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3 years ago

Which of the following is not a way to represent the solution of the inequality 7 - 9x - (x + 12) less than or greater to 25?

1 answer:

8 0

<span>To answer the question above first we need toclarify what the inequality is actually saying:

7 - 9x - (x + 12) </= 25 (simplify)

-5 - 10x </= 25 (add 5 to both sides)

-10x </= 30 (divide by -10 to get x)

x >/= -3 (don't forget to flip the signs when you divide by a negative number)

So this says x is greater than or equal to -3, so which of these statements is not a way to represent that?

I'd say it's the second one. x is greater than not less than.</span>

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A forestry company hopes to generate credits from the carbon sequestered in its plantations.The equation describing the forest w

Dmitry [639]

Answer:

Explanation:

Given:

The equation describing the forest wood biomass per hectare as a function of plantation age t is:

y(t) = 5 + 0.005t^2 + 0.024t^3 − 0.0045t^4

The equation that describes the annual growth in wood biomass is:

y ′ (t) = 0.01t + 0.072t^2 - 0.018t^3

To find:

a) The year the annual growth achieved its highest possible value

b) when does y ′ (t) achieve its highest value?

To determine the year the highest possible value was achieved, we will set the derivative y'(t) to zero. The values of t will be substituted into the second derivative to get the highest value

$\begin{gathered} 0\text{ = 0.01t + 0.072t}^2\text{ - 0.018t}^3 \\ using\text{ a graphing tool,} \\ t\text{ = -0.1343} \\ \text{t = 0} \\ t\text{ = 4.1343} \\ \\ Since\text{ we can't have time as a negative value, t = 0 or t = 4.1343} \end{gathered}$ $\begin{gathered} To\text{ ascertain which is the maximum, we take a second derivative} \\ y^{\prime}\text{'\lparen t\rparen = 0.01 + 0.144t - 0.054t}^2 \\ \\ substitute\text{ t = 0 and t = 4.13 respectively} \\ when\text{ t = 0 } \\ y^{\prime}\text{'\lparen t\rparen= 0.01 + 0.144\lparen0\rparen - 0.054\lparen0\rparen}^2 \\ y^{\prime}\text{'\lparen t\rparen= 0.01 + 0 - 0} \\ y^{\prime}\text{'\lparen t\rparen= 0.01 > 0} \\ \\ y^{\prime}\text{'\lparen t\rparen= 0.01 + 0.144\lparen4.13\rparen - 0.054\lparen4.13\rparen}^2 \\ y^{\prime}\text{'\lparen t\rparen= -0.316 < 0} \\ \\ if\text{ }y^{\prime}\text{'\lparen t\rparen > 0 , then it is minimum, } \\ if\text{ }y^{\prime}\text{'\lparen t\rparen < 0, then it is maximum} \end{gathered}$

SInce t = 4.13, gives y ′' (t) = -0.316 (< 0). This makes it the maximum value of t

The year the annual growth achieved its highest possible value to the nearest whole number will be

year 4

b) y ′ (t) will achieve its highest value, when we substitute the value of t that gives into the initial function.

Initial function: y(t) = 5 + 0.005t^2 + 0.024t^3 − 0.0045t^4

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6 0

1 year ago

The average cost per car crash in Thousand Oaks was $1,599 in 2014. Suppose this average cost was based on a sample of 50 person

artcher [175]

Ok so djdmdjdjfndjdjdjdjdmdd dmdmdd

5 0

3 years ago

One number is 6 more than twice another. If their sum is 51, find the numbers.

joja [24]

Answer:

y=2x+6 ; x+y=51

Step-by-step explanation:

assuming x is one number and y is the other -

one number (y) is 6 more (+6) than twice another (2x) -

using that knowledge we form an equation -

y=2x+6

the sum (x+y) is 51

using this knowledge we can make the equation -

x+y=51

now you have -

y=2x+6 or 2x-y=-6

x+y=51

using system of equations -

you add the equations -

3x=45

x=15

y=51-x => y=36

hope this helps!!

7 0

3 years ago

What angle is this and explain

REY [17]

The measures of the angles are 59 degrees

<h3>How to determine the value of the angles?</h3>

The angles are given as:

Angle 1 = 2x + 17

Angle 2 = 3x - 4

By the interior angle theorem, the angles are congruent

So, we have

Angle 1 = Angle 2

Substitute the known values in the above equation

2x + 17= 3x - 4

Collect the like terms

3x - 2x = 17 + 4

Evaluate the like terms

x = 21

Substitute x = 21 in Angle 1 = 2x + 17

Angle 1 = 2 * 21 + 17

Evaluate

Angle 1 = 59

This means that

Angle 1 = Angle 2 = 59

Hence, the measures of the angles are 59 degrees