3 years ago

If a 4 x 16 rectangle has the same area as a square, what is the length of a side of the square?

Mathematics

2 answers:

Dima020 [189]3 years ago

5 0

The length of a side of the square would be 8.

Sedbober [7]3 years ago

4 0

The length of the square is 8 hope this helps

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3 years ago

Two vectors A⃗ and B⃗ are at right angles to each other. The magnitude of A⃗ is 5.00. What should be the length of B⃗ so that th

creativ13 [48]

Answer:

Length of B is 7.4833

Step-by-step explanation:

The vector sum of A and B vectors in 2D is

$C=A+B=(a_1+b_1,a_2+b_2)$

And its magnitude is:

$C=\sqrt{(a_1+b_1)^2+(a_2+b_2)^2} =9$

Where

$a_1=Asinx$

$a_2=Acosx$

$b_1=Bsin(x+90)$

$b_2=Bcos(x+90)$

Using the properties of the sum of two angles in the sin and cosine:

$b_1=Bsin(x+90)=B(sinx*cos90+sin90*cosx)=Bcosx$

$b_2=Bcos(x+90)=B(cosx*cos90-sinx*sin90)=-Bsinx$

Sustituying in the magnitud of the sum

$C=\sqrt{(Asinx+Bcosx)^2+(Acosx-Bsinx)^2} =9$

$C=\sqrt{A^2sin^2x+2ABsinxcosx+B^2cos^2x+A^2cos^2x-2ABsinxcosx+B^2sin^2x} =9$

$C=\sqrt{A^2(sin^2x+cos^2x)+B^2(cos^2x+sin^2x)}$

$C=\sqrt{A^2+B^2} =9$

Solving for B

$A^2+B^2 =9^2$

$B^2 =9^2-A^2$

Sustituying the value of the magnitud of A

$B^2=81-5^2=81-25=56$

$B= 7. 4833$

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