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2 years ago

The sum lf two numbers is 10. The difference between the two numbers is 4: what is the smaller numerical?

Mathematics

2 answers:

FrozenT [24]2 years ago

6 0

Answer:

Step-by-step explanation:

The two numbers are 3 and 7, and 3 is the smaller one

spayn [35]2 years ago

5 0

Step-by-step explanation:

x, y are the 2 numbers.

x + y = 10

y - x = 4

that gives us

y = x + 4

and we use that in the first equation :

x + x + 4 = 10

2x = 6

x = 3

y = x + 4 = 3 + 4 = 7

so, yes, the smaller number is 3.

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A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the bar

Luba_88 [7]

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

In this question we shall use the first and second derivative tests to determine the optimal dimensions of a rectangular plot of land. The perimeter ( $p$ ), in feet, and the area of the rectangular plot ( $A$ ), in square feet, of land are described below:

$p = 2\cdot (w+l)$ (1)

$A = w\cdot l$ (2)

Where:

$w$ - Width, in feet.
$l$ - Length, in feet.

In addition, the cost of fencing of the rectangular plot ( $C$ ), in monetary units, is:

$C = c\cdot p$ (3)

Where $c$ is the fencing unit cost, in monetary units per foot.

Now we apply (2) and (3) in (1):

$p = 2\cdot \left(\frac{A}{l}+l \right)$

$\frac{C}{c} = 2\cdot (\frac{A}{l}+l )$

$\frac{C\cdot l}{c} = 2\cdot (A+l^{2})$

$\frac{C\cdot l}{c}-2\cdot l^{2} = 2\cdot A$

$\frac{C\cdot l}{2\cdot c} - l^{2} = A$ (4)

We notice that fencing costs are directly proportional to the area to be fenced. Let suppose that cost is the maximum allowable and we proceed to perform the first and second derivative tests:

FDT

$\frac{C}{2\cdot c}-2\cdot l = 0$

$l = \frac{C}{4\cdot c}$

SDT

$A'' = -2$

Which means that length leads to a maximum area.

If we know that $c = 8$ and $C = 4000$ , then the dimensions of the rectangular plot of land are, respectively:

$l = \frac{4000}{4\cdot (8)}$

$l = 125\,ft$

$A = \frac{(4000)\cdot (125)}{2\cdot (8)} -125^{2}$

$A = 15625\,ft^{2}$

$w = \frac{15625\,ft^{2}}{125\,ft}$

$w = 125\,ft$

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

We kindly invite to check this question on areas: brainly.com/question/11952845

8 0

2 years ago

What values are needed to make each expression a perfect square trinomial?

Ivahew [28]

Answer:

Step-by-step explanation:

x² + 2(x)(2) + 2²

x² + 4x + 4

x² - 2(x)(5) + 5²

x² - 10x + 25

3 0

3 years ago

Read 2 more answers

Use the function below to find

il63 [147K]

Answer:

f(x) =1/3 × 4^x

f(4) = 1/3 × 4⁴

= 1/3 × 256

= 256/3

Hope this helps

8 0

3 years ago

What is the range of each function given below let g(x)=3^2x?

Naya [18.7K]

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In function composition, you're plugging entire functions in for the x. In other words, you're always getting "fancy". But let's start simple. Instead of dealing with functions as formulas, let's deal with functions as sets of (x, y) points

Hope this awnsers your question

4 0

3 years ago

NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=-4.9t2+64t+

ryzh [129]

Using the vertex of the quadratic equation, it is found that:

The rocket will reach its peak height of 345 meters above sea level at 6.53 seconds.

<h3>What is the vertex of a quadratic equation?</h3>

A quadratic equation is modeled by:

$y = ax^2 + bx + c$