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3 years ago

Which of the following statements must be true about this diagram? Check

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

4 0

Answer:

Step-by-step explanation:

I'm pretty sure it's f from what I know

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Find the solution of the given initial value problems in explicit form. Determine the interval where the solutions are defined.

natali 33 [55]

Answer:

The solution of the given initial value problems in explicit form is $y=x-x^2-2$ and the solutions are defined for all real numbers.

Step-by-step explanation:

The given differential equation is

$y'=1-2x$

It can be written as

$\frac{dy}{dx}=1-2x$

Use variable separable method to solve this differential equation.

$dy=(1-2x)dx$

Integrate both the sides.

$\int dy=\int (1-2x)dx$

$y=x-2(\frac{x^2}{2})+C$ $[\because \int x^n=\frac{x^{n+1}}{n+1}]$

$y=x-x^2+C$ ... (1)

It is given that y(1) = -2. Substitute x=1 and y=-2 to find the value of C.

$-2=1-(1)^2+C$

$-2=1-1+C$

$-2=C$

The value of C is -2. Substitute C=-2 in equation (1).

$y=x-x^2-2$

Therefore the solution of the given initial value problems in explicit form is $y=x-x^2-2$ .

The solution is quadratic function, so it is defined for all real values.

Therefore the solutions are defined for all real numbers.

4 0

3 years ago

Solve for X: Correctly answer the question

Klio2033 [76]

Answer:

x=16

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(8+24) * 8 = x^2

32*8 = x^2

256 =x^2

Take the square root of each side

sqrt(256) = sqrt(x^2)

16 = x

3 0

2 years ago

The diagram shows , , and . Which statement can be proven true from the diagram?

tresset_1 [31]

What can be proven true in the diagram is the statement in letter C. angle CGB is complementary to angle AGD. It is because they both had the same vertex which is point G. Complementary angles are angles which are equal to 90 degrees wherein when you add both angles which are obviously 45 degrees, the sum is 90 degrees.

3 0

3 years ago

One mirror is to be in the shape of a triangle whose height is 6 feet less than twice the base of the mirror. If the mirror has

Vlad1618 [11]

Answer:

Base of the mirror is 12 feet and height of the mirror is 18 feet.

Step-by-step explanation:

Given:

Area of the triangular mirror = 108 sq ft.

Let base (b) of the mirror be x.

Now given:

height is 6 feet less than twice the base of the mirror

So we can say that;

Height (h) = $2x-6$

We need to find the base and height of the mirror.

Solution:

Now we know that mirror is in triangular shape so we will apply area of triangle formula to find base and height.

Now Area of triangle is half times base times height.

framing in equation form we get;

$108=\frac{1}{2} \times x \times(2x-6)\\\\108=\frac{1}{2}\times x \times 2(x-3)\\\\108=x(x-3)\\\\108=x^2-3x\\\\x^2-3x-108=0$

Now we will find the roots of x by factorizing the equation we get;

$x^2-12x+9x-108=0\\\\x(x-12)+9(x-12)=0\\\\(x-12)(x+9)=0$

Now we will solve for 2 values of x we get;

$x-12=0\\\\x=12\ ft\\\\Also;\\\\x+9=0\\\\x=-9\ ft$

Now we get 2 values of 'x' one positive and one negative.

Since x is base of the triangle which cannot be negative.

so we will discard the negative value.

Hence;

base of triangle = 12 ft

Height of the triangle = $2x-6=2\times12-6 =24-6 =18\ ft$

Hence Base of the mirror is 12 feet and height of the mirror is 18 feet.

7 0

3 years ago

You are designing a wall Mural that will be composed of squares of different sizes. One of the requirements of your design is th

Oxana [17]

Answer:

1. Area of a square = (x^2)^2 = x^4

(each side is x^2, area of a square = side^2

so (x^2)(x^2) = x^4 )

2. when x = 5

area = 5^4 = 625

3. when x = 10

area = 10^4 = 10000

Step-by-step explanation:

Hope its right!

6 0

3 years ago