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3 years ago

1. Which of the following is the sale price for an item with an original price of $8.95 after it has been discounted 40%?

1 answer:

dsp733 years ago

8 0

Hey there!

1, 8.95*.4= 3.58 was take off. 8.95-3.58= 5.37
$5.37

2.<span>A change from 85 to 72 represents a negative change (decrease) of -15.294117647058824%</span>

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A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

4 0

3 years ago

Alice plants carrots in a rectangular garden bed. The garden bed has a width of 1.5 meters

mojhsa [17]

Answer:

1. L= A/W

2. 4m

Step-by-step explanation:

We can define this problem as a word problem relating to mensuration of flat shapes, a

rectangle

1. Let the length be L and the width be W

Given

Area A= 6m²

W= 1.5m

We know that the area of a rectangular shape is

Area = L x W

The expression for the length is

L= A/W

2. The solution for the length is

6=1.5L

L= 6/1.5= 4m

8 0

4 years ago

Read 2 more answers

Please help me I need the answer

VMariaS [17]

Check the picture below.

well, since the triangle is an isosceles, with twin sides and twin angles at the "base", let's check what the angle at R is, 15(7) - 31 = 74, and her twin sister at T is also 74, that means that the angle at S is 180 - 74 - 74 = 32.

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3 years ago

The expression below is the factorization of what trinomial?(5x + 4)(2x - 5)

Soloha48 [4]

Answer: 10x^2-17x-20

Step-by-step explanation:

8 0

4 years ago

What us the difference in the ares of a circle with diameter 4 m and a circle with diameter 6 m? Round your answer to the neares

enyata [817]

Let's calculate each area.
4 m:
We need to divide it by 2 to find the radius.
4÷2=2
Now let's put it in the formula.
2²π
4π=12.5663706≈13
6 m:
We need to divide it by 2 for the radius.
6÷2=3
Now put it in the formula.
3²π
9π=28.2743≈28
Now subtract 13 from 28.
28-13=15
So, the difference between their area is 15 m².

6 0

4 years ago