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2 years ago

To graph the inequality x > -3, draw an open circle on -3 and shade to the left.

1 answer:

7 0

That'd be true. Because even though > points to the right, it's a -3, therefore, you flip the sign, making it <. I hope this helps!

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Consider the function V=g(x), where g(x) =x(6-2x)(8-2x), with x being the length of a cutout in cm and V being the volume of an

Andrej [43]

Answer:

The maximum volume of the open box is 24.26 cm³

Step-by-step explanation:

The volume of the box is given as $V=g(x)$ , where $g(x)=x(6-2x)(8-2x)$ and $0\le x\le3$ .

Expand the function to obtain:

$g(x)=4x^3-28x^2+48x$

Differentiate wrt x to obtain:

$g'(x)=12x^2-56x+48$

To find the point where the maximum value occurs, we solve

$g'(x)=0$

$\implies 12x^2-56x+48=0$

$\implies x=1.13,x=3.54$

Discard x=3.54 because it is not within the given domain.

Apply the second derivative test to confirm the maximum critical point.

$g''(x)=24x-56$ , $g''(1.13)=24(1.13)-56=-28.88\:$

This means the maximum volume occurs at $x=1.13$ .

Substitute $x=1.13$ into $g(x)=x(6-2x)(8-2x)$ to get the maximum volume.

$g(1.13)=1.13(6-2\times1.13)(8-2\times1.13)=24.26$

The maximum volume of the open box is 24.26 cm³

See attachment for graph.

6 0

3 years ago

A necklace and earrings cost $144. Six necklaces and five pairs of earrings cost $825

hram777 [196]

Step-by-step explanation:

let necklace : x

let earrings : y

x+y=144 -1st eqn

6x+5y=825 -2nd eqn

y=144-X -3rd eqn

substitute eqn into 2nd eqn

6x+5(144-x)= 825

6x +720-5X =825 (expanded)

X = 825-720

X =105

substitute "X=105" into 1st eqn

(105)+y=144

y= 144-105

y=39

1 necklace = 105$

1 pair of earrings = 39$

(to check back: substitute the value into the original eqn)

6 0

2 years ago

two circles are externally tangent to each other. One circle has a diameter of 62 yards and the distance between the centers of

maksim [4K]

Answer:

108 yards

Step-by-step explanation:

Let circle A be the circle with the 62 yard diameter

Let circle B be the circle whose diameter we are trying to solve for.

Externally tangent circles are circles which touch each other and share a common external tangent.
Circle A has a tangent of 62 yards and thus a radius ( half the diameter) of 31 yards.
The distance between the centers of the 2 circles is 85 yards. If you subtract the radius ( distance from the center of the circle to its circumference) of circle A then we'll only be left with the radius of circle B.
85 - 31= 54 yards which is the radius of circle B
To get the diameter: 54 x 2 = 108 yards

8 0

2 years ago

A number is multiplied by 4 and then 12 is added. the result is 36. what is the number?

musickatia [10]

Answer:

Step-by-step explanation:

4 * x + 12= 36

-12 -12

4x = 24

x= 6

6 0

2 years ago

Read 2 more answers

What is 1+4=5 2+5=12 3+6=21 what does 8 plus 11 equal

Paladinen [302]

This is a classic math problem, and it is not solved in a normal way.

1+4=5
2+5=12
3+6=21
8+11=?

There is a pattern that can be spotted. 2+5 does not equal twelve, however 2*(2+5) does equal 12. Below is how to solve the rest of the equations:

1+4=5 -> 1*(4+1)=5
2+5=12 -> 2*(5+1)=12
3+6=21 -> 3*(6+1)=21 
8+11=? -> 8*(11+1)=96

This is one way to answer the problem, HOWEVER there is another way to answer the problem that gives the SAME answer, but many people mistakenly believes it gives a different answer. If anyone tries to post the other way of doing this problem, but tells you the answer is 40, please comment on this post or message me and let me know. I will explain why the answer is actually 96 either way.

4 0

2 years ago