + 2

4x = 52

x = 13

Answer:

Step-by-step explanation:

Answer:

[tex]{ \tt{x = 41 \degree}}[/tex]

Interior alternate angles.

[tex]{ \tt{y + x = 180 \degree}} \\ { \tt{y + 41 \degree = 180 \degree}} \\ { \tt{y = 139 \degree}}[/tex]

Answer:

x = 45°

y = 135°

Step-by-step explanation:

Hi, Ace here!

Over here, we have a transversal with m parallel to n. Because those two lines are parallel, we can apply many theorems to this transversal.

First, we can say that m<45° and m<x° are corresponding angles. According to this theorem, that means both these degree measures are equal, thus x = 45°.

To find y, we can do 1 of two things in 1 step. We can name m<45° and m<y° as same side exterior angles, which means that they'd be supplementary angles (add up to 180°).

The second thing we can do is say m<x and m<y supplement each other because the measure of a flat line equals 180°, and according to Part-Whole-Postulate, that means all the parts of the flat line would also equal up to 180°.

Of course, these methods are practically the same due to substitution (m<x=m<45°). So m<y = 180° - m<x or m<y = 180° - 45° = 135°.

Hope this helped, let me know if you have any questions.

Answer:

answer for this question is 4

Step-by-step explanation:

2+2=4

Answer:

252

Step-by-step explanation:

Answer:

a. 35 Kilometres.

b. 60 litres.

c. 8150 sweets.

Step-by-step explanation:

Given the following data;

a. To find how many kilometres he traveled in one day;

770 km = 22 days

X km = 1 day

Cross-multiplying, we have;

22X = 770

X = 770/22

X = 35 Kilometres.

b. To find how many litres he would need to go 840 km;

1 litre = 14 kilometres

X litres = 840

Cross-multiplying, we have;

14X = 840

X = 840/14

X = 60 litres.

c. To find how many sweets are there in his car;

Number of sweet box, Ns = 326 boxes

Number of sweets in each box, Sw = 25 sweets

Total number of sweets = Ns * Sw

Total number of sweets = 326 * 25

Total number of sweets = 8150 sweets.

Answer:

Slope=[tex]\frac{11}{-4}[/tex]

Step-by-step explanation:

Answer:

262.44 [tex]m^{3}[/tex]

Step-by-step explanation:

Volume of cylinder = [tex]\pi r^{2}[/tex]h  

Volume of cube = [tex]s^{3}[/tex]

Cylinder  

[tex](\pi )(2.5)^{2}[/tex](7) = 137.44468

Cube

[tex]5^{3}[/tex] = 125

125 + 137.44 = 262.44

Answer:

24units

Step-by-step explanation:

Since the triangle CME is an equilateral triangle, hence all the sides are equal. This shows that BE =DM

Given that;

BE = 27 - 5x

DM= 5x - 3

On equating, we will have;

27-5x = 5x - 3

-5x-5x = -3-27

-10x = -30

x = 30/10

x = 3

Length of EC = 2BE

EC = 2(27-5x)

EC = 2(27-5(3))

EC = 2(27-15)

EC = 2(12)

EC = 24

Hence the length of a side is 24units

Answer:

5 inches

Step-by-step explanation:

To find the area of a square the formula is A = bh which with a square is essentially one side squared. We know this because every side of a square is the same. We also know that 5 squared is 25 meaning the answer is 5 inches(You could also use the formula A = bh : A = 5 x 5 : A = 25).

Answer:

The side is 5 square inches.

Step-by-step explanation:

Area of square formula:

A = s x s or [tex]s^2[/tex]

To figure out the sides, we use this formula:

A = 25 ÷ s = s

But to figure out s = side, think of factors of 25 like this:

25: 1,5,25

Now let's plug in the factors of 25 to figure out the missing side length.

A = 25 ÷ 1 = 25

This is not true.

A = 25 ÷ 5 = 5

This is true.

A = 25 ÷ 25 = 1

This is not true.

So our answer is 5 square inches on each side.

Answer:

B) Rays AB and AE

Step-by-step explanation:

Though A-F, A-D, and A-C all meet at one point on line B-E, point A, they aren't a part of it. Point A on line B-E marks the "midpoint" of it, and therefore, ray A-E and A-B are part of line B-E.

Answer:

22+g=65

Step-by-step explanation:

take the 22 add (sum) to g (the variable) and have them = 65

Answer:

Step-by-step explanation:

Let's see how well I can explain this. [tex]\frac{\pi}{6}[/tex] is the same as a 30 degree angle which is in quadrant 1. If you picture the unit circle, right in the center of it is the origin. If you draw a straight line from 30 degrees and through the center (the origin), you will automatically "connect" with the reference angle of 30 (this is true for ALL angles on the unit circle). This puts us in quadrant 3. In quadrant 3, x is negative and so is y. So the terminal point of the reference angle for 30 degrees has the same exact values, but both of them are negative (again, because both x and y are negative in quadrant 3). I can't see your choices but the one you want looks like this:

[tex](-\frac{\sqrt{3} }{2},-\frac{1}{2})[/tex]

Answer:

y = 5/4x-15

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 5/4x+b

Substitute the point into the equation and solve for b

-5 = 5/4(8)+b

-5 = 10+b

Subtract 10 from each side

-5-10 = b

-15 = b

y = 5/4x-15

Step-by-step explanation:

y-y'=m(x-x')

y-(-5)=5/4(x-8)

y+5=5x/4-10

4(y+5)=4(5x/4)-10(4)

4y+20=5x-40

4y-5x=-40-20

4y-5x=-60

5x-4y-60=0

y=5x/4-15

Answer:

56

Step-by-step explanation:

that is the procedure above

The missing segment in the image below is 8.

The missing segment is the side length of the small triangle that is formed by the two red lines and the green line. We can find the length of this side length by using the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the missing segment, and the other two sides are 4 and 5.

missing [tex]segment^2[/tex] = [tex]4^2[/tex] + [tex]5^2[/tex]

missing [tex]segment^2[/tex] = 16 + 25

missing [tex]segment^2[/tex] = 41

missing segment = √41

Therefore, the missing segment is √41.

Here are the steps in detail:

Identify the small triangle that is formed by the two red lines and the green line.

Label the sides of the triangle with the letters A, B, and C, where C is the missing segment.

Substitute the known side lengths into the Pythagorean Theorem.

Solve for the length of the missing segment.

To learn more about segment here:

https://brainly.com/question/12622418

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