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2 years ago

A dice is a perfect cube. The length of the side of the dice is 1 cm. The density of a dice is 2 g/cm.

Mathematics

1 answer:

vfiekz [6]2 years ago

5 0

Answer: I handdbbdhddhdndnndnddnndjdjdjdjdjdjdjdjdjdjdjdjdjdjdjd

Step-by-step explanation:

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

A basketball was originally priced at $25, but Tucker waited to buy it until the basketball was on sale for 20% off. If he paid

kotegsom [21]

Answer:

The answer to your question is $21.0

Step-by-step explanation:

Data

Original price = $25

Discount = 20%

Taxes = 5%

Process

1.- Calculate the price with the discount

$25 ------------------- 100%

x ------------------- 20%

x = (20 x 25) / 100

x = 500 / 100

x = $5

Price after the discount = $25 - $5

= $20

2.- Calculate the price after taxes

$20 ---------------------- 100%

x ----------------------- 5%

x = (5 x 20) / 100

x = 100 / 100

x = $1

Final price = $20 + $1

= $21

3 0

3 years ago

I need help with number 5

Tju [1.3M]

Answer:

B. BD = 9

Step-by-step explanation:

Simply set the 2 equations equal to each other (both are congruent due to perpendicular bisector):

6x + 3 = 3x = 6

3x + 3 = 6

3x = 3

x = 1

Then substitute 1 for <em>x</em> in BD

6(1) + 3

6 + 3

BD = 9

7 0

3 years ago

Read 2 more answers

at an amusement park there are 5150 moon shoes and 3041 cactus plants there are a total of 10881 prizes how many hats are at the

Mariana [72]

Easy. 8 hats because no one likes hats anymore.

3 0

3 years ago

What is the quotient of 8 and 72.16

Wittaler [7]

72.16./8 is equal to 9.02.

72 divided by 8 is 9.

,16 divided by 8 is .02.

8 0

3 years ago