Translate to a system of equations: daniela invested a total of $50,000, some in a certificate of deposit (cd) and the remainder in bonds. the amount invested in bonds was $5,000 more than twice the amount she put into the cd. how much did she invest in each account? call the amount that daniela invested in the cd d and the amount she invested in bonds b.

Daniela invested $35,000 in bonds and $15,000 in a certificate of deposit (CD)

Step-by-step explanation:

We call d the amount Daniela invested in the certificate of deposit (CD) and b the amount she invested in bonds.

The first conditions of the problem is the total amount invested is $50,000, so

The second demands that the amount invested in bonds was $5,000 more than twice the amount she put into the CD

a)

The system of equations is

b) To solve the system, we take b from the last equation and replace it in the first equation:

Rearranging

Solving

And  

Daniela invested $35,000 in bonds and $15,000 in a certificate of deposit (CD)

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm