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3 years ago

John drove 270 miles

Mathematics

1 answer:

Juliette [100K]3 years ago

5 0

Answer:

3 hrs. Realistically tho he would get a ticket or killed from a crash.

Step-by-step explanation:

270/2 to get mph which is 135mph

405/135 which is 3

So it will take him 3 hrs.

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A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

3 years ago

Dan grew 22 pumpkins but tge rabbits ate 25 pumpkins.how many pumpkins does dan have left

rodikova [14]

Answer:

Step-by-step explanation:

0 because he grew 22 but the rabbit ate 25 which does not make sense

8 0

3 years ago

Read 2 more answers

A bag contains nine red balls, four green balls, and fifteen yellow balls. What is the probability of pulling out one red ball?

Aleksandr [31]

Answer:

32.1%

Did you type something in wrong?

Step-by-step explanation:

9+4+15=28 total balls

9=total red balls

total red balls/total balls= probability of pulling out one red ball

9/28

9÷28=32.1%

8 0

3 years ago

Sixty-one diminished by ten x. Answer: _______________________ . The product of twice a number k. Answer: ______________________

KengaRu [80]

Answer:

61 - 10x

42 / 6 = 7

38 + 2m

3y - 6

Step-by-step explanation:

A. Sixty-one diminished by ten x

= 61 - 10x

B. The product of twice a number k

= 2 * k

= 2k

C. The quotient of forty-two and six is seven

42 / 6 = 7

D. Twice the total of nineteen and a number m.

= 2(19 + m)

= 38 + 2m

E. Six less than 3 times y

3y - 6

6 0

3 years ago

A spinner with 8 equal parts, labeled 1 to 8, is used in a board game. you spin the spinner one time. what is the theoretical pr

stiks02 [169]

Answer:

1 in 8; or 12.5% of the time

Step-by-step explanation:

There are eight outcomes. One of eight of those outcomes is a 2.

1/8 = 0.125

5 0

3 years ago