MATHEMATICS COLLEGE

1. Trapezoid BEAR has a height of 8.5 centimeters and parallel bases that measure 6.5 centimeters and 11.5 centimeters. To the nearest square centimeter, find the area of the trapezoid.Area of trapezoid BEAR = _______ square centimeters

2. Regular pentagon PENTA has side lengths that are 9 meters long. To the nearest square meter, find the area of the pentagon.

Area of pentagon PENTA = _square centimeter

Answers

Answer 1

Answer:

Given

1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.

2) Regular pentagon PENTA with side lengths 9 m

Find

The area of each figure, rounded to the nearest integer

Solution

1) The area of a trapezoid is given by

... A = (1/2)(b1 +b2)h

... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77

The area of BEAR is about 77 cm².

2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...

... A = (1/2)ap

... A = (1/2)(s/(2tan(180°/n)))(ns)

... A = (n/4)s²/tan(180°/n)

We have a polygon with s=9 and n=5, so its area is

... A = (5/4)·9²/tan(36°) ≈ 139.36

The area of PENTA is about 139 m².

Answer 2

Answer:

Answer:139 cm squared

The area of a trapezoid is given by

... A = (1/2)(b1 +b2)h

... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77

The area of BEAR is about 77 cm².

The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...

... A = (1/2)ap

... A = (1/2)(s/(2tan(180°/n)))(ns)

... A = (n/4)s²/tan(180°/n)

We have a polygon with s=9 and n=5, so its area is

... A = (5/4)·9²/tan(36°) ≈ 139.36

The area of PENTA is about 139 m².

Related Questions

When you roll a pair of dice, there are several outcomes, as shown below:When rolling the dice, the outcome is expressed as a sum of the two dice. Forexample, if after you rolled the dice, and one die was a 3 and the other was a 4, youwill have rolled a 7.Select all of the TRUE statements below. There may be more than one.The probability of rolling the same digit with each die is 1/4.The odds in favour of rolling a 10 is 1:13.The odds against rolling a number less than 7 is 7:5.
What are the zeros of the quadratic function f (x) = 2x^2 -10x-3?
Solve 3sqrt(x) = 8/(sqrt(9x - 32)) + sqrt(9x - 32)
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A soup can has a height of 4 inches and a radius of 2.5 inches. What's the area ofpaper needed to cover the lateral face of one soup can with a label? OA) 62.8 in? B) 15.7 in? C) 78.5 in2 125.7 in2

A library contains only paperback and hardback books. If the ratio of paperback books to the total number of books is 3 to 5, which statement must be true? The ratio of paperback books to hardback books is 2 to 3. The ratio of paperback books to hardback books is 2 to 3. The ratio of paperback books to hardback books is 3 to 2. The ratio of paperback books to hardback books is 3 to 2. There are exactly 2 paperback books in the library. There are exactly 2 paperback books in the library. There are exactly 8 hardback books in the library. There are exactly 8 hardback books in the library.

Answers

Answer:

A library contains only paperback and hardback books. If the ratio of paperback books to the total number of books is 3 to 5, the true statement is:

The ratio of paperback books to hardback books is 3 to 2.

Step-by-step explanation:

The number of books in the library = 5

The number of paperback books in the library = 3

Therefore, the number of hardback books in the library = 2 (5 - 3)

Then, the relationship between the paperback books and the hardback books in the library can be expressed as a ratio of 3:2. This still gives the sum of the ratios as 5, which is the total number of books in the library, including paperback and hardback books.

Final answer:

The correct statement is that the ratio of paperback to hardback books is 3:2. The ratios provided do not indicate the exact quantity of books in the library.

Explanation:

The ratio of paperbacks to the total number of books is 3:5. This means that for every 5 books, 3 are paperbacks and therefore, the remaining 2 must be hardbacks. Hence the ratio of paperback to hardback books is actually 3:2, not 2:3.

Note that the ratios given do not indicate the exact number of books. Therefore, we cannot confidently say that there are exactly 2 paperback books or exactly 8 hardback books in the library.

Learn more about Ratios here:

brainly.com/question/32531170

#SPJ3

Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither. f(x) = x + 4 if x < 0 ex if 0 ≤ x ≤ 1 8 − x if x > 1 x = (smaller value) continuous from the right continuous from the left neither

Answers

Using continuity concepts, it is found that the function is left-continuous at x = 1.

-------------------------------

A function f(x) is said to be continuous at x = a if:

$\lim_(x \rightarrow a^(-)) f(x) = \lim_(x \rightarrow a^(+)) f(x) = f(a)$

If only $\lim_(x \rightarrow a^(-)) f(x) = f(a)$ , the function is left-continuous.

If only $\lim_(x \rightarrow a^(+)) f(x) = f(a)$ , the function is right-continuous.

-------------------------------

The piece-wise definition of the function $f(x)$ is:

$x + 4, x < 0$

$x, 0 \leq x \leq 1$

$8 - x, x > 1$

We have to check the continuity at the points in which the definitions change, that is, x = 0 and x = 1.

