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3 years ago

My rectangular soccer field site has a length equal to twice its width. Find its area in terms of its length x

1 answer:

8 0

The area of a rectangle = (length)(width)

let's call the width x. the length is twice the width, so the length = 2x.

so the area = (x)(2x)
area = 2x^2

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Find the absolute maximum and minimum values of the function below. f(x) = x3 − 9x2 + 3, − 3 2 ≤ x ≤ 12 Solution Since f is cont

Neko [114]

Answer:

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

Step-by-step explanation:

The correct statement is described below:

Find the absolute maximum and minimum values of the function below:

$f(x) = x^{3}-9\cdot x^{2}+ 3$ , $2 \leq x \leq 12$

Given that function is a polynomial, then we have the guarantee that function is continuous and differentiable and we can use First and Second Derivative Tests.

First, we obtain the first derivative of the function and equalize it to zero:

$f'(x) = 3\cdot x^{2}-18\cdot x$

$3\cdot x^{2}-18\cdot x = 0$

$3\cdot x \cdot (x-6) = 0$ (Eq. 1)

As we can see, only a solution is a valid critical value. That is: $x = 6$

Second, we determine the second derivative formula and evaluate it at the only critical point:

$f''(x) = 6\cdot x -18$ (Eq. 2)

x = 6

$f''(6) = 6\cdot (6)-18$

$f''(6) =18$ (Absolute minimum)

Third, we evaluate the function at each extreme of the given interval and the critical point as well:

x = 2

$f(2) = 2^{3}-9\cdot (2)^{2}+3$

$f(2) = -25$

x = 6

$f(6) = 6^{3}-9\cdot (6)^{2}+3$

$f(6) = -105$

x = 12

$f(12) = 12^{3}-9\cdot (12)^{2}+3$

$f(12) = 435$

There are an absolute minimum (x = 6) and an absolute maximum (x = 12).

6 0

3 years ago

Please help me! I will give brainliest to the person who answers correctly.

Sveta_85 [38]

Answer:

sin(X) = 6/7.5
XY = 4.5
cos(X) = 4.5/7.5
tan(X) = 6/4.5

Step-by-step explanation:

It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...

XZ² = YZ² + XY²

Solving for XY, you find ...

XY² = XZ² - YZ²

XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25

XY = 4.5

The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...

Sin = Opposite/Hypotenuse

sin(X) = 6/7.5

Cos = Adjacent/Hypotenuse

cos(X) = 4.5/7.5

Tan = Opposite/Adjacent

tan(X) = 6/4.5

_____

<em>Comment on the triangle and ratios</em>

The side lengths of this triangle are in the ratios ...

XY : YZ : XZ = 3 : 4 : 5

If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.

The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.

3 0

4 years ago

What are the first four terms of the sequence represented by the expression n(n - 1) - 4?

lesya692 [45]

The first four are n,n,-1,-4

4 0

3 years ago

Read 2 more answers

The triangles are isosceles and ΔABC : ΔJKL. What is the length of J-L?

Tatiana [17]

You know ABC is isoceles, so AB = BC and BC = 2.5 cm.
That means that the scale factor is KL/BC = 2
So JL = 2AC = 8 cm

5 0