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3 years ago

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Please help with math! See image below!

1 answer:

ASHA 777 [7]3 years ago

6 0

$A(b)=10\cdot\dfrac{b+7}{2}=5(b+7)=5b+(5)(7)=5b+35\\\\a=5b+35\qquad\text{solve for b}\\\\5b+35=a\qquad\text{subtract 35 from both sides}\\\\5b=a-35\qquad\text{divide both sides by 5}\\\\b=\dfrac{a}{5}-\dfrac{35}{5}\\\\b=\dfrac{a}{5}-7\\\\Answer:\ \boxed{D.\ B(a)=\dfrac{a}{5}-7}$

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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

In Alaska, the temperature can get cold really quickly. Yesterday, the temperature dropped 3° (° means degrees) for 9 straight h

Tju [1.3M]

Answer:

Step-by-step explanation:

Idk

4 0

4 years ago

Solve each system of equations by substitution. Clearly identify your solution.

Stels [109]

Answer:

(-3, 5)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality<u> </u>

<u>Algebra I</u>

Coordinates (x, y)
Terms/Coefficients
Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = x + 8

x + y = 2

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Substitution</em>

Substitute in <em>y </em>[2nd Equation]: x + x + 8 = 2
Combine like terms: 2x + 8 = 2
[Subtraction Property of Equality] Subtract 8 on both sides: 2x = -6
[Division Property of Equality] Divide 2 on both sides: x = -3

<u>Step 3: Solve for </u><em><u>y</u></em>

Substitute in <em>x</em> [1st Equation]: y = -3 + 8
Add: y = 5

4 0

3 years ago

Read 2 more answers

If the area of a rectangle is 8.4 x 1012 ft2 and the length of the rectangle is 2.0 x 108 ft, what is the width of the rectangle

KATRIN_1 [288]

I hope this helps you

6 0

3 years ago

Kayla has 18 bottles of bubbles. She wants to give 2 bottles to each of her 6 friends. How many bottles will she have left over?

FrozenT [24]

Answer:

6

Step-by-step explanation:

You started with 18 and you multiply 6×2 and you get 12 able your answer is 6 I believe. sorry if I'm wrong

3 0

3 years ago

Read 2 more answers