Will give brainliest !! Helpppp please!

Assume that f is a one-to-one function.

Pavlova-9 [17]

It is given in the question that f is a one-to-one function.

And for a one-to - one function,

If

$f(a)=b, \ then \ f^{-1} (b) =a$

So we will get

$a. If \ f(3)=15, \ then \ f^{-1} (15) =3
\\
b. If \ f^{-1}(6)=4, \ then \ f(4)=6$

3 0

3 years ago

(1 point) (a) Find the point Q that is a distance 0.1 from the point P=(6,6) in the direction of v=⟨−1,1⟩. Give five decimal pla

natima [27]

Answer:

following are the solution to the given points:

Step-by-step explanation:

In point a:

$\vec{v} = -\vec{1 i} +\vec{1j}\\\\|\vec{v}| = \sqrt{-1^2+1^2}$

$=\sqrt{1+1}\\\\=\sqrt{2}$

calculating unit vector:

$\frac{\vec{v}}{|\vec{v}|} = \frac{-1i+1j}{\sqrt{2}}$

the point Q is at a distance h from P(6,6) Here, h=0.1

$a=-6+O.1 \times \frac{-1}{\sqrt{2}}\\\\= 5.92928 \\\\b= 6+O.1 \times \frac{-1}{\sqrt{2}} \\\\= 6.07071$

the value of Q= (5.92928 ,6.07071 )

In point b:

Calculating the directional derivative of $f (x, y) = \sqrt{x+3y}$ at P in the direction of $\vec{v}$

$f_{PQ} (P) =\fracx{f(Q)-f(P)}{h}\\\\$

$=\frac{f(5.92928 ,6.07071)-f(6,6)}{0.1}\\\\=\frac{\sqrt{(5.92928+ 3 \times 6.07071)}-\sqrt{(6+ 3\times 6)}}{0.1}\\\\= \frac{0.197651557}{0.1}\\\\= 1.97651557$

$\vec{v} = 1.97651557$

In point C:

Computing the directional derivative using the partial derivatives of f.

$f_x(x,y)= \frac{1}{2 \sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{2 \sqrt{22}}\\\\f_x(x,y)= \frac{1}{\sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{\sqrt{22}}\\\\f_{(PQ)}(P)= (f_x \vec{i} + f_y \vec{j}) \cdot \frac{\vec{v}}{|\vec{v}|}\\\\= (\frac{1}{2 \sqrt{22}}\vec{i} + \frac{1}{\sqrt{22}} \vec{j}) \cdot \frac{-1}{\sqrt{2}}\vec{i} + \frac{1}{\sqrt{2}} \vec{j}$

4 0

3 years ago

A plane descends to sea level from 36 comma 400 feet after being airborne for 1 and one half hours. The entire flight time is 3

andrew-mc [135]

Answer:

350 feet per minute

Step-by-step explanation:

The amount of time it took the plane to descend is 3 hours 14 minutes minus 1 hour 30 minutes.

This means it took 104 minutes for the plane to descend 36,400 feet.

Dividing 36400 by 104, you get 350 which is the average rate of descent in feet per minute.

6 0

3 years ago

Read 2 more answers

Suppose that Fx) = x3 and G(x) = -2x2. Which statement best compares the

Rudiy27

Answer:

D

Step-by-step explanation:

you can just find the value of y and try some number of x

i.e. if x = 0, both of them will be 0

x = 1

G(x) result is -2

F(x) result is 1

x= -1

G(x) result will be 2

F(x) result is -1

so from these we can prove that G(x) is bigger graph than F(x) but flip vertically by y axis

8 0

3 years ago

If 48% of the students in a certain college are female and there are 1440 female students, what is the total number of students

Andrews [41]

Answer:

3000 students

Step-by-step explanation:

If 48% of the students are female, and there are 1440 female students, we can set up a percentage proportion, assuming x is the total amount of students.

$\frac{1440}{x} = \frac{48}{100}$

We can use the cross products property to find the value of x.

$1440\cdot100=144000\\\\144000\div48=3000$

Hope this helped!

5 0

3 years ago