A container in form of a frustum of a cone is 16 cm in diameter at the open end and 24 cm diameter at the bottom. If the vertical depth of the container is 8 cm calculate the capacity of the container.

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Work Shown:

[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]

Notice how 33*77 = 2541 and 11*231 = 2541

[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.

So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]

Answer:

Explained below.

Step-by-step explanation:

(11)

Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).

[tex][(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z[/tex]

Thus, the final expression is (-11x + y - 12z).

(12)

From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).

[tex][(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5[/tex]

Thus, the final expression is (7x² - y² - x + y + 5).

(13)

What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?

[tex]A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2[/tex]

Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).

(14)

What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?

[tex]A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7[/tex]

Thus, the expression is (3xy - 7zx + 7yz + 7).

(15)

How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?

[tex]A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy[/tex]

Thus, the expression is (x² - 6y² + 3xy).

Answer:

The middle of the sailboat is approximately 268.8 feet from the shore.

Step-by-step explanation:

Let the distance from shore to the middle of the boat be represented by x, the angle of elevation of Sandra from the shore to the top of the boat mast  is 7°. Applying the required trigonometric function to this question, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan 7° = [tex]\frac{23}{x}[/tex]

⇒  x = [tex]\frac{23}{Tan 7^{0} }[/tex]

       = [tex]\frac{23}{0.12279}[/tex]

      = 268.7515

∴ x = 268.8 feet

The middle of the sailboat is approximately 268.8 feet from the shore.

Best way to solve this is by using

[tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]

[tex]where \: s = \frac{a + b + c}{2} [/tex]

s=(12+8+17)/2

=18.5

using the formulae

area =43.5

Answer:

x = 20

Step-by-step explanation:

Intersecting Chords Theorem: ab = cd

Step 1: Label our variables

a = x

b = x - 11

c = x - 8

d = x - 5

Step 2: Plug into theorem

x(x - 11) = (x - 5)(x - 8)

Step 3: Solve for x

x² - 11x = x² - 8x - 5x + 40

x² - 11x = x² - 13x + 40

-11x = -13x + 40

2x = 40

x = 20

Answer: x=20

Step-by-step explanation:

[tex]ab=cd[/tex]

[tex]x(x - 11) = (x - 5)(x - 8)[/tex]

[tex]x^2 - 11x = x^2 - 13x + 40[/tex]

[tex]x^2 - 11x = x^2 - 8x - 5x + 40[/tex]

[tex]-11x = -13x + 40\\2x = 40\\x = 20[/tex]

Answer: [tex]y-1=\dfrac32(x+3)[/tex]

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]

Since parallel lines have equal slope . That means slope of the required line would be .

Equation of a line passing through (a,b) and has slope m is given by :_

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]

Required equation: [tex]y-1=\dfrac32(x+3)[/tex]

Answer:

h = 10

Step-by-step explanation:

Given

[tex]\frac{3}{7}[/tex] = [tex]\frac{h}{14}[/tex] - [tex]\frac{2}{7}[/tex]

Multiply through by 14 to clear the fractions

6 = h - 4 ( add 4 to both sides )

10 = h

Answer:

10

Step-by-step explanation:

We start out with 3/7 = h/14 - 2/7

add 2/7 to both sides:

(5/7) = h/14

Multiply both sides by 14 to get rid of the fraction:

h = 10

Answer:

answer is D

Step-by-step explanation:

2^4=16

16+(16-12)=20

over

(6+9)/(7-4)

15/3=5

so the new equation is 20/5=4

Answer:

D. 4

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Exponents

[tex]\frac{16 + (16 -3(4))}{(6+9)/(7-4)}[/tex]

Step 2: Parenthesis

[tex]\frac{16 + (16 -12)}{15/3}[/tex]

Step 3: Parenthesis

[tex]\frac{16 + 4}{15/3}[/tex]

Step 4: Divide

[tex]\frac{16 + 4}{5}[/tex]

Step 5: Add

[tex]\frac{20}{5}[/tex]

Step 6: Divide

4

Answer:

The answer can be interpreted by the distance moved by each gallon :))

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Just took it. Edg 2020. Hope this helps :)

Answer:

C = 35x pence

Step-by-step explanation:

1 pen costs 15 , thus x will cost 15x

1 ruler costs 20, thus x will cost 20x

Total cost (C) will then be

C = 15x + 20x = 35x pence

The total cost of pens and rulers, C = 35x pence

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Cost 1 pens is 15.

