Which of these is a correct statement?

At which value in the domain does f(x) = 0?

bekas [8.4K]

Answer:

C

Step-by-step explanation:

f(x)=0 at points of intersection of the graph of the function with x-axis.

From the diagram you can see that the graph of the function intersects x-axis at three points:

somewhere between -3 and -2;

somewhere between -1 and 0;

at x=1.

Since x=1 is the value of x from the domain, then correct choice is option C.

5 0

2 years ago

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 144 in. Find

mr Goodwill [35]

Answer:

The volume in such a package is 27648 in³

Step-by-step explanation:

Consider the provided information.

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 144 in.

Let the dimension are x by x by y.

Where x is the variable for the square base package and y is the variable for length.

Thus l=x, b=x and h=y

Then the volume of the box is: $V(x)=x^2y$ (∵V=lbh)

The maximum combined length and girth is 144.

Therefore, $4x+y=144$

$y=144-4x$

Substitute the value of y in volume of the box.

$V(x)=x^2(144-4x)$

$V(x)=144x^2-4x^3$

$V'(x)=288x-12x^2$

Substitute V'(x)=0.

$0=288x-12x^2$

$12x(24-x)=0$

$x=0\ or\ x=24$

Now apply second derivative test.

$V''(x)=288-24x$

$V''(0)=288-24(0)>0$ (Min)

$V''(24)=288-24(24)$ (Max)

Hence, the maximum volume is at x=24

If x=24 then $y=144-4(24)=48$

Substituting value of x = 24 and y = 48 $V(x)=x^2y$ gives 27648.

Hence, the volume in such a package is 27648 in³

5 0

2 years ago

which set of number could represent the length of the sides of a right triangle? A 9 11 14 B 15 18 21 C 7 24 25 D 8 9 10

EastWind [94]

Common Pythagorean triples include
(3, 4, 5)
(5, 12, 13)
(7, 24, 25)
(9, 40, 41)
The only Pythagorean triple that is an arithmetic sequence is (3, 4, 5), so any arithmetic sequence that is a Pythagorean triple must be a multiple of that, such as (9, 12, 15) or (15, 20, 25).

The arithmetic sequences of selections B and D are unrelated to the (3, 4, 5) triple, so cannot be Pythagorean triples. For selection A, we know that 9² + 11² = 81 + 121 = 202 > 14², so that is not a right triangle.

The appropriate selection is ...
C. 7, 24, 25

8 0

2 years ago

Read 2 more answers

Solve each equation in the interval from 0 to 2pi. Round your answer to the nearest hundredth.

kirill115 [55]

I think the answer is b. cos(pi theta)= -0.6

6 0

2 years ago

Mitchell walked 5/12 of a mile in 1/2 of an hour. At this rate, how far could Mitchell walk in 1 hour?

vovangra [49]

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$2 \times \frac{1}{2} hour = 1hour \\$