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3 years ago

Area of triangles and trapezoids

Mathematics

1 answer:

lianna [129]3 years ago

8 0

Answer:

bh/2 and (top base+bottom base)/2

Step-by-step explanation:

first one for triangles and second one for trapezoids

I hope i'm right

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The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Sav [38]

Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then

$\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v$

$\implies\ln|u|=\ln|v|+C$

$\implies\ln(y^2+4)=\ln|\ln x|+C$

$\implies y^2+4=e^{\ln|\ln x|+C}$

$\implies y^2=C|\ln x|-4$

$\implies y=\pm\sqrt{C|\ln x|-4}$

4 0

3 years ago

13,406,109 pennis into dollars

geniusboy [140]

Answer:

$134,061.09

Step-by-step explanation:

hope this helps

4 0

3 years ago

Read 2 more answers

Elements can have a positive charge, a negative charge, or no charge. Determine the magnitude of each element given below. Eleme

Ipatiy [6.2K]

Answer: $||q_{A}||=5$ , $||q_{B}||= 3$ , $||q_{C}|| = 0$ .

Step-by-step explanation:

The magnitude is an absolute value by definition. Hence, each element has the respective value:

$||q_{A}|| = 5\\||q_{B}|| = 3\\||q_{C}|| = 0\\$

5 0

3 years ago

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-1

Doss [256]

The amount of the substance (At) at any time t is calculated through the equation,
At = (A0)(e^-kt)
where A0 is the initial amount and k is constant.

For the half-life,
ln (At / A0) = ln 0.5 = -k(5270 years)
The value of k is 1.3153x10^-4 / year.
Substituting this value to the same equation, where At = 0.25A0
ln 0.25 = -(1.3153 x 10^-4)(t)
The value of t from this equation is 10540 years. The closest value to this is letter A.

4 0

3 years ago

Read 2 more answers

Consider the function f(x) = x(x-4.

jeyben [28]

Step-by-step explanation:

point (c-2, y) lies on the graph of f(x)=x(x-4)f(x)=x(x−4) .

Step-by-step explanation:

Given function f(x)=x(x-4)f(x)=x(x−4) also point (2+ c,y) is on the graph of f(x) ,

We have to find out of given point which point will also be on the graph of f(x).

Consider the given function f(x)=x(x-4)f(x)=x(x−4)

f(x)=x(x-4)f(x)=x(x−4) can be rewritten f(x)=x^2-4xf(x)=x

−4x

Now we substitute the given point (2+ c, y) in the function given ,

we have,

f(x)=y=x(x-4)f(x)=y=x(x−4)

put for x as 2+c , we have,

\Rightarrow y=(2+c)(2+c-4)⇒y=(2+c)(2+c−4)

Solve, we get

\Rightarrow y=(2+c)(c-2)⇒y=(2+c)(c−2)

Thus, both point (2+c, y) and (c-2, y) lies on the graph of f(x)=x(x-4)f(x)=x(x−4)

Thus, option (1) is correct.

3 0

3 years ago