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3 years ago

The numbers 7, 24, and c are a Pythagorean triple. What is the value of c? A. 31 B. 24 C. 25 D. 27

Mathematics

1 answer:

zavuch27 [327]3 years ago

5 0

$7;\ 24;\ c-Pythagorean\ triple,\ then\\\\c^2=7^2+24^2\\\\c^2=49+576\\\\c^2=625\\\\c=\sqrt{625}\\\\c=25\\\\Answer:C$

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What fraction has the greatest value?

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5/6

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After a 75% reduction, you purchase a new clothes dryer on sale for $125. What was the original price of the clothes dryer?

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The clothes dryer would've been $500 originally :)

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3 years ago

X- 12 = 5x2 in standard form

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3 years ago

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

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3 years ago

Dedi had a combination lock.To open the lock he started at 37.He made 3 half turns clockwise and 3 quarter turns anticlockwise

Lerok [7]

Turning clockwise means the number increase, and counterclockwise means the number decreases

Therefore your answer is 37 + (3*1/2)-(3*1/4)

= 37.75

Hope this helped :)

5 0

2 years ago