Then, cost for x pen is 15x

Cost of 1 ruler is 20

Then, cost of x ruler is 20x

So, the total cost is

= 15x + 20x

= 35x

Learn more about Equation here:

https://brainly.com/question/29538993

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Answer:

1st side: 150

2nd side: 30

As per the question,

We have to find what's the coefficient.

Let's start to seperate the expression.

Here,

x is the variable,

4 is a number.

-3 is also a number.

4, -3x

The number with x here is -3 in (-3x) as the coefficient is (-3) in the given equation.

Answer:

Hey there!

Rearrange the expression to: -3x+4

The coefficient would be -3.

Let me know if this helps :)

Answer:

1) The ship is closer

2) 675.73 m

Step-by-step explanation:

1) The given parameters are;

The initial angle between the ship's course and the lighthouse = 32°

The final angle between the ship's course and the lighthouse = 72°

The distance traveled by the sip between he two positions = 1500 m

Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b

Where;

a = The initial distance fro the lighthouse

b = The final distance fro the lighthouse

The angles of the triangle are

32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°

By sine rule we have;

1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =

Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m

b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m

Therefore, a  > b

The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer

2) By cosine rule we have

a² = b² + c² - 2× b×c×cos(A)

Where the given measurements by Kendra are;

410 m and 805 m with an included (in between) angle of 57°, we have;

Let b = 410 m, c = 805 m, and A  = 57°, we have;

a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²

a = The length of the stream = 675.73 m.

Step-by-step explanation:

Example 1:

a+c=b+c then a=b

First let the value of a and b be different (not equal)

a=5

b=7

c=10

a+c=b+c

5+10=7+10

15≠17

Example 2:

Let the value a and b be equal (the same)

a=5

b=5

c=10

a+c=b+c

5+10=5+10

15=15

So when,

a+c and b+c is equal, a and b are always equal.

Hope this helps ;) ❤❤❤

Answer:

a=b

Step-by-step explanation:

Reason:

a+c=b+c

a-b=c-c

c-c would be 0

if a-b=c-c=0

a-b=0

Only if a=b can a-b=0

You can also take it as:

b-a=c-c (a+c=b+c)

b-a=0=c-c

Therefore b=a

By the way even I am a BTS army

Answer:

c

Step-by-step explanation:

The expression (9⁶ x 7⁻⁹)⁻⁴ is equivalent to expression 7³⁶ / 9²⁴. Then the correct option is D.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

⇒ (9⁶ x 7⁻⁹)⁻⁴

Simplify the expression, we have

⇒ (9⁻⁶ x 7⁹)⁴

⇒ 9⁻²⁴ x 7³⁶

⇒ 7³⁶ / 9²⁴

Then the correct option is D.

More about the equivalent link is given below.

https://brainly.com/question/889935

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Answer:

5,383,000  / *improvments cost 8,074,500

Step-by-step explanation:

if 2.5 is by 'times' then,

13,457,500 / 2.5 =

5,383,000

Which means the cost of the land is 5,383,000

To check just multiply:

5,383,000 x 2.5 = 13,457,500

*Extra

13,457,500 - 5,383,000

= the cost of improvements =  8,074,500

Hope this helps, and have a good day :)

Answer:

$3,845,000

Step-by-step explanation:

As per given:

Then total is:

Cost of the land alone is  $3,845,000

Answer:

(0,3), graph is attached.

Step-by-step explanation:

We know that the first equation will increase 2 points in y for every 1 x, since the constant next to x is 2. We also know it's y-intercept will be 3.

As for the second equation, we know it will have no y and instead run through the y=3 line, crossing every value of x.

Graphing this, we see that these lines intersect at (0,3) so that's the solution to this system.

Hope this helped!

Answer:

He had a different number of points to the left of the vertical line than to the right of the vertical line.

Step-by-step explanation:

Divide-center method is the method which involves dividing the data on the graph into two equal parts and then fin the line of best fit. The center of each group is approximated and then a line is constructed between two centers which is estimated as line of best fit.

Answer:

A

Step-by-step explanation:

[tex] \sin(2 \alpha ) = 2 \sin( \alpha ) \cos( \alpha ) [/tex]

[tex] \sin( \alpha ) \cos( \alpha) = \frac{1}{2} \sin( 2\alpha ) [/tex]

Answer:

288.4m

Step-by-step explanation:

This track is split into a rectangle and two semi-circles.

We can find the length of the semi-circles by finding its circumference with the formula [tex]2\pi r[/tex].

[tex]2\cdot3.14\cdot30\\188.4[/tex]

However this is half a circle, so:

[tex]188.4\div2=94.2[/tex].

