An architect is designing a hexagonal gazebo. The floor is a hexagon made up of six isosceles triangles. The function y=4 tan θ models the height of one triangle, where θ is the measure of one of the base angles and the base of the triangle is 8 ft long.

c. Find the area of the gazebo floor in square feet when the triangles forming the hexagon are equilateral.

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Answer:

Nani means what in japanese.

Step-by-step explanation:

I am a anime weeb lol

Average velocity = 0 gives the horizontal component of the launch velocity .

What does average velocity mean?

The difference between the change in position or displacement (x) and the time periods (t) during which the displacement happens is known as average velocity.

                     Depending on how the displacement is displaced, the average velocity may be positive or negative. Meters per second (m/s or ms-1) is the standard international unit for average velocity.

Typical flight of a projectile is as shown in the picture above.

In the problem it is given that initial velocity V₀ at an angle θ

above the horizontal. As such inn the picture U=  V₀

This velocity can be resolved into its  x and y components.

Component along x axis, and

Component along y  axis = V₀ Sin θ

Let t be time of flight.

    Average velocity = Displacement/time of flight

  It is given that "It lands at the same level from which it was launched", means that displacement in the y axis is = 0  

      Average velocity  = 0/t  = 0  ............1

cos  θ component.

 Average velocity  =    V₀  cos  θ ............ 2

Average velocity we need to add both vectors along x and y directions

. In this instant it is simple as one of the vectors is  

                        Average velocity  = 0

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Answer: y=x-9

Step-by-step explanation:

Answer:

Using only dilation

Step-by-step explanation:

This is because dilation is to make bigger or smaller.

Answer:

c

Step-by-step explanation:

dilation is when you shrink the square, but maintain similarity between the four side lengths. Theoretically, you can shrink square EFGH to the size of ABCD

As per area of rectangle, the dimensions of the box that yield the lowest cost is (1,1,6)

Area of rectangle:

The standard formula for area of rectangle is calculated as,

A = length x breadth

Given,

A closed rectangular box with volume 6 cubic feet is made from two different types of cardboard. the top and bottom are made with a heavy-duty cardboard that costs 30 cents per square foot. The sides are made from a light-weight cardboard that costs 5 cents per square foot.

Here find the dimensions of the box that yield the lowest cost.

Here let's consider the dimensions of the rectangular box be length l, breadth is b, and height is h.

Now, from the given information, the total cost can be derived as,

=> C=2lb×48+(2bh+2lh)×8

=> C=96lb+16bh+16lh

=> C=16(6lb+bh+lh) -----------------→(1)

Then the given volume is, V = lbh = 6 ---------------→(2) cubic feet.

Then the equation 2,

=> lbh = 6h = 6/lb

And then we have to substitute the value of h in equation 1, we get

=> C(l,b,h)=16(6lb+6/l+6/b)

Now we need to minimize the resulting function of two variables.

Therefore, we need to partially derivative the above function with respect to l,b. And set these equal to zero.

And the for l=0,b is undefined. So we can eliminate l=0.

Here we have to substitute l=1,b=112⇒1 in equation 2, we get

=> lbh=6(1)(1)h=6h=6h=6

Therefore, the critical point is, (1,1,6)

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Answer:

y + 1 = 6(x - 4)

Answer: y + 1 = 6(x - 4)

Answer:

\(2\sqrt{3}+3\)

Step-by-step explanation:

\($\frac{3}{2 \sqrt 3 - 3}$\)

Rationalize the fraction.

\($\frac{3}{2 \sqrt 3 - 3}\cdot \frac{2 \sqrt 3 + 3}{2 \sqrt 3 + 3} =\frac{6\sqrt{3}+9 }{12-9} =\frac{6\sqrt{3}+9 }{3} =2\sqrt{3}+3 $\)

Note that I used the positive signal because we would have a difference of squares.

Answer: D

Step-by-step explanation:

Answer:

a. 75 degrees

b. 14.5ft

Step-by-step explanation:

a) tan x = 6/8

= 0.75

b) sin 75 degrees = x/15

Sin 75 degrees = 0.97

(0.97)*(15) = x

x = 14.5ft

Answer:

\(\frac{4a^{2} + 15b}{10ab}\)

Step-by-step explanation:

find the least common denominator for both fractions then combine them to find:

\(\frac{4a^{2} + 15b}{10ab}\)

Answer: It will be (B)

Step-by-step explanation:

Answer:

\(f(x) = 5x - 2 \\ \\ \)

B ) Replace f ( x ) with f' ( x )

Answer:

y=-2(×-1/2)

Step-by-step explanation:

...........

The correct answer is b. A normal probability distribution is a continuous probability distribution, which means that it can take on any value within a given range.

This type of distribution is often used to model real-world phenomena that are measured on a continuous scale, such as height or weight. Unlike discrete probability distributions, which have a finite number of possible outcomes, a continuous distribution has an infinite number of possible outcomes. It's important to note that while a normal distribution is continuous, not all continuous distributions are normal. A normal distribution has a specific bell-shaped curve that is defined by its mean and standard deviation, and it is often used in statistical analysis to make predictions about the likelihood of certain events occurring within a given population. In summary, a normal probability distribution is a type of continuous probability distribution that is often used to model real-world phenomena. While it has a specific shape and can be described by its mean and standard deviation, it is not always the best model for every situation.

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C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

Answer:

1. If you live in Manila(hypothesis) then you live in the Philippines ( conclusion)

2. If a triangle is a right triangle (hypothesis), then one of its interior angle is a 90-degree angle ( conclusion)

3. A square is not a triangle (conclusion)

4. An even number is divisible by 2. (conclusion)

5. The measure of an acute angle is less than 90. (conclusion)

Answer:

y-(-10)=0*(x-0)

Step-by-step explanation:

y-y₁=m(x-x₁)

m=0 (0,-10) x₁=0 , y₁=-10

y-(-10)=0*(x-0)

y+10=0

y=-10

Answer:

d = 2\(\sqrt{3}\)

Step-by-step explanation:

\(d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d= \sqrt{(3-9)^2+(6-2)^2} \\d= \sqrt{(-6)^2+(4)^2} \\d= \sqrt{(36)+(16)} \\d= \sqrt{52} \\d=2 \sqrt{13}\)