My last question

A cone is cut into a cube as shown below. If the cone has a diameter of

Butoxors [25]

Answer:

184.43in².

Step-by-step explanation:

Total surface area of the solid = volume of the cube - the volume of the cone

For the CUBE;

Volume of the cube = L³ where L is the length of one side of the cube.

Since a cone of diameter of 6in is cut into a cube, then the length of the cube will be 6in.

Volume of the cube = 6³ = 216in³

For the CONE;

Volume of the cone = 1/3 πr²h

r is the radius of the cone = diameter/2

r = 6/2 = 3in

slant height l = 4.5in

the height h of the cone will be derived using the Pythagoras theorem.

l² = h²+r²

4.5² = h²+3²

h² = 4.5²-3²

h² = 11.25

h=√11.25

h = 3.35in

Volume of the cone = 1/3 × π × 3²× 3.35

= 31.57in³

Total surface area of the solid = 216in³-31.57in³

= 184.43in²

3 0

3 years ago

Choose the point slope form of the equation below that represents the line that passes through the points (-3, 2) and (2, 1)

mihalych1998 [28]

Answer:

$\large\boxed{y-1=-\dfrac{1}{5}(x-2)}$

Step-by-step explanation:

The point-slope form of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-3, 2) and (2, 1). Substitute:

$m=\dfrac{1-2}{2-(-3)}=\dfrac{-1}{5}=-\dfrac{1}{5}$

$y-1=-\dfrac{1}{5}(x-2)$

4 0

3 years ago

Helpp! i will mark you as brainliest:) <br> &’ please show your work<br> (Easy)

Alborosie

Answer:

1. is a supplementary angle so it adds up to 180 so 180-145=x and x=35

2. is also a supplementary angle so 180-130=x and x =50

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A rectangular garden of area 208 square feet is to be surrounded on three sides by a brick wall costing $ 8 per foot and on one

vova2212 [387]

Answer:

Therefore the dimensions of the garden is 16 feet by 13 feet.

Step-by-step explanation:

Let the length of the garden be x and the width of the garden be y.

Given that the area of the rectangular garden is 208 square feet.

Therefore,

xy =208

$\Rightarrow y = \frac{208}{x}$

Again given that,

The garden is to be surrounded on three sides by a brick wall costing $ 8 per feet and the remaining sides by a fence costing $5 per feet.

The perimeter of the rectangle is = 2(length+ breadth)

= 2(x+y)

=2x+2y

The total cost of fence

$C= [ (2x\times 8)+(y\times 8)+(y\times 5)]$

= (16x+ 8y +5y)

$=16x+13y$

$=16x+\frac{13\times 208}{x}$

$=16x +\frac{2704}{x}$

To find the maximum or minimum point, we need to find out $\frac{dC}{dx}$ and set $\frac{dC}{dx}$ =0.

$\frac{dC}{dx}=16 -\frac{2704}{x^2}$

Then

$16 -\frac{2704}{x^2}=0$

$\Rightarrow \frac{2704}{x^2}=16$

$\Rightarrow x^2 =\frac{2704}{16}$

$\Rightarrow x=\pm \sqrt{169}$

$\Rightarrow x=\pm 13$

Again $\frac{d^2C}{dx}= \frac {8112}{x^3}$

$\therefore\left| \frac{d^2C}{dx}\right |_{x=13}= \frac {8112}{13^3}>0$

Therefore at x= 13 , the cost is minimum.

Therefore x = 13 feet.

The other side of the garden is $=\frac{208}{13}$ feet = 16 feet.

Therefore the dimensions of the garden is 16 feet by 13 feet.

4 0

3 years ago

Caroline won $205000 in a lottery. After paying $96000 in taxes, she placed the remaining amount in a savings account at a 2% in

natka813 [3]

Answer: $1090

Step-by-step explanation:

Since Caroline won $205000 in a lottery and then paid $96000 in taxes, the remaining amount will be:

= $205000 - $96000

= $109000

The interest that the account will earn after just 6 months will be:

Interest = PRT

= 109000 × 2% × 6/12

= 109000 × 0.02 × 0.5

= $1090

6 0

3 years ago