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3 years ago

If the sum of the two numbers is 4 and the sum of their squares minus three times their product is 76,find the number

Engineering

1 answer:

alexandr402 [8]3 years ago

6 0

Answer:

-2 and 6

Explanation:

Let "x" and "y" be 2 numbers.

The sum of the two numbers is 4. The mathematical expression is:

x + y = 4

y = 4 - x [1]

The sum of their squares minus three times their product is 76. The mathematical expression is:

x² + y² - 3 x y = 76 [2]

If we substitute [1] in [2], we get:

x² + (4 - x)² - 3 x (4 - x) = 76

x² + 16 - 8 x + x² - 12 x + 3 x² = 76

5 x² - 20 x - 60 = 0

We apply the solving formula for second order equations and we get x₁ = 6 and x₂ = -2.

If we replace these x values in [1], we get:

y₁ = 4 - x₁ = 4 - 6 = -2

y₂ = 4 - x₂ = 4 - (-2) = 6

As a consequence, one of the numbers is 6 and the other is -2.

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What are factor of safety for brittle and ductile material

galben [10]

Explanation:

Step1

Factor of safety is the number that is taken for the safe design of any component. It is the ratio of failure stress to the maximum allowable stress for the material.

Step2

It is an important parameter for design of any component. This factor of safety is taken according to the environment condition, type of material, strength, type of component etc.

Step3

Different material has different failure stress. So, ductile material fails under shear force. Ductile material’s FOS is based on yield stress as failure stress as after yield point ductile material tends to yield. Brittle material’s FOS is based on ultimate stress as failure stress.

The expression for factor of safety for ductile material is given as follows:

$FOS=\frac{\sigma_{yp}}{\sigma_{a}}$

Here, $\sigma_{f}$ is yield stress and $\sigma_{a}$ is allowable stress.

The expression for factor of safety for brittle material is given as follows:

$FOS=\frac{\sigma_{ut}}{\sigma_{a}}$

Here, $\sigma_{ut}$ is ultimate stress and $\sigma_{a}$ is allowable stress.

5 0

3 years ago

4.7 If the maximum tensile force in any of the truss members must be limited to 22 kN, and the maximum compressive force must be

ki77a [65]

Answer:

588.55 kg

attached below is a sketch of the members of the truss

Explanation:

Given data:

Maximum tensile force = 22 KN

maximum compressive force = 20 KN

To determine the largest permissible mass m which may be supported by the truss

First we have have to find the summation of forces in the Y and X direction along Joint C

<u>Summation of forces in the Y direction</u>

∑Fy = 0

= BC sin30° - W = 0. hence BC = 2WT

<u>summation of forces in the X direction </u>

∑Fx = 0

= -CD - BC cos30°

therefore CD = -2W cos30°

hence ; CD = - 1.732W

ignoring the compression on CD. therefore CD = 1.732W C

Next we have to analyze Joint B

summation of forces in the X direction

∑Fx = 0

= - AB + BC cos30° = 0

therefore AB = BC cos30°

AB = 1.732W T

∑Fy = 0

- BD - BC sin30° = 0

therefore BD = -W = W C

Analyzing Joint D

∑Fy = 0

AD sin30° + BD = 0

hence ;AD = 2W T

∑Fx = 0

-DE - ADcos30° + CD = 0

hence DE = -3.464W = 3.464W C

At Joint E

∑Fy = 0

i.e. AE = 0

from the above analysis The tensile force is greatest on members AD and BC

AD = BC = 2W

from the question the maximum tensile force in any of the truss members = 22KN

Hence ;

2W = 22KN

2mg = 22000N

m = 22000 / ( 2 * 9.81 )

= 1121.30 kg

from the above analysis the greatest compressive force is found in DE which is the critical part of the Truss hence the maximum mass it can carry is the largest permissible mass which may be supported by the Truss

DE = 3.464 W

from the question the maximum compressive force = 20 KN

hence ;

3.464 W = 20KN

3.464 mg = 20000N

m = 20000 / ( 3.464 * 9.81 )

m = 588.55 kg

4 0

3 years ago

Question 2: write a program for smart garage system using:

natulia [17]

Answer:

Explanation:

8 0

2 years ago

What is programming and sensory?

NNADVOKAT [17]

Answer:

Programing is using data or codes to make something happen A sensory is like when you move your arm in front of a device and like it has a light that turns on then that is sensory it like can tell your moving

7 0

3 years ago

A cannon ball is fired with an arching trajectory such that at the highest point of the trajectory the cannon ball is traveling

ELEN [110]

Answer:

The radius of curvature is 979 meter

Explanation:

We have given velocity of the canon ball v = 98 m/sec

Acceleration due to gravity $g=9.81m/sec^2$