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Gwar [14]
3 years ago
15

(PYTHAGOREAN THEOREM)

Mathematics
1 answer:
tiny-mole [99]3 years ago
5 0
First draw a picture (see attached).

You want to find the diagonal of the cube, length AB.
The right triangle formed is trianagle ABD.
AD = 10m

DB will be the hypotenuse of triangle BCD.
(BC)^2 + (CD)^2 = (DB)^2 \\ 
(10)^2 + (10)^2 = (DB)^2 \\
DB =  \sqrt{200}= 10 \sqrt{2}.

If we know the length of AD and DB, we can find AB.
(AD)^2+(BC)^2 = (AB)^2 \\
(10)^2 + (10 \sqrt{2})^2 = (AB)^2 \\
AB =  \sqrt{300} = 10 \sqrt{3}

In fact, the diagonal of any cube is √3 times the side length of the cube.
Let <em>s</em> be the side length (as in AD or CD in the attached) and
h be the hypotenuse of the base, (DB in the attached) and
<em>d</em> be the diagonal of the cube (AB in the attached).

The hypotenuse of the base will be:s^2+s^2 = h^2 \\&#10;.

The cube's diagonal will be:
h^2+s^2 = d^2.

Substituting s^2+s^2 as h^2, you have
s^2+s^2+s^2 = d^2 \\&#10;3s^2 = d^2 \\&#10;d =  \sqrt{3s^2} =  s\sqrt{3}

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I’m so confused I need help please!!
shutvik [7]

Answer:

5. 9 8. 2\sqrt{10}

Step-by-step explanation:

a²+b²=c²

so for #5 12²+b²=15²

144+b²=225 (subtract 144 from both sides)

b²=81

b=9

For #8

9²+b²=11²

81+b²=121 (subtract 81 from both sides)

b²=40

b=\sqrt{40}

\sqrt{40}=

2\sqrt{10}

6 0
3 years ago
Read 2 more answers
How many kilograms of a 5% salt solution and how many kilograms of a 15% salt solution must be mixed together to make 45kg of an
JulsSmile [24]

Answer:

31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Step-by-step explanation:

Let us assume that the number of kilograms of a 5% salt solution used be x .

Let us assume that the number of kilograms of a 15% salt solution used be y .

As given

A 5% salt solution and 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Equation becomes

x + y = 45

5% is written in the decimal form .

= \frac{5}{100}

= 0.05

15% is written in the decimal form .

= \frac{15}{100}

= 0.15

8% is written in the decimal form .

= \frac{8}{100}

= 0.08

Thus

Concentration of 5% salt solution × Number of kilograms of 5% salt solution used + Concentration of 15% salt solution × Number of kilograms of  15% solution used = Concentration of 8% salt solution × Number of kilograms of 8% salt solution

Thus

0.05x + 0.15y = 0.08 × 45

Simplify the above

\frac{5x}{100} + \frac{15y}{100} = \frac{8\times 45}{100}

5x + 15y = 360

Thus two equations becomes

x + y = 45

5x + 15y = 360

Multiply x + y = 45 by 5 and subtracted from 5x + 15y = 360 .

5x - 5x + 15y - 5y = 360 - 225

10y = 135

y = \frac{135}{10}

y = 13.5 kilograms

Put value of y in the equation

x + 13.5 = 45

x = 45 - 13.5

x = 31.5 kilograms

Therefore the 31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

5 0
3 years ago
Find the vertex of the given quadratic function.
ki77a [65]

B

given f(x) in factored form, equate to zero for x-intercepts

(x - 8)(x - 4) = 0, hence

x = 4, x = 8 ← x- intercepts

The vertex lies on the axis of symmetry which is situated at the midpoint of the x- intercepts

x- coordinate of vertex = \frac{4+8}{2} = 6

f(6) = (6 - 8 )(6 - 4 ) = -2 × 2 = - 4 ← y-coordinate

vertex = (6, - 4 ) → B




8 0
3 years ago
a bicycle shop advertised all mountain bikes priced at a 1/3 discount.the original price of the bicycle is 327 dollars what is t
Andre45 [30]

It should be $109 for the bike because if u divide 327 by 3 it equals 109.

6 0
3 years ago
Given right triangle ABC with right angle at C, find sin A if a=8 and b=15​
Svetllana [295]

Answer:

if you are lookng for C it is 17

Step-by-step explanation:

7 0
3 years ago
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