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3 years ago

A rope to length 30m is divided in the ratio 2:3. calculate the length of the longest

Mathematics

2 answers:

Vlada [557]3 years ago

8 0

longest part = 18 m

add the parts of the ratio 2 + 3 = 5

divide 30 by 5 to find the value of 1 part of the ratio

$\frac{30}{5}$ = 6 ← 1 part

2 parts = 2 × 6 = 12 m

3 parts = 3 × 6 = 18 m ← longest part

olga2289 [7]3 years ago

4 0

30 : (2 + 3) *3 =

6 * 3 =

18 cm (your answer)

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Find an equation of the circle that satisfies the given conditions. Endpoints of a diameter are P(−2, 1) and Q(8, 9)

IrinaK [193]

Answer:

Equation of the circle (x-3)²+(y-5)²=(6.4)²

x² -6x +9 +y² -10y +25 = 40.96

Step-by-step explanation:

Step(i):-

Given endpoints of diameter P(−2, 1) and Q(8, 9)

Centre of circle = midpoint of diameter

Centre = $(\frac{-2+8}{2} ,\frac{1+9}{2} )$

Centre (h, k) = (3 , 5)

Step(ii):-

The distance of two end points

PQ = $\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }$

$PQ= \sqrt{(8+2 )^{2} +(8 )^{2} }$

PQ = √164 = 12.8

Diameter d = 2r

radius r = d/2

Radius r = 6.4

Final answer:-

Equation of the circle

(x-h)²+(y-k)² = r²

(x-3)²+(y-5)²=(6.4)²

x² -6x +9 +y² -10y +25 = 40.96

x² -6x +y² -10y = 40.96-34

x² -6x +y² -10y -7= 0

4 0

4 years ago

Put them in order from least to greasiest 3/5 1/4 1/2 2/5

alexira [117]

1/4 < 2/5 < 3/5 < 1/2

3 0

3 years ago

Read 2 more answers

Write the equation of the line that passes through the points (- 4, - 3) and (3, - 5) . Put your answer in fully reduced slope i

bekas [8.4K]

Answer:

(-4, -3) y (3, -5)

{-12 y, 15 y}

-12 y + 15 y = 3 y

(3 y)/2

3 sqrt(41) abs(y)

6 0

3 years ago

Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at

Anna007 [38]

Answer:

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84

Step-by-step explanation:

Loan payment per month=Amount to pay÷discount factor

Mathematically P=A÷D

where D is the discount factor calculated using the formula;

$\frac{(1+i)^n-1}{i(1+i)^n}$

where i=periodic interest rate=annual rate divided by number of payment periods

A is the amount to pay after downpayment

P is the loan monthly payment amount

n=number of periodic payments=payments per year times number of years

⇒In this question you find the discount factor then divide the amount remaining to pay with the discount factor to get monthly payments

Given;

Cost of boat=$32000

Down payment=$14000

Loan to pay=$32000-$14000=$18000

Annual rate=5.5%=i=5.5%÷12=0.458%⇒0.00458

Periodic payments, n=4×12=48

Finding the discount factor D;

$D=\frac{(1+i)^n-1}{i(1+i)^n} \\\\\\D=\frac{(1+0.00458)^{48} -1}{0.00458(1+0.00458)^{48} } \\\\\\D=\frac{1.2455-1}{0.005703} \\\\\\D=\frac{0.2455}{0.005703} =43.05$

To get the amount to pay monthly divide the loan to pay with the discount factor

$=\frac{18000}{43.05} =418.14$

Monthly payments=$418.14

Total amount will be=down payment + 48×$418.14

$14000+$20070.84=$34070.84

8 0

3 years ago

Is 4 to 7 the same as 7 to 4 explain why it why not

tino4ka555 [31]

It’s not the same because if you simplify them there going to end up looking different (the answers) And they get a whole different do you denominator a numerator

6 0

3 years ago