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3 years ago

The height of a cone shaped statue is 9 feet and the diameter is 12 feet .what is the approximate volume of the statue?

Mathematics

2 answers:

Eddi Din [679]3 years ago

8 0

Answer:the answer is 339.12

Step-by-step explanation:

i took the test and i got this one wrong because people got it wrong

dalvyx [7]3 years ago

4 0

Answer:

113.04

Step-by-step explanation:

6*6=36

36*3.14=113.04

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Cos^2 x+4sin^2 x/2=1

lana [24]

$Let\ \dfrac{x}{2}=a,\ therefore\ x=2a.\\\\\cos^2x+4\sin^2\dfrac{x}{2}=\cos^22a+4\sin^2a\\\\\text{use}\ \cos2x=\sin^2x-\cos^2x\\\\=(\sin^2a-\cos^2a)^2+4\sin^2a\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(\sin^2a)^2-2(\sin^2a)(\cos^2a)+(\cos^2a)^2+4\sin^2a\\\\=\sin^4a-2\sin^2a\cos^2a+\cos^4a+4\sin^2a\\\\=\underbrace{\sin^4a+2\sin^2a\cos^2a+\cos^4a}_{(*)}-4\sin^2a\cos^2a+4\sin^2a\\\\\text{use}\ (*)\qquad(a+b)^2=a^2+2ab+b^2$

$=\underbrace{(\sin^2a)^2+2\sin^2a\cos^2a+(\cos^2a)^2}_{(*)}-4\sin^2a(\cos^2a-1)\\\\=(\sin^2a+\cos^2a)^2-4\sin^2a(\cos^2a-1)\\\\\text{use}\ \sin^2a+\cos^2a=1\to\sin^2a=\cos^2a-1\\\\=1^2-4\sin^2a(\sin^2a)=1-4\sin^4a=1-(2\sin^2a)^2$

$\cos^22a+4\sin^2a=1\\\\1-(2\sin^2a)^2=1\qquad\text{subtract 1 from both sides}\\\\-(2\sin^2a)^2=0\to2\sin^2a=0\qquad\text{divide both sides by 2}\\\\\sin^2a=0\to\sin a=0\\\\a=k\pi\ for\ k\in\mathbb{Z}\\\\\dfrac{x}{2}=k\pi\qquad\text{multiply both sides by 2}\\\\\boxed{x=2k\pi\ for\ k\in\mathbb{Z}}$

6 0

3 years ago

What’s the area of this figure?

11Alexandr11 [23.1K]

Answer:

13 sq cm.

Step-by-step explanation:

To find the area of this irregular figure, we will need to find the areas of a rectangle and triangle within this figure.

To find the area of the rectangle, we can simply do:

1 × 4= 4 sq cm.

Now, this is where it gets a little trickier. To find the area of the triangle, we will first need to determine the base and height.

We can see from the diagram that to find the base, we need to subtract:

7-4= 3 cm. This is the base of ONLY the triangle.

To find the height, we will need to do:

5+1= 6 cm. This is the total height of the entirety of the triangle.

We can now use the Triangle Area formula: $\frac{1}{2}$ (bh), to calculate the area of the triangle.

$\frac{1}{2}$ (6*3)= 9 sq cm.

Finally, add the areas of the rectangle and triangle together, giving you:

9+4= 13 sq cm.

3 0

3 years ago

Find the value of x.

Karolina [17]

Answer:

x=21

Step-by-step explanation:

Following the vertical angles, we can assume that the equation that has x and 87 are equal to each other. From then, you set them equal to each other and solve for x.

87=4x+3

84=4x subtract 3 from both sides

21=x divide by 4 to get the x alone on both sides

6 0

2 years ago

Mr. Bradley purchased 20 trays of flowers. Each tray had 3 dozen flowers. Mr. Bradley's total for all the flowers was 273.60. Al

aev [14]

Answer: Each flower costs $0.38.

Step-by-step explanation:

1 dozen = 12 units

Flowers in each tray = 3 dozen = 3 x 12 = 36

Flowers in 20 trays = 20 x 36 = 720

Price of 20 trays = $ 273.60

Price of each flower = (Price of 20 trays ) ÷ (Flowers in 20 trays)

= 273.60 ÷ 720

= $ 0.38

Hence, each flower costs $0.38.

7 0

3 years ago

PLEASEEEE HELPPPPPP ASAPPPPP

Burka [1]

Answer:

7.07

Step-by-step explanation:

Angle M is 63 degrees because all 3 angles must add to 180.

Now use the law of sines:

sin(90)/x = sin(63)/6.3

Cross multiply: 6.3 sin (90) = x sin (63)

Divide by sides by sin (63): (6.3 sin (90))/sin (63) = x

Use a calculator: 7.07

5 0

3 years ago