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3 years ago

F(x)= y-x/x^2-16 (that’s a fraction; and the ^ indicates the 2 is a exponent)

Mathematics

1 answer:

bulgar [2K]3 years ago

4 0

Answer:

= 1/x^2

Step-by-step explanation:

Possible derivation:

d/dx(-16 - 1/x + y)

Differentiate the sum term by term and factor out constants:

= d/dx(-16) - d/dx(1/x) + d/dx(y)

The derivative of -16 is zero:

= -(d/dx(1/x)) + d/dx(y) + 0

Simplify the expression:

= -(d/dx(1/x)) + d/dx(y)

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = -1.

d/dx(1/x) = d/dx(x^(-1)) = -x^(-2):

= d/dx(y) - -1/x^2

Simplify the expression:

= 1/x^2 + d/dx(y)

The derivative of y is zero:

= 1/x^2 + 0

Simplify the expression:

Answer: = 1/x^2

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a rectangle prism has a volume of 3x^2 + 18x+ 24. its base has a length of x + 2 and width of 3, what expression represents the

OlgaM077 [116]

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\qquad 
\begin{cases}
l=x+2\\
w=3\\
V=3x^2 + 18x+ 24
\end{cases}\implies \cfrac{V}{lw}=h
\\\\\\
\cfrac{3x^2 + 18x+ 24}{3(x+2)}=h\implies \cfrac{\underline{3}(x^2 + 6x+ 8)}{\underline{3}(x+2)}=h
\\\\\\
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6 0

3 years ago

Suppose that the amount of time T a customer spends in a bank is exponentially distributed with an average of 10 minutes. What i

Bad White [126]

Answer:

The probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.

Step-by-step explanation:

The random variable T is defined as the amount of time a customer spends in a bank.

The random variable T is exponentially distributed.

The probability density function of a an exponential random variable is:

$f(x)=\lambda e^{-\lambda x};\ x>0$

The average time a customer spends in a bank is β = 10 minutes.

Then the parameter of the distribution is:

$\lambda=\frac{1}{\beta}=\frac{1}{10}=0.10$

An exponential distribution has a memory-less property, i.e the future probabilities are not affected by any past data.

That is, P (X > s + x | X > s) = P (X > x)

So the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is:

P (X > 15 | X > 10) = P (X > 5)

$\int\limits^{\infty}_{5} {f(x)} \, dx =\int\limits^{\infty}_{5} {\lambda e^{-\lambda x}} \, dx\\=\int\limits^{\infty}_{5} {0.10 e^{-0.10 x}} \, dx\\=0.10\int\limits^{\infty}_{5} {e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10}|^{\infty}_{5}\\=[-e^{-0.10 \times \infty}+e^{-0.10 \times 5}]\\=0.6065$

Thus, the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.

8 0

3 years ago

Which value must be added to the expression x2 – 3x to make it a perfect-square trinomial?

Vitek1552 [10]

Answer:

$\frac{9}{4}$

Step-by-step explanation:

Given

x² - 3x

To make the expression a perfect square

add ( half the coefficient of the x- term )²

x² + 2( - $\frac{3}{2}$ )x + $\frac{9}{4}$ , thus

x² - 3x + $\frac{9}{4}$

= (x - $\frac{3}{2}$ )² ← a perfect square

7 0

3 years ago

If f(x)=1/9x-2 , what is f–1(x)?

Anna71 [15]

Lets get started :)

f(x) = $\frac{1}{9}x$ - 2
y = $\frac{1}{9}x$ - 2
This is the original equation, and now we have to find the inverse.

When finding the inverse, just flip the variables, x as y and y as x

f ⁻¹(x)
↓
x = $\frac{1}{9}y$ - 2
We have to isolate y as it is our f ⁻¹(x)

Take 2 to the other side { When you see subtraction, you do addition }
x + 2 = $\frac{1}{9} y$

Take 9 to the other side { When you see division, you do multiplication }
9 ( x + 2 ) = y
9x + 18 = y

f ⁻¹ (x) = 9x + 18

7 0

3 years ago

Help plz..........................................................................................

Zarrin [17]

The answer is the last one

3 0

3 years ago

Read 2 more answers