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Arturiano [62]
3 years ago
15

A line is a(n) _____ for a function if the graph of the function gets closer and closer to touching the line but never reaches i

t. A. asymptote B. diagonal C. array D. diagram E. estimation
Mathematics
2 answers:
Nostrana [21]3 years ago
5 0
I think the correct answer from the choices listed above is option A. <span>A line is an asymptote for a function if the graph of the function gets closer and closer to touching the line but never reaches it. Hope this answers the question. Have a nice day.</span>
valkas [14]3 years ago
4 0

A) asymptote (apex) : )

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From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh
Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

Step-by-step explanation:

Volume =  height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x  (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so,  4 (3x² - 60x +225)=0

3x² - 60x+225=0   (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

7 0
4 years ago
Michael breeds chickens and ducks.
Paladinen [302]
4 and a half ducks.
That's pretty much the answer.
8 0
4 years ago
Read 2 more answers
For the following hypothesis test, determine the null and alternative hypotheses. Also, classify the hypothesis test as two-tail
bagirrra123 [75]

Answer:

Option B:

H_0: \mu = 22.1

H_a: \mu \neq 22.1

Classification:

The hypothesis test is Two-tailed.

Step-by-step explanation:

The mean length of imprisonment for motor-vehicle theft offenders in this country is 22.1 months.

This means that the null hypothesis is that the mean is of 22.1 months, that is:

H_0: \mu = 22.1

A hypothesis test is to be performed to determine whether the mean length of imprisonment for motor-vehicle theft offenders in this city differs from the national mean of 22.1 months.

At the alternate hypothesis, we test if this mean is different of 22.1, that is:

H_a: \mu \neq 22.1

Which means that the answer is given by option b).

Which of the following is the correct classification of the hypothesis test?

We test if the mean is different from a value, which means that the hypothesis test is Two-tailed.

7 0
4 years ago
How would I simplify the equation 5u^6x^2+20wx/15x^4
Akimi4 [234]

Answer:

The simplified form is 5u^6x^2+\frac{4w x^{-3}}{3}

Step-by-step explanation:

To simplify the expression given to use, we need to reduce the given expression in its simplest form. There should not be any possibility for the further cancelling out of the division terms, if any.

Now the expression that is given to us is:

5u^6x^2+\frac{20wx}{15x^4}\\

Here we will simplify it, as follows:

5u^6x^2+\frac{20wx}{15x^4}\\=5u^6x^2+\frac{4w}{3x^3}\\=5u^6x^2+\frac{4w x^{-3}}{3}

So this is the required simplified form.

3 0
3 years ago
Please Help! The graph of y=f(x) is shown below. What are all of the real solutions of f(x)=0? (Picture of graph included)
qwelly [4]

Answer:

(7, 0), (-8, 0), (0, 0)

Step-by-step explanation:

y = f(x) = 0

the real solutions are the ones that cross the x-axis because when a point is on the x-axis, its y coordinate will be 0.

=> (7, 0), (-8, 0), (0, 0)

6 0
3 years ago
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