There are two semi-circles.

[tex]94.2\cdot2=188.4[/tex]

Since there are two legs of 50m each, we add 100 to 188.4

[tex]188.4+100=288.4[/tex]m

Hope this helped!

Answer:

Step-by-step explanation:

To solve for the perimeter, we first look at the rectangle in the middle. the length is 50m, and there are two sides to it, so: 50 * 2 = 100m for the top and bottom of the track.

For the circle, we can see the diameter is 30m. To solve for the circumference, we need to use the formula 2πr.

15 * 2π ≈ 94.2477796077

We add that to 100m and get:

194.2477796077

Answer:

3.03 • 10⁻³ is scientific notation

0.00303 is decimal form

Answer:

  451. No, the angles are wrong.

Step-by-step explanation:

450. AB = 15, BC = 10, and CD= 7. Find the length DA.

  This cannot be done without additional information about the sort of figure that ABCD is. If these are points on a line segment, we need to know their order. If these are points on a quadrilateral, we need to know its description in more detail.

If these are points ordered ABCD on a line, then AD = 15+10+7 = 32.

__

451. See the attached figure. BPQD is not a parallelogram: BCQ is not a straight line. (The internal angles of a pentagon are 108°, but would need to be 120° for BCQ to be a straight line, making BP parallel to DQ.) Instead, BPQD is an isosceles trapezoid.

Answer:  D.  (-4, -2)

Step-by-step explanation:

Rotating 180° about the origin means the signs for the x- and y-values are opposite.

(x, y) → (-x, -y)

(4, 2) → (-4, -2)

The coordinate after 180° of rotation will be (-4, -2). Then the correct option is D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The line is y = mx, then the point (4, 2).

The point (4, 2) is in the first quadrat.

The line is rotated by 180° about the origin.

Then the coordinate will lies in the third quadrant.

Then the value of the abscissa and ordinate will be transformed into negative.

Then the coordinate after 180° of rotation will be (-4, -2).

Then the correct option is D.

More about the transformation of a point link is given below.

https://brainly.com/question/27224339

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Answer:

Option B.

Step-by-step explanation:

Consider the correct question is "Which statement correctly compares

1. -201  and  151

-201 = 151

-201 < 51

-201 > 151"

The given numbers are -201 and 151. We need to compare these numbers.

We know that all negative numbers are less than positive numbers.

So,

-201 < 151

If both numbers are negative, then the larger negative number is the smaller number.

Therefore, the correct option is B.

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Explanation:

A drawing may be helpful to see what's going on. Check out the diagram below. This is one way of drawing out the two triangles. The locations of the points don't really matter, and neither does the the orientation of how you rotate things. What does matter is we have the right points connected to form the segments mentioned.

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For now, focus on triangle TIP only. In order to have this be isosceles, we must make TP = 5 or TP = 7.

If TP = 5, then it's the same length as TI.

If TP = 7, then it's the same length as PI.

In either case, we have exactly two sides the same length (the other side different) which is what it means for a triangle to be isosceles.

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Let's consider triangle TOP. For it to be isosceles, we must have two sides the same length. We already locked in TP to be either 5 or 7 in the previous section above. So there's no way that TP could be 11 units long to match up with PO = 11.

If TP = 5, then OT must also be 5 units long so that triangle TOP is isosceles.

If TP = 7, then OT = 7 for similar reasoning.

Either way, TP only has two choices on what it could be.

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In short, we basically just write the first two values given to us to get the two triangles to be isosceles. We can't use TP = 11 as it would make triangle TIP to be scalene (all sides are different lengths).

Answer:

So we all cheat AOPS huh

Step-by-step explanation:

Answer:

d. (9, 13)

Step-by-step explanation:

5x-3y=6  /*6

6x-4y=2  /*(-5)

30x - 18y = 36

-30x +20y = - 10

            2y = 26

              y = 13

5x-3y=6

5x - 3*13 = 6

5x - 39 = 6

5x = 45

x = 9

(9, 13)

Answer:

She sold 10 pounds of peaches and 45pounds of grapes

Step-by-step explanation:

X= pounds of peaches

x+35=pounds of grapes

2x+4(x+35)=200

2x+4x+140=200

6x=200-140

6x=60

x=10

She sold 10 pounds of peaches and 45pounds of grapes. (Sorry, can’t help you graph it.)

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.

Answer:

C. 2[tex]\sqrt{29}[/tex]

Step-by-step explanation:

Square root of 116 is 10.7703296

Square root of 29 is 5.38516481, but as it is multiplied by 2, it becomes 10.7703296