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3 years ago

What can you say about the yvalues of the two functions f(x)=3^x-3 and g(x)=7x^2-3 please answer

Mathematics

1 answer:

NARA [144]3 years ago

4 0

Answer:

Step-by-step explanation:

This question is too general. We can take a look at the behaviors of the two different graphs:

f(x)=3^x-3 is an exponential function whose y-intercept is (0, -2). Note that 3^0 = 1. To draw this function, we'd drawn f(x)=3^x first and then translate the whole graph down by 3 units. The graph appears in Quadrants III, IV and I, in that order.

g(x)=7x^2-3 is not an exponential function, but rather a quadratic whose graph is a parabola. Here the parabolic graph opens up. Its y-intercept is (0, -3). This graph will intersect that of f(x)=3^x-3 in two places.

A: False. It is g that has minimum y value of -3. The minimum y value of f is -2.

B: The smallest y value f can have is just above y = -2. y = -2 is the horizontal asymptote for this function. The smallest y value g can have is -3. So B is False.

C: True. g has the smallest possible y-value; it is -3.

D: True. The min. y-value of g is -3.

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If Vector u=(5,-7) and v=(-11,3), 2v-6u=_____ and ||2v-6u||≈_____

Sauron [17]

<h2>Answer:</h2>

$2\vec{v}-6\vec{u}=(-52,48) \\ \\ ||2\vec{v}-6\vec{u}||=75.28}$

<h2>Step-by-step explanation:</h2>

In this problem we have two vectors:

$\vec{u}=(5,-7) \ and \ \vec{v}=(-11,3)$

So we need to find two things:

$2\vec{v}-6\vec{u}$

and:

$||2\vec{v}-6\vec{u}||$

FIRST:

In this case we have the multiplication of vectors by scalars. A scalar is a simple number, so:

$2\vec{v}-6\vec{u} \\ \\ Replace \ \vec{v} \ and \ \vec{u} \ by \ the \ given \ vectors: \\ \\ 2(-11,3)-6(5,-7) \\ \\ Multiply \ each \ component \ by \ the \ corresponding \ scalar:\\ \\ (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7)) \\ \\ (-22,6)+(-30,42) \\ \\ Sum \ of \ vectors: \\ \\ (-22-30,6+42) \\ \\ \therefore \boxed{(-52,48)}$

SECOND:

If we name:

$\vec{w}=2\vec{v}-6\vec{u}$

Then, $||2\vec{v}-6\vec{u}||$ is the magnitude of the vector $\vec{w}$ . Therefore:

$||\vec{w}||=||2\vec{v}-6\vec{u}|| \\ \\ ||\vec{w}||=||(-52,48)|| \\ \\ ||\vec{w}||=\sqrt{(-58)^2+48^2} \\ \\ ||\vec{w}||=\sqrt{3364+2304} \\ \\ ||\vec{w}||=\sqrt{5668} \\ \\ \boxed{||\vec{w}||=75.28}$

5 0

3 years ago

Read 2 more answers

$85 Restaurant Bill; 15% Tip

svp [43]

Answer:

97.75

Step-by-step explanation:

15% of 85 is 12.75

12.75 + 85 = 97.75

Hope this helps have a nice day

8 0

3 years ago

A scale diagram of a statue is drawn using a scale of 1 cm to 6 m.

barxatty [35]

Answer:

5cm in the diagram

Step-by-step explanation:

30/6=5

4 0

2 years ago

Read 2 more answers

A CD usually sells for $17.00. If the CD is 20% off, and sales tax is 6%, what is the total price of the CD, including tax?

Alinara [238K]

Answer:

14.42

Step-by-step explanation:

17.00 x .80 20% off means price is 80% (or .80) of price

=13.6

13.6 x .06 = .82 sales tax

13.60 + .82 = 14.42 sales price plus sales tax

8 0

3 years ago

Given the points A (-4,-2) and B (4, 10), find the

mafiozo [28]

Answer:

P = (2, 7)

Step-by-step explanation:

You want to find coordinates of P on segment AB such that P is 3/4 is of the way from A to B.

<h3>Equation for P</h3>

For some fraction q of the distance from A to B, the point P that lies at that fraction of the distance is given by ...

P = A +q(B -A) = (1 -q)A +qB

<h3>Application</h3>

For q = 3/4, the location of P is ...

P = (1 -3/4)A + 3/4B = (A +3B)/4

Using the given point coordinates, we have ...

P = ((-4, -2) +3(4, 10))/4 = (-4 +12, -2 +30)/4 = (8, 28)/4

P = (2, 7)

8 0

1 year ago