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2 years ago

What is the range of the function f(x) = 3x2 + 6x – 8?

2 answers:

5 0

F(x) is a quadratic equation with the x-side squared and a is positive which means that the graph of the function is a parabola facing up. The range of f(x) is given by {y|y ≥ k}, where k is the y-coordinate of the vertex.
$f(x)=3 x^{2} +6x-8$ , written in vertex form is
$y=3 (x+1)^{2} -11$ , where (h, k) = (-1, -11)
Therefore, range ={y|y ≥ -11}

Alecsey [184]2 years ago

4 0

Answer:

Step-by-step explanation:

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A simple model for the shape of a tsunami is given by dW/dx = W √(4 − 2W), where W(x) > 0 is the height of the wave expressed

NeX [460]

Answer:

a) $W=0,2$

b) $W = 2 [1- tanh^2 (x+c)] = 2 sech^2 (x+c)$

Step-by-step explanation:

Part a

For this case we have the following differential equation:

$W \sqrt{4-2W}=0$

If we square both sides we got:

$W^2 (4-2W) =0$

And we have two possible solutions for this system $W=0, W=2$

So then that represent the constant solutions for the differential equation.

So then the solution for this case is :

$W=0,2$

Part b: Solve the differential equation in part (a)

For this case we can rewrite the differential equation like this:

$\frac{dW}{dx} =W \sqrt{4-2W}$

And reordering we have this:

$\frac{dW}{W \sqrt{4-2W}} = dx$

Integrating both sides we got:

$\int \frac{dW}{W \sqrt{4-2W}} = \int dx$

Using CAS for the left part we got:

$-tanh^{-1} (\frac{1}{2} \sqrt{4-2W})= x+c$

We can multiply both sides by -1 we got:

$tanh^{-1} (\frac{1}{2} \sqrt{4-2W})=-x-c$

And we can apply tanh in both sides and we got:

$\frac{1}{2} \sqrt{4-2W} = tanh(-x-c)$

By properties of tanh we can rewrite the last expression like this:

$\frac{1}{2} \sqrt{4-2W} = -tanh(x+c)$

We can square both sides and we got:

$\frac{1}{4} (4-2W) = tanh^2 (x+c)$

$1-\frac{1}{2}W = tanh^2 (x+c)$

And solving for W we got:

$W = 2 [1- tanh^2 (x+c)] = 2 sech^2 (x+c)$

And that would be our solution for the differential equation

3 0

2 years ago

Michael has 3 quarters, 2 dimes, and 3 nickels in his pocket. He randomly draws two coins from his pocket, one at a time, and th

Annette [7]

Answer: No. Choosing two dimes are dependent events. The probability of choosing the first dime is 1/4 and the probability of choosing the second dime is 1/7. The probability that both coins are dimes is (1/4)(1/7) = 1/28.

4 0

2 years ago

Read 2 more answers

Find the simplified product b-5/2b x b^2+3b/b-5

White raven [17]

Answer:

The product $\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}=\frac{b+3}{2}$

Step-by-step explanation:

Given expression $\frac{b-5}{2b}$ and $\frac{b^2+3b}{b-5}$

We have to find the product of $\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}$

Consider the given expression $\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}$

Multiply fractions, we have,

$\frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}$

$=\frac{\left(b-5\right)\left(b^2+3b\right)}{2b\left(b-5\right)}$

Cancel common factor ( b - 5 )

we have, $=\frac{b^2+3b}{2b}$

Apply exponent rule,

$\:a^{b+c}=a^ba^c$

$b^2=bb$

$=bb+3b=b(b+3)$

$=\frac{b\left(b+3\right)}{2b}$

Cancel common factor b , we have,

$=\frac{b+3}{2}$

Thus, the product $\frac{b-5}{2b}\times\frac{b^2+3b}{b-5}=\frac{b+3}{2}$

8 0

2 years ago

Read 2 more answers

Nancy was laid off and applied for unemployment benefits in July. In her state, the weekly unemployment benefit is 55% of the 2

tankabanditka [31]

Answer:

$277.91

Step-by-step explanation:

"The 26-week average of the two highest salaried quarters of the year leading to her application" would be the average of $13,500 and $12,775, or

$13,500 + $12,775

---------------------------- = $13137.50

Dividing this by 26 weeks (equivalent to 6 months), we get $505.29.

Nancy's weekly employment benefit would be 55% of that, or $277.91.

8 0

2 years ago

Jose is applying to college. He receives information on 7 different colleges. He will apply to all of those he likes. He may lik

marta [7]

Answer:

128 posibilities

Step-by-step explanation:

We have 7 colleges (A,B,C,...,H) which form a set with seven elements.

What you are asking is the number of elements (or cardinality) of the set that contains all possible sets formed by those 7 elements (or the "power set").

It is known that if n is the number of elements of a given set X, then the cardinality of the power set is $2^n$ .

Therefore, there are $2^7$ or 128 possibilities (or elements) for the set of colleges that he applies to.

6 0

2 years ago