Th polynomial x3+8 is equal to

A rectangular parcel of land has an area of 3,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than o

Kazeer [188]

Answer:

40 ft × 75 ft

Step-by-step explanation:

Let x be the one side ( in feet ) of the rectangular parcel,

So, the diagonal between opposite corners = ( x + 10 ) feet,

Let y be the other side of the rectangle ( adjacent to side x ),

The area of the rectangle,

A = x × y,

According to the question,

A = 3000 square ft,

$\implies xy = 3000\implies y=\frac{3000}{x}$

∵ In a rectangle,

$D^2=a^2+b^2$

Where, a and b are the adjacent side of the rectangle and D is the diagonal,

$(x+10)^2 = x^2 + y^2$

$(x+10)^2 = x^2 + \frac{9000000}{x^2}$

$x^2(x+10)^2 = x^4 + 9000000$

$x^2(x^2+100+20x) = x^4 + 9000000$

$x^4+100x^2 + 20x^3 = x^4 + 9000000$

$20x^3 + 100x^2 - 9000000=0$

$x^3 + 5x^2 - 450000 = 0$

By graphing the equation,

We found that,

The only real zeros of the equation is at x = 75,

Hence, the one side of the rectangle = 75 ft,

And, second side = $\frac{3000}{75}$ = 40 ft

Hence, the dimension of the land is 40 ft × 75 ft

3 0

3 years ago

Read 2 more answers

Nelly owns farm land that has an area of 4.2 × 102 acres. Each year, the farm produces 6.72 × 104 bushels of corn. What is the a

juin [17]

The average amount of corn produced per acre represented in scientific notation can be found using the below formula:

$The \;average\; amount\; of\; corn\; per\; acre=\frac{Bushels \; of\; corn\; produced\; in\; farm}{Area\; of\; farm\; in\; acres}$

We are given:

$Area \; of\; FARM\; land= 4.2 \times 10^2 \; acres\\ \\ Amount \; of\; corn\; produced=6.72\; \times \; 10^4 \; bushels$

Substituting the above information in the formula, we get...

$The \; Average\; amount\; of\; corn=\frac{6.72 \times 10^4}{4.2 \times 10^2} \\ \\ \frac{6.72}{4.2} \times \frac{10^4}{10^2}\; =\; 1.6 \times 10^{4-2}\; =\; 1.6 \times 10^2\\ \\$

Conclusion:

$The \; Average \; amount\; of \; corn \; is\; 1.6 \times 10^2 \; Bushes\; per\; corn$

The average amount of corn produced per acre represented in scientific notation is option B) $1.6 \times 10^2$ bushels per acre

5 0

3 years ago

Read 2 more answers

Translate this sentence into an equation.

aliya0001 [1]

Answer:

20+h = 46

Step-by-step explanation:

it doesn't ask to solve it so that's the answer

7 0

2 years ago

Read 2 more answers

Need help on this math problem!!!

Colt1911 [192]

Answer:

$(fof^{-1})(x)=x$

Step-by-step explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤ $-\frac{8}{6}$ ]

Another function is the inverse of f(x),

$f^{-1}(x)=-\frac{\sqrt{x}+8}{6}$

Now composite function of these functions will be,

$(fof^{-1})(x)=f[f^{-1}(x)]$

= $[-6(\frac{\sqrt{x}+8}{6})-8]^{2}$

= $[-\sqrt{x}+8-8]^2$

= $(-\sqrt{x})^2$

= x

Therefore, $(fof^{-1})(x)=x$

4 0

3 years ago

34 + 4 ⋅ 5 = ____. (Input whole numbers only.)

muminat

Answer:

54

4 x 5 = 20

20 + 34 = 54

6 0

3 years ago

Read 2 more answers