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2 years ago

Find the area of the SHADED region. Round to the nearest TENTH if necessary.

Mathematics

1 answer:

VLD [36.1K]2 years ago

5 0

Answer:

The area of the SHADED region is 21 cm.²

Step-by-step explanation:

The area of the SHADED region is the difference between the area of the entire figure and the area of the UNSHADED region

The shape of the UNSHADED region is a rectangle

The area of a rectangle, A = The length × The width

∴ The area of the UNSHADED region, A = 1 cm × 4 cm = 4 cm²

The area enclosed by the entire figure is in the shape of a square

The area of a square s similar to the area of the rectangle, but because a square has equal side length, the area of a square, A = Side length × Side length

Therefore, the area enclosed by the entire figure = 5 cm × 5 cm = 25 cm²

The area of the SHADED region = The area enclosed by the entire figure - The area of the UNSHADED rectangular figure inside

That is the area of the SHADED region = 25 cm² - 4 cm² = 21 cm².

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Deshawn makes jewelry from sea glass and sells it online. for every order he adds a 3.50 shipping fee to the price of the jewelr

Stells [14]

Answer:

This should be it

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y = x + 3.50.

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2 years ago

In this problem, y = c1ex + c2eâx is a two-parameter family of solutions of the second-order DE y'' â y = 0. Find a solution of

SCORPION-xisa [38]

Answer:

$y(t) = 2e^t -e^{-t}$

Step-by-step explanation:

Assuming this complete problem: "In this problem,

y = c1ex + c2e−x

is a two-parameter family of solutions of the second-order DE

y'' − y = 0.

Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.

y(0) = 1, y'(0)= 3"

Solution to the problem

For this case we have a homogenous, linear differential equation with order 2, and with the general form:

$ay'' +by' +cy=0$

Where $a =1, b=0, c=-1$

And we can rewrite the differential equation in terms $y = e^{rt}$ like this:

$[e^{rt}]'' -e^{rt}=0$

And applying the second derivate we got:

$r^2 e^{rt} -e^{rt}=0$

We can take common factor $e^{rt}$ and we got:

$e^{rt} (r^2-1) =0$

And for this case the two only possibel solutions are $r=1, r=-1$

And the general solution for this case is given by:

$y = c_1 e^{r_1 t} + c_2 e^{r_2 t}$

Replacing the roots that we found we got:

$y = c_1 e^{t} +c_2 e^{-t}$

Now we can find the derivates for this last espression

$y' = c_1 e^t -c_2 e^{-t}$

$y'' = c_1 e^t +c_2 e^{-t}$

From the initial conditions we have this:

$y(0)=1 =c_1 e^{0} +c_2 e^{-0}= c_1 +c_2$ (1)

$y'(0) =3= c_1 e^{0} -c_2e^{-0}= c_1 -c_2$ (2)

If we add equations (1) and (2) we got:

$4 = 2c_1 , c_1 = 2$

And solving for $c_2$ we got:

$c_2=3-c_1= 3-2 = 1$

So then our general solution is given by:

$y(t) = 2e^t -e^{-t}$

8 0

2 years ago

How many 8-inch square tiles are needed to cover a rectangle floor that is 10 ft. long and 8 ft. wide?

olganol [36]

Answer:

180 tiles

Step-by-step explanation:

It's easiest to work with only one unit for length and one unit for area. We will work with inches and square inches, and we will convert feet to inches.

An 8-inch square tile is a tile shaped like a square whose side measures 8 inches.

area of square = side^2

area of 1 tile = (8 in.)^2 = 64 in.^2

One 8-inch, square tile has an area of 64 sq in.

Now we need to find the area of the floor in square inches.

1 ft = 12 in.

We multiply each dimension in ft by 12 to find inches.

10 ft = 10 * 12 in. = 120 in.

8 ft = 8 * 12 in. = 96 in.

Now we find the area of the rectangular floor.

area of rectangle = length * width

area of rectangle = 120 in. * 96 in.

area of rectangle = 11,520 sq in.

The rectangular floor has an area of 11,520 sq in.

Each tile has an area of 64 sq in.

To see how many tiles are needed, we divide the area of the floor by the area of one tile.

number of tiles = (11,520 sq in.)/(64 sq in.) = 180

Answer: 180 tiles

3 0

2 years ago

What’s the answer to Log₅4

Dmitry [639]

The answer to this is 625

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2 years ago

use the drawing below to answer the questions that follow. what scale factor (as a decimal) was used to create the larger rectan

Oksana_A [137]

Answer:

A) 3.5

B) 15cm

Step-by-step explanation:

Part A:

length of rec2/length of rec1 = 21/6 = 3.5

Part B:

breadth of rec2/scale = 52.5/3.5 = 15cm

7 0

2 years ago