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9 months ago

A one to one function is given. Write an equation for the inverse function M(x)=4x^3-3

Mathematics

1 answer:

polet [3.4K]9 months ago

6 0

Step-by-step explanation:

M(x) = 4x^3 - 3

let M(x) = Y

Y = 4x^3 - 3...swap places of x & y.

X = 4y^3 - 3

look for x in terms of y.

4y^3 = x + 3

Y^3 = x + 3 / 4...put both sides under cube root.

y = ( x + 3 / 4 )^1/3

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A company interested in lumbering rights for a certain tract of slash pine trees is told that the mean diameter of these trees i

brilliants [131]

Answer:

97.6% of the trees will have diameters between 7.6 and 18.6 inches.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 12 inches

Standard Deviation, σ = 2.2 inches

We are given that the distribution of diameter of tree is a mound shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(diameters between 7.6 and 18.6 inches)

$P(7.6 \leq x \leq 18.6) = P(\displaystyle\frac{7.6 - 12}{2.2} \leq z \leq \displaystyle\frac{18.6-12}{2.2}) = P(-2 \leq z \leq 3)\\\\= P(z \leq 3) - P(z < -2)\\= 0.999 - 0.023 = 0.976= 97.6\%$

$P(7.6 \leq x \leq 18.6) = 97.6\%$

97.6% of the trees will have diameters between 7.6 and 18.6 inches.

8 0

2 years ago

The measures of the base angles of an isosceles triangle are 3x 5 and 5x - 25. The measure of the vertex angle is 6x - 10. Find

lukranit [14]

Answer: The measure of the vertex angle = 80°

Step-by-step explanation:

Angle sum property of triangle : The sum of the measures of the angles for any triangle is 180 degrees.

So,

$3x+ 5 + 5x-25+6x-10= 180\\\\\Rightarrow\ 14x-30=180\\\\\Rightarrow\ 14x= 210\\\\\Rightarrow x=\dfrac{210}{14}=15$ '

Then, vertex angle = $6(15)-10=90-10= 80$

Hence, The measure of the vertex angle = 80°

5 0

2 years ago

dee’s age is twice Max’s age plus two more.Write an expression to represent Dee’s age.Then evaluate the expression when Max is 7

Mandarinka [93]

D=2x+2

X=7

Plug in the value for Max's age.

D=2(7)+2

D=14+2

D=16

Max is 7

Dee is 16

5 0

2 years ago

Read 2 more answers

Choose one of the factors of x^3 + 343.

Debora [2.8K]

First, note that $343=7^3.$ Then use the formula for the sum of perfect cubes:

$a^3+b^3=(a+b)(a^2-ab+b^2).$

Therefore,

$x^3 + 343=x^3+7^3=(x+7)(x^2-7x+49).$

The quadratic trinomial $x^2-7x+49$ couldn't be factored anymore, so the expression $x^3 + 343$ has two factors $x+7$ and $x^2-7x+49.$

Answer: correct choice is A.

3 0

3 years ago

What is the next term of AP : √2, √8, √18, .......?

solmaris [256]

Answer:

$\sqrt {32}$

Step-by-step explanation:

Next term of the given AP can be obtained by adding common difference (d) in the last term $\sqrt {18}$

$d = \sqrt{18} - \sqrt{8} = 3 \sqrt{2} - 2 \sqrt{2} = \sqrt{2} \\ next \: term = \sqrt{18} + \sqrt{2} \\ = 3 \sqrt{2} + \sqrt{2} \\ = 4 \sqrt{2} \\ = \sqrt{ {4}^{2} \times 2 } \\ = \sqrt{16 \times 2} \\ \huge \red{ \boxed{next \: term = \sqrt{32} }}$

8 0

2 years ago