A rectangular prism has dimensions 2 feet by 3 by h feet.

Find the lateral area and the surface area of the right cone. Round your nearest answers to the nearest hundredth

S_A_V [24]

Step-by-step explanation:

Given that,

The height of the cone, h = 24 cm

The radius of the cone, r = 10 cm

The slant height of the cone is :

$l=\sqrt{h^2+r^2} \\\\l=\sqrt{24^2+10^2} \\\\l=26\ cm$

The lateral area of the cone is given by :

$A=\pi rl\\\\=3.14\times 10\times 26\\\\=816.4\ cm^2\approx 816\ cm^2$

The surface area of the cone is given by :

$A=2\pi rh\\\\=2\times 3.14\times 10\times 24\\\\=1507.2 \approx 1507\ cm^2$

5 0

2 years ago

The regular price of a baseball hat is 14.45$. If Carlos buys the baseball hat on sale for 20% off the regular price, how much c

otez555 [7]

Answer:

$8.44

Step-by-step explanation:

To find the 20%

x/14.45=20/100

14.45×20=289

289÷100=2.89

We then subtract 2.89 from 14.45 to get the selling price.

14.45-2.89=11.56

$11.56 is the price of the baseball hat on sale.

To get the change

20-11.56=8.44

$8.44 is the change

I hope this helped! :)

5 0

2 years ago

An open metal tank of square base has a volume of 123 m^3

snow_lady [41]

Answer:

a) h = 123/x^2

b) S = x^2 +492/x

c) x ≈ 6.27

d) S'' = 6; area is a minimum (Y)

e) Amin ≈ 117.78 m²

Step-by-step explanation:

a) The volume is given by ...

V = Bh

where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:

123 = x^2·h

h = 123/x^2

__

b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

$S=x^2+Ph=x^2+(4x)\dfrac{123}{x^2}\\\\S=x^2+\dfrac{492}{x}$

__

c) The derivative of the area with respect to x is ...

$S'=2x-\dfrac{492}{x^2}$

When this is zero, area is at an extreme.

$0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583$

__

d) The second derivative is ...

$S''=2+\dfrac{2\cdot 492}{x^3}=2+\dfrac{2\cdot 492}{246}=6$

This is positive, so the value of x found represents a minimum of the area function.

__

e) The minimum area is ...

$S=x^2+\dfrac{2\cdot 246}{x}=(246^{\frac{1}{3}})^2+2\dfrac{246}{246^{\frac{1}{3}}}=3\cdot 246^{\frac{2}{3}}\approx 117.78$

The minimum area of metal used is about 117.78 m².

3 0

2 years ago

The total cost (c) in dollars of renting a car for n days is given by the inequality LaTeX: c\ge125+50nc ≥ 125 + 50 n. What is t

zysi [14]

Answer:

Step-by-step explanation:

Given the inequality expression of the total cost (c) in dollars of renting a car for n days as c ≥ 125 + 50n

To get the maximum number of days for which a car could be rented if the total cost was $425, substitute c = 425 into the expression and find n

425 ≥ 125 + 50n

Subtract 125 from both sides

425 - 125 ≥ 125 + 50n - 125

300≥ 50n

Divide both sides by 50

300/50≥50n/50

6 ≥n

Rearrange

n≤6

Hence the maximum number of days for which a car could be rented if the total cost was $425 is 6days

5 0

2 years ago

Help please! 50 points! Troll answers WILL be reported

natka813 [3]

Answer:

Think its B. but if not it should be E.

Step-by-step explanation:

4 0

2 years ago