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3 years ago

5

A carpenter cuts a board into three pieces of equal length ... smallest board is 1 ft. in length, how long was the original boar

d?

1 answer:

Nadusha1986 [10]3 years ago

4 0

3 feet? maybe. This question was confusing to read.

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(Please show step by step workings)

matrenka [14]

Answer:

a. They will need $90,000.00 for the down payment

b. The mortgage amount (principal) will be $360,000.00

c. The monthly principal payment will be $1,500,00

The monthly interest payment will be $634.40

d. The total interest they will pay: $152,256.00

Step-by-step explanation:

house price= $450,000

down payment = 20%

20-year mortgage

Interest rate= 3.75%

a. How much they will need for the down payment?

The down payment (DoP) is 20% of the house price

DoP= 20% de $450,000

DoP= 0.20*450,000

DoP= $90,000

b. What will be the mortagage amount (the principal)?

The mortgage amount (MoA) (principal) is the difference between the house price and the down payment.

MoA= $450,000 - $90,000

MoA= $360,000

c. How much will their monthly payment be for the principal and interest?

This equation represents the monthly payment (M):

$M=P \frac{r(1+r)^{n} }{(1+r)^{n}-1}$

where

P= the principal = $360,000

r= monthly interest rate = 3,75% divided by 12 = 0,31%

n= number of payments = 20 years multiplied by 12 months = 240

Let´s input these data into the equation:

$M= 360,000\frac{0.0031(1+0.0031)^{240} }{(1+0.0031)^{240} -1}$

$M= 360,000\frac{0.0031(1.0031)^{240} }{(1.0031)^{240} -1}$

Solving the equation:

M= $2,134.40

the principal component of this M would be

$360,000 divided by the 240 months

So, the principal component of M = $1,500.00

And the interest component of M is the difference

$2,134.40 - $1,500.00

So, the interest component of M = $634.40

d. How much total interest will they pay if they take the full 20 years to pay off the mortgage?

With every payment, they will be paying:

$634.40 per month, multiplied by 240 months

The total interest will be $152,256.00

5 0

3 years ago

Please prove this........

Crazy boy [7]

Answer: see proof below

<u>Step-by-step explanation:</u>

Given: A + B + C = π → C = π - (A + B)

→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))

→ sin C = sin (A + B) cos C = - cos(A + B)

Use the following Sum to Product Identity:

sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]

cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]

Use the following Double Angle Identity:

sin 2A = 2 sin A · cos A

<u>Proof LHS → RHS</u>

LHS: (sin 2A + sin 2B) + sin 2C

$\text{Sum to Product:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-\sin 2C$

$\text{Double Angle:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-2\sin C\cdot \cos C$

$\text{Simplify:}\qquad \qquad 2\sin (A + B)\cdot \cos (A - B)-2\sin C\cdot \cos C$

$\text{Given:}\qquad \qquad \quad 2\sin C\cdot \cos (A - B)+2\sin C\cdot \cos (A+B)$

$\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]$

$\text{Sum to Product:}\qquad 2\sin C\cdot 2\cos A\cdot \cos B$

$\text{Simplify:}\qquad \qquad 4\cos A\cdot \cos B \cdot \sin C$

LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C $\checkmark$

7 0

3 years ago

Find the amount received by Mr Kumar to paint two walls of the bridge if cost per m^2 is Rs 30.

statuscvo [17]

Step-by-step explanation:

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8 0

3 years ago

You plan to go snowboarding this weekend in Colorado. The resort charges $20.75 per hour addition to a $35 deposit to rent a sno

zhannawk [14.2K]

Answer:

$160.75

Step-by-step explanation:

Step one:

given data

The resort charges $20.75 per hour in addition to a $35 deposit to rent a snowboard

The time spent from 8:30 am to 12:30 pm = 4hours

Step two:

Let the number of hours be and the total cost be y

Now the expression for the situation can be represented as

y= 20.75+35x

for x= 4

y=20.75+35(4)

y=20.75+140

y=160.75

8 0

2 years ago

you find an apartment on Craigslist that is advertised as having an area of 700 square feet. How big is the apartment in square

skelet666 [1.2K]

Answer:

x = 77.8 square yards

Step-by-step explanation:

Given the following data;

Area = 700 square feet

To find the area in square yards;

Conversion:

1 yard = 3 feet

1 square yard = 9 square feet

x square yard = 700 square feet

Cross-multiplying, we have;

700 = 9x

x = 700/9

x = 77.8 square yards

3 0

2 years ago