A swimming pool is being constructed so that it is the upper part of aninverted square-based pyramid.a. Calculate H.b. Calculate the volume of the pool.c. How many 6 m3bins will be required to take the dirt away?d. How many litres of water are required to fill this pool?e. How deep is the pool when it is half-filled?

Explanation:

On taking LHS

Cos[(3π/2)+θ]Cos(2π+θ)[Cot{(3π/2)-θ}+Cot(2π+θ)]

We know that

π = 180°

2π = 2×180° = 360°

3π/2 = (3×180°)/2 = 540°/2 = 270°

Now

LHS becomes

Cos(270°+θ)Cos(360°+θ)[Cot(270°-θ)+Cot(360°+θ)]

We know that

Cos (270°+θ) = Sin θ

Cos (360°+θ) = Cos θ

Cot (270°-θ) = Tan θ

Cot (360°+θ) = Cot θ

→ Sin θ Cos θ [Tan θ + Cot θ]

→ Sinθ Cosθ[(Sinθ/Cosθ)+(Cosθ/Sinθ)]

→ Sinθ Cosθ[(Sin²θ+Cos²θ)/(SinθCosθ)]

→ Sin θ Cos θ [1/(Sin θ Cos θ)]

Since Sin²θ+Cos²θ = 1

→ (Sin θ Cos θ)/(Sin θ Cos θ)

→ 1

→ RHS

→ LHS = RHS

Hence, Proved.

Here are the formulae that I have used:

→ π = 180°

→ Cos (270°+θ) = Sin θ

→ Cos (360°+θ) = Cos θ

→ Cot (270°-θ) = Tan θ

→ Cot (360°+θ) = Cot θ

Here are the Trigonometric Identities that I have used:

→ Sin²θ+Cos²θ = 1

Answer:

B) [tex]-10x+30[/tex]

Step-by-step explanation:

You distribute:    

-10 times X minus 3 ( -10*x-3)

Which gives you:

Answer: -10x+30

Hope this helps!

Answer:

Step-by-step explanation:

[tex]\sf -10(x -3)[/tex]

[tex]\sf -10x-\left(-10\right)\times \:3[/tex]

[tex]\sf -10x+30[/tex]

Answer:  A) The volume of the pyramid is 1/3 the volume of the rectangular prism.

Explanation:

Let's say we had a rectangular block that has a volume of 90 cubic meters. If we wanted a pyramid that had the same base as the block, then the pyramid would have 1/3 of that 90 m^3 volume. The pyramidal volume would be (1/3)*90 = 30 m^3.

Put another way: we can fit 3 pyramids into one rectangular block.

Answer:

put it in desmos and turn it into table

Answer:

90

and

20

i think so ye

Step-by-step explanation:

Answer:

Nvm

Step-by-step explanation:

U don’t need help anymore?

Answer:

thanks for your points and the time

Answer:

(7+x)°=180-130

x=50-7

x=43

Step-by-step explanation:

length of missing side = sqrt(5^2 + 12^2) = sqrt(169) = 13

distance = sqrt(50^2 +25^2) =sqrt(3125)= 55.90metres

Answer:

im srry what

Step-by-step explanation:

DYK?

— Pretty face is everywhere, but a woman who cheer you up at your weakest and stay after knowing about your flaws and bad sides are rare, so you better keep her dude!.

#moodchallenge

Answer:

60 students are divided into equal groups of 5 student each.

Groups of 5 students per group totaled up to 60 students.

The quotient in both expression is 60:5 = 12 students per group.

Step-by-step explanation:

The ratio expression is a way of expressing the division of numerator by a denominator.

Here,

The total number of students is the numerator = 60

The denominator is the number of students per group = 5

Hence, the quotient is the value of the divison obtained which is (60/2) = 12

Therefore, there are 12 groups of 5 students.

Answer:

Step-by-step explanation:

3^2=9

2^3=8

9+8=17

Answer:

17

Step-by-step explanation:

3²+2³

= (3×3)+(2×2×2)

= 9+8

= 17

Answer:

Step-by-step explanation:

Take 2 points:

Find the slope:

Find the y- intercept:

The line is:

Answer:

Thus, width is 6 and length is 25.

Step-by-step explanation:

Let us assume the width is x, then, the length is (4x+1).

Therefore, 2x + 2(4x+1) = 62

Or, 2x + 8x + 2 =62

Or, 10x = 60

Or, x = 6

Answer:

27 units.

Step-by-step explanation:

The perimeter is equal to 2 x length + 2 x width.

