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3 years ago

Cavalieri's principle states that two solids with equal heights and base areas

Mathematics

1 answer:

azamat3 years ago

4 0

Cavalieri's principle states that two solids with equal heights and base areas have equal volumes is a TRUE statement.

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- 5 4 = 2x - 3 5x -5

Zinaida [17]

Answer:

x = 49/33

Hope this helps you! Even though there's no explanation... (I'm really bad at explaining, I'm just good at doing...)

3 0

3 years ago

Find the value of x to the nearest tenth!

sergij07 [2.7K]

Answer:

5.7

Step-by-step explanation:

sine cosine tangent

soh cah toa

sine = opposite/hypotenuse

so sin(35)= x/10

you can multiply 10 to both sides to get rid of the 10 denominator on the right leaving you with 10sin(35)=x

be sure your calculator is in degrees.

put that into a calculator leaving you with 5.7

5 0

3 years ago

Find an equation of the line that goes through the points (10,34) and (-1,10)

kotykmax [81]

Answer:

Given points are ( 10 ,34 ) and ( -1 , 10)

Step-by-step explanation:

The equation of line is given by 

first we can find slope (m) 

= (y2 - y1) / ( x2 - x1)

= 34-10/10+1

 =24/11

Now the equation is

y - y1 = m ( x - x1) 

y - 10 = 24/11 ( x +11)

11 ( y - 10 ) = 24 (x + 11)

11y - 110 = 24x + 264

24x + 264 +110-11y =0

24x - 11y + 374 = 0

which is the required equation 

3 0

3 years ago

2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.

vaieri [72.5K]

Answer:

Dimension of box:-

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

$500=x^2y$

Therefore, $y=\dfrac{500}{x^2}$

It is open box. The surface area of box, S .

$S=x^2+4xy$

Put $y=\dfrac{500}{x^2}$

$S(x)=x^2+\dfrac{2000}{x}$

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

$S'(x)=2x-\dfrac{2000}{x^2}$

For critical point, S'(x)=0

$2x-\dfrac{2000}{x^2}=0$

$x^3=1000$

$x=10$

Put x = 10 into $y=\dfrac{500}{x^2}$

y = 5

Double derivative of S(x)

$S''(x)=2+\dfrac{4000}{x^3}$ at x = 10

$S''(10) > 0$

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

7 0

4 years ago

Create and Solve an equation to find the unknown angle.

valentina_108 [34]

Answer:

Equation: 2x + 3x + 10 = 180

x = 34

Top angle = 68 degrees

Bottom angle = 112 degrees

Step-by-step explanation:

The two angles add to 180, so set them equal to 180.

2x + 3x + 10 = 180

5x + 10 = 180

- 10 - 10

5x = 170

/ 5 / 5

x = 34

Plug x into angles,

2(34) = 68

3(34) + 10 = 112

8 0

3 years ago

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