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3 years ago

What is the area of the shape

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

4 0

Answer:

36cm(squared)

Step-by-step explanation:

The top rectangle is 8*(6-4)2=16cm

the bottom is the square which is 4*5=20cm

16+20=36cm(squared)

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7. Simplify this what’s the answer?

trasher [3.6K]

first the square root of 4 is 2 so we can sub that in.

now we have 2(2*2)^-2.

2 * 2 of course is 4

with 2(4)^-2, keep in mind that negative exponents just mean to "flip" the number and turn the exponents positive.

so 4^-2 is the same as 1/4^2 or 1/16.

finally 1/16 * 2 = 2/16. 2/16 simplified is 1/8.

3 0

3 years ago

Convert the angle \theta=260^\circθ=260

mel-nik [20]

Question:

Convert the angle θ=260° to radians.

Express your answer exactly.

θ = ___ radians

Answer:

260° = 13π/9 or 4.54 rad

Step-by-step explanation:

Given

θ=260°

Required

Convert from degree to radians

To convert an angle in degrees to radians, we simply follow the steps below.

1° = 1 * π/180 rad

Replace the 1° with x

So,

x° = x * π/180 rad.

Now, we assume that x = 260

This means that we substitute 260 for x. This gives

260° = 260 * π/180

260° = 260π/180

Divide numerator and denominator by 20

260° = 13π/9

We can leave the answer in this form or solve further.

Take π as 22/7. This gives

260° = 13/9 * 22/7

260° = 286/63

260° = 4.5396825397

260° = 4.54 rad (Approximated)

3 0

3 years ago

Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

3 years ago

Re-write the equation after you combine

tekilochka [14]

- 2x - 11 = - 25 :) hope this is ok

4 0

3 years ago

Read 2 more answers

Write an EQUATION for the nth term of each arithmetic sequence<br><br> -1,-0.5,0,0.5,...

kaheart [24]

Ninth term is 2.5

you are adding 0.5 each time

-1,-0.5,0,0.5,1,1.5,2,2.5

8 0

3 years ago