I need to know how to do this 14+(64/8)-11

A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric

mamaluj [8]

Answer:

The largest area is 125000 m²

The dimensions of the farmland are 250 m and 500 m

Step-by-step explanation:

* Lets pick the information from the problem

- The farmland is shaped a rectangle

- The farmland will be bounded on one side by a river

- The other three sides are bounded by a single-strand electric fence

- The length of wire is 1000 m

- Lets consider the width of the rectangle is x and the length is y

- The side which will be bounded by the river is y

∴ The perimeter of the farmland which will be bounded by the electric

fence = x + x + y = 2x + y

- We will use the wire to fence the farmland

∵ The length of the wire is 1000 m

∵ The perimeter of the farmland is equal to the length of the wire

∴ 2x + y = 1000

- Lets find y in term of x

∵ 2x + y = 1000 ⇒ subtract 2x from both sides

∴ y = 1000 - 2x

- Now lets find the area can enclose by the wire

∵ The area of the rectangle = length × width

∵ The width of the farmland is x and its length is y

∴ The area of the farmland (A) = x × y = xy ⇒ (2)

- Use equation (1) to substitute the value of y in equation (2)

∴ A = x (1000 - 2x) ⇒ simplify

∴ A = 1000 x - 2 x²

- To find the maximum area we will differentiate A with respect to x

and equate the answer by zero to find the value of x which will make

the enclosed area largest

* Lets revise the rule of differentiation

- If y = ax^n, then dy/dx = a(n) x^(n-1)

- If y = ax, then dy/dx = a

- If y = a, then dy/dx = 0 , where a is a constant

∵ A = 1000 x - 2 x² ⇒ (3)

- Differentiate A with respect to x using the rules above

∴ dA/dx = 1000 - 2(2) x^(2-1)

∴ dA/dx = 1000 - 4x

- Put dA/dx = 0 to find the value of x

∵ 1000 - 4x = 0 ⇒ add 4x to both sides

∴ 1000 = 4x ⇒ divide both sides by 4

∴ 250 = x

∴ The value of x is 250

- Lets substitute this value in equation 3 to find the largest area

∵ A = 1000 x - 2 x²

∴ A = 1000 (250) - 2(250)² = 125000 m²

* The largest area is 125000 m²

∵ The width of the farmland is x

∵ x = 250

∴ The width of the farmland = 250 m

- Substitute the value of x in the equation (1) to find y

∵ y = 1000 - 2x

∵ x = 250

∴ y = 1000 - 2(250) = 1000 - 500 = 500

∵ The length of the farm lend is y

∴ The length of the farm land = 500 m

* The dimensions of the farmland are 250 m and 500 m

6 0

3 years ago

Determine if the given function can be extended to a continuous function at xequals0. If so, approximate the extended function

Akimi4 [234]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The correct option is A

Step-by-step explanation:

Now from the question we are given the function

$f(x) = \frac{10^{2 x} -4}{x}$

Now as $\lim_{x \to 0} [f(x) ] = \frac{10^{2*0} -4 }{0}$

=> $\lim_{x \to 0} [f(x) ] = - \infty$

This implies that as $x\to 0$ the function $f(x) \to -\infty$ which means that at x = 0 the function is not continuous

3 0

4 years ago

Find the lengths of the sides of the rectangle if it is known that one of them is 14cm bigger than the other, and the diagonal o

slega [8]

Let's call the smaller side $s$ . This means that the other side of the rectangle is $s + 14$ .

In this problem, we are trying to find the lengths of the sides. The problem gives us someinformation about the sides, but that's really it. However, the problem also let's us know that the diagonal of the rectangle (the line connecting opposite corners of the rectangle) is 34 cm long.

This fact is very important, because we can actually make a triangle, with the smaller side, bigger side, and the diagonal of the rectangle. Additionally, since we are working with rectangles, we know that the sides form a right angle. Since we are constructing a triangle with the sides as the legs, we know that we are going to be constructing a right triangle, which means that we can work with Pythagorean's Theorem.

Remember that Pythaogrean's Theorem is:

$a^2 + b^2 = c^2$

$a$ and $b$ are the lengths of the legs of the triangle
$c$ is the length of the hypotenuse

Applying the Pythagorean Theorem to this problem, we get:

$s^2 + (s + 14)^2 = 34^2$

Let's simplify and solve for $s$ :

$s^2 + (s + 14)^2 = 34^2$

Set up

$s^2 + (s^2 + 28s + 196) = 1156$

Simplify left hand side and evalutate $34^2$

$2s^2 + 28s -962 = 0$

Subtract 1156 from both sides of the equation and combine like terms

$(s + 30)(s - 16) = 0$

Factor

$s = -30, 16$

Apply the Zero Product Property to solve for $s$

$s = 16$

$s = -30$ is an extraneous solution because you can't have a negative side length

We have now found that the smaller side is 16 cm long. Since the larger side is 14 cm longer, it can be found as shown:

$16 \,\textrm{cm} + 14 \,\textrm{cm} = 30 \,\textrm{cm}$

The sides are length 16 cm and 30 cm.

4 0

3 years ago

Given a triangle with vertices A , B and C list all possible correspondences of the triangle with itself.

Mademuasel [1]

Answer:

Step-by-step explanation:

Yes

7 0

3 years ago

Find −5 5/6÷(−4 9/10). Write your answer as a mixed number in simplest form.

uranmaximum [27]

Answer: $1\dfrac{4}{21}$ .

Step-by-step explanation:

Given problem : $\left(-5\dfrac{5}{6}\right)\div\left(-4\dfrac{9}{10}\right)$

First we convert mixed fraction into improper fractions as

$-5\dfrac{5}{6}=-\dfrac{5\times6+5}{6}=-\dfrac{30+5}{6}=-\dfrac{35}{6}\\-4\dfrac{9}{10}=-\dfrac{10\times4+9}{10}=-\dfrac{40+9}{10}=-\dfrac{49}{10}$

Now , plug these values in the given expression , we get

$\left(-5\dfrac{5}{6}\right)\div\left(-4\dfrac{9}{10}\right)=-\dfrac{35}{6}\div\left(-\dfrac{49}{10}\right)\\\\=\dfrac{-35}{6}\times\dfrac{-10}{49}\ \ \ [\text{By Property of fraction}]\\\\=\dfrac{350}{294}\\\\=\dfrac{25}{21}=1\dfrac{4}{21}$

Hence, the answer is $1\dfrac{4}{21}$ .

8 0

3 years ago