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3 years ago

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A rancher has 300 feet of fencing to enclose a pasture bordered on one side by a river. the river side of the pasture needs no f

ence. find the dimensions of the pasture that will produce a pasture with a maximum area.

1 answer:

Mashcka [7]3 years ago

8 0

I think your best answer is a pasture that is 75 feet by 150 feet, which will give you 11,250 sq ft of pasture

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What percent is equivalent to 24/50 24% 48% 50% 52%

gizmo_the_mogwai [7]

Answer:

48%

Step-by-step explanation:

(24/50)2

= 48/100

= 48%

4 0

3 years ago

The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.

andrezito [222]

Answer:

Given the equation: $3x^2+10x+c =0$

A quadratic equation is in the form: $ax^2+bx+c = 0$ where a, b ,c are the coefficient and a≠0 then the solution is given by :

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

Simplify:

$x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}$

Also, it is given that the difference of two roots of the given equation is $4\frac{2}{3} = \frac{14}{3}$

i.e,

$x_1 -x_2 = \frac{14}{3}$

Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

then;

$\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}$

simplify:

$\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}$

or

$\sqrt{100- 12c} = 14$

Squaring both sides we get;

$100-12c = 196$

Subtract 100 from both sides, we get

$100-12c -100= 196-100$

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve $x_1 , x_2$

$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

or

$x_1 = \frac{-10 + \sqrt{100- 96}}{6}$ or

$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

Now, to solve for $x_2$ ;

$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

or

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

Simplify:

$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

3 0

3 years ago

A student is using a spinner with four equal sections numbered 1 through 4. He also tosses a fair coin. What is the correct samp

nignag [31]

Answer:

C. {(1,H), (2,H), (3,H), (4,H), (1,T), (2,T), (3,T), (4,T)}

8 0

3 years ago

Read 2 more answers

22/25 is what percentage of that number

Romashka [77]

Answer:

As a percent, that is 88%.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Factorize the following Equation and show your work <br><br>x^{2} - 10x +25

Irina18 [472]

Answer:

(x-5)(x-5)

Step-by-step explanation:

x^2 factors into two binomials, the square root of 25 is 5 (-5*-5=25), -5+-5=-10, think of the big and the little equal the middle to help deal with these types of problems. hope I have helped.

8 0

2 years ago