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2 years ago

Find the value of x in the figure

Mathematics

1 answer:

Archy [21]2 years ago

7 0

Answer:

x = 35

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6, thus

sum = 180° × 4 = 720°

Sum the given angles and equate to 720

4x - 5 + 117 + 3x - 3 + 3x + 6 + 118 + 4x - 3 = 720, that is

14x + 230 = 720 ( subtract 230 from both sides )

14x = 490 ( divide both sides by 14 )

x = 35

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Suppose that x and y are both differentiable functions of t and are related by the given equation. Use implicit differentiation

stepan [7]

Answer:

Let z = f(x, y) where f(x, y) =0 then the implicit function is

$\frac{dy}{dx} =$ $\frac{-δ f/ δ x }{δ f/δ y }$

Example:- $\frac{dy}{dx} = \frac{-(y+2x)}{(x+2y)}$

Step-by-step explanation:

Partial differentiation:-

Let Z = f(x ,y) be a function of two variables x and y. Then

$\lim_{x \to 0} \frac{f(x+dx,y)-f(x,y)}{dx}$ Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to x.

It is denoted by δ z / δ x or δ f / δ x

Let Z = f(x ,y) be a function of two variables x and y. Then

$\lim_{x \to 0} \frac{f(x,y+dy)-f(x,y)}{dy}$ Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to y

It is denoted by δ z / δ y or δ f / δ y

Implicit function:-

Let z = f(x, y) where f(x, y) =0 then the implicit function is

$\frac{dy}{dx} =$ $\frac{-δ f/ δ x }{δ f/δ y }$

The total differential co-efficient

d z = δ z/δ x + $\frac{dy}{dx}$ δ z/δ y

Implicit differentiation process

differentiate both sides of the equation with respective to 'x'

move all d y/dx terms to the left side, and all other terms to the right side

factor out d y / dx from the left side
Solve for d y/dx , by dividing

Example : $x^2 + x y +y^2 =1$

solution:-

differentiate both sides of the equation with respective to 'x'

$2x + x \frac{dy}{dx} + y (1) + 2y\frac{dy}{dx} = 0$

move all d y/dx terms to the left side, and all other terms to the right side

$x \frac{dy}{dx} + 2y\frac{dy}{dx} = - (y+2x)$

Taking common d y/dx

$\frac{dy}{dx} (x+2y) = -(y+2x)$

$\frac{dy}{dx} = \frac{-(y+2x)}{(x+2y)}$

7 0

3 years ago

If you roll a fair six-sided die and a fair four-sided die, what is the probability that the dice add to 7?

sveticcg [70]

1/6.

For any given roll on a four-sided die, there is exactly one roll on a six-sided die (1/6 chance) which will sum to 7.

Since it doesn’t matter what you roll on the four-sided die, the chance is always 1/6 with a fair six-sided die.

One interesting result of this is that only the 6-sided die has the be fair for this result to hold. The 4-sided die can be very biased in any direction and the final result will still be 1/6.

4 0

3 years ago

The perimeter of the dodecagon is 54 cm. by joining every other vertex of the dodecagon a hexagon is formed. if each side of the

lawyer [7]

Answer:

x = 8.69

Step-by-step explanation:

we know that the perimeter of the dodecagon is 54, so each edge will be 54/12

54/12 = 4.5 cm

if we draw the lines to remove 6 vertices and form a hexagon, 6 triangles with 2 sides of 4.5 cm are formed.

we know that the angle of each vertex is 150 ° because it is a dodecagon

if we apply the law of cosines we can take the other side of the triangle, since we only need 2 side and the opposite angle to the side we want to know

a would be our x

b = 4.5

c = 4.5

A = 150°

a^2 = b^2 + c^2 - 2bc * cos (A)

x^2 = 4.5^2 + 4.5^2 - 2 * 4.5 * 4.5 * cos (150)

x^2 = 20.25 + 20.25 - 40.50 * -0.866

x^2 = 40.50 + 35.07

x = √ 75.57

x = 8.69

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2 years ago

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vitfil [10]

Answer:

Step-by-step explanation:

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2 years ago

Grade 10 math please help

grandymaker [24]

Tip: Ask google and they will give you answers.

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3 years ago

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