-------------------------------

At x = 0:

The definition at 0 is $f(0) = 0$
Approaching x = 0 from the left, we have values less than 0, thus:

$\lim_(x \rightarrow 0^(-)) f(x) = \lim_(x \rightarrow 0) x + 4 = 0 + 4 = 0$

Approaching x = 0 from the right, we have values greater than 0, thus:

$\lim_(x \rightarrow 0^(+)) f(x) = \lim_(x \rightarrow 0) x = 0$

Since the limits are equal, and also equal to the definition at the point, the function is continuous at x = 0.

-------------------------------

At x = 1:

The definition at 1 is $f(1) = 1$

Approaching x = 1 from the left, we have values less than 1, thus:

$\lim_(x \rightarrow 1^(-)) f(x) = \lim_(x \rightarrow 1) x = 1$

Approaching x = 1 from the right, we have values greater than 1, thus:

$\lim_(x \rightarrow 1^(+)) f(x) = \lim_(x \rightarrow 1) 8 - x = 8 - 1 = 7$

To the right, the limit is different, thus, the function is only left continuous at x = 1.

A similar problem is given at brainly.com/question/21447009

Answer:

the function is continuous from the left at x=1 and continuous from the right at x=0

Step-by-step explanation:

a function is continuous from the right , when

when x→a⁺ lim f(x)=f(a)

and from the left when

when x→a⁻ lim f(x)=f(a)

then since the functions presented are continuous , we have to look for discontinuities only when the functions change

for x=0

when x→0⁺ lim f(x)=lim e^x = e^0 = 1

when x→0⁻ lim f(x)=lim (x+4) = (0+4) = 4

then since f(0) = e^0=1 , the function is continuous from the right at x=0

for x=1

when x→1⁺ lim f(x)=lim (8-x) = (8-0) = 8

when x→1⁻ lim f(x)=lim e^x = e^1 = e

then since f(1) = e^1=e , the function is continuous from the left at x=1

What is 221, 000, 000, 000, 000, 000, 000, expressed in scientific notation

Answers

Answer:

2.21 × 10^17

stepbystepexplanation:

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. (Let x, y, and z be the dimensions of the aquarium. Enter your answer in terms of V.)

Answers

Answer:

The dimensions of the aquarium that minimize the cost of the materials:

$x=y=\sqrt[3]{(2V)/(5)}\nz=\sqrt[3]{(25V)/(4)}$

Step-by-step explanation:

Let x, y and z be the dimensions of aquarium .

Surface area of an aquarium = xy+2yz+2xz

Volume of aquarium V= $Length * Breadth * Height=xyz$ ----A

We are given that slate costs five times as much (per unit area) as glass

So, Cost function : C=5xy+2yz+2xz

Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.

$\nabla C =\lambda \nabla V$

$((\partial C)/(\partial x),(\partial C)/(\partial y),(\partial C)/(\partial z))= \lambda ((\partial V)/(\partial x),(\partial V)/(\partial y),(\partial V)/(\partial z))$

$(5y+2z,5x+2z,2y+2x)=\lambda(yz,xz,xy)$

So,

$5y+2z=\lambda yz$ ----1

$5x+2z=\lambda xz$ -----2

$2y+2x=\lambda xy$ ----3

Multiply 1 ,2 and 3 by x,y and z respectively.

$5xy+2xz=\lambda xyz$ ----4

$5xy+2yz=\lambda xyz$ -----5

$2yz+2xz=\lambda xyz$ ----6

Now equate 4 and 5

5xy+2xz=5xy+2yz

x=y

Substitute y=x in 5 and 6 and equate them

$5x(x)+2(x)z=2(x)z+2xz\n5x^2=2xz\n5x=2z\n(5)/(2)x=z$

Substitute the values in A

$V = xyz = x * x * (5)/(2)xV=(5)/(2)x^3\n\sqrt[3]{(2)/(5)V}=x\nx=y=\sqrt[3]{(2)/(5)V}\nz=(5)/(2)x=(5)/(2)(\sqrt[3]{(2)/(5)})=\sqrt[3]{(25V)/(4)}$

Hence,

The dimensions of the aquarium that minimize the cost of the materials:

$x=y=\sqrt[3]{(2V)/(5)}\nz=\sqrt[3]{(25V)/(4)}$

Hey can you please help me posted picture of question

Answers

For this case we have the following equation:
y = 4 (x-2) ^ 2-1
Rewriting we have:
y = 4 (x ^ 2-4x + 4) ^ 2-1
Multiplying the common factor 2 we have:
y = 4x ^ 2-16x + 16-1
Adding the constant term we have:
y = 4x ^ 2-16x + 15
Answer:
y = 4x ^ 2-16x + 15
option D

the answer is D y=4x^2-16x+15

What is the average rate of change for this function for the interval from x= 2
to x = 4?

Answers

Answer:

Step-by-step explanation:

hn hn

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