If the width is 4 then:

62 = 2 x length + 2 x 4

62 = 2 x length + 8

Then, we can subtract 8 from both sides.

54 = 2 x length

Next, divide both sides by 2

27 = length

so,

The length is 27 units.

Answer:

-1

Step-by-step explanation:

Step-by-step explanation:

Given by your question

2(3x-1)≥4x-6

Distributive property to take off the parentheses

2×3x-2×1≥4x-6

6x-2≥4x-6

Subtract 4x on both sides (Subtractive property of equality)

6x-2-4x≥4x-6-4x

2x-2≥-6

Add 2 on both sides (Addition property of equality)

2x-2+2≥-6+2

2x≥-4

Divide 2 on both sides (Division property of equality)

2/2 x≥-4/2

x≥-2

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

Looking at the options you've provided.

-10 INCORRECT, it is not greater or equal to -2

-5 INCORRECT, it is not greater or equal to -2

-3 INCORRECT, it is not greater or equal to -2

-1 CORRECT, it is greater than -2

Answer:

2(3x -1) = 4x - 6

6x - 2 = 4x - 6

6x -2+2 = 4x -6 + 2

6x - 4x = 4x - 4x -6 + 2

6x - 4x = -6 + 2

2x = -4

2 2

x = -2

Answer:

a. 2.50(6) + X = 22.50

b. $25.00

Step-by-step explanation:

A.

a ride = $2.50

total spent = $22.50

2.50(6) + X = 22.50

15.00 + X = 22.50

X = 22.50 - 15.00

X = 7.50

entrance fee = $7.50

B.

10*2.50= $25.00

Answer:

$22.50

Step-by-step explanation:

:)

Answer:

3/4

Step-by-step explanation:

Answer:

47%

Step-by-step explanation:

720+640=

1360. 640/1360 = 47

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

as said in my comment

A: (3x-2)X(x+1)

B: substitute 3 in(if m=meters),

(3x3-2)

9-2

7X(x+1)

3+1

4

7X4

28

Answer:

a) 3x^2 + x - 2

b) 28m

Step-by-step explanation:

a) Since the Area for a normal square is b*l (base x length)

Do the same with this (Using FOIL ig)

(3x - 2) * (x + 1)

3x^2 + 3x - 2x - 2

3x^2 + x - 2

b) Since it's asking us to find out what the number will be while x = 3m, just substitute 3 for every "x" in the answer we got for a

3(3)^2 + (3) - 2

3(9) + (3) - 2

27 + 3 - 2

30 - 2

28m

Therefore the actual area of this rectangle is 28m

Answer:

good luck i need to conquer europe

Answer:

1 / 12

Step-by-step explanation:

one hour = 60 minutes

so

5 / 60

= 1 / 12

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

There are 60 minutes in 1 hour , then 5 minutes as a fraction of an hour is

[tex]\frac{5}{60}[/tex] = [tex]\frac{1}{12}[/tex] ← in simplest form

Answer:

P = 5/8 or 15/24

Step-by-step explanation:

p = 18/12 - 7/8

p = 36/24 - 21/24

p = 15/24   ( Simplify )

p = 5/8

Answer:

Step-by-step explanation:

[tex]p+\dfrac{7}{8}=\dfrac{18}{12}\\\\p=\dfrac{18}{12}-\dfrac{7}{8}\\\\\\LCM \ of 8 \ and \ 12 \ is \ 24\\\\p=\dfrac{18*2}{12*2}-\dfrac{7*3}{8*3}\\\\p=\dfrac{36}{24}-\dfrac{21}{24}\\\\p=\dfrac{15}{24}[/tex]

[tex]p=\dfrac{5}{8}[/tex]

Answer:

10%=1500

so 100% = 15000

90%= 100% - 10%

15000-1500=13500

90%=13500

Answer:

Step-by-step explanation:

According to the matrix, the system is:

Correct match is A

Answer:

4(2x+1)(x−1)

Step-by-step explanation:

8x2−4x−4

8x2−4x−4

=4(2x+1)(x−1)

Answer:

5

Step-by-step explanation:

a) Se simplifica la b) Se simplifica

potencia, en este la potencia, en

caso 5 este caso 4.

Step-by-step explanation:

Espero que te sirva

Answer:

42.3148

Step-by-step explanation:

3.26% of 1298

3.26/100*1298

42.3148

Answer:

$6.69

Step-by-step explanation:

Since we know the total cost of 5 pairs of gloves, all we have to do to find the unit price is divide the total cost by how many gloves were are being sold:

33.45 / 5 = 6.69

Therefore, one pair of gloves costs $6.69

Hope this helps :)