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3 years ago

What is the area of the triangle? 6 2 3

Mathematics

1 answer:

Llana [10]3 years ago

7 0

Answer:

Step-by-step explanation:

Find the area of both triangles inside the bigger triangle and add them together.

Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:

a² + b² = c²

2² + b² = 3²

4 + b² = 9

5 = b²

2.2 ≈ b

Calculate the area of the smaller triangle:

1/2(bxh)

1/2(2 x 2.2)

1/2(4.4)

2.2

Calculate the area of the bigger triangle:

<em>We know that the longer leg is 3.8 units because we were able to subtract the length of the smaller triangle's leg from 6. </em>

1/2(bxh)

1/2(2 x 3.8)

1/2(7.6)

3.8

Add both areas to find the area of the largest triangle:

3.8 + 2.2 = 6

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3 years ago

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3 years ago

Find the integration of (1-cos2x)/(1+cos2x)

slega [8]

Given:

The expression is:

$\dfrac{1-\cos 2x}{1+\cos 2x}$

To find:

The integration of the given expression.

Solution:

We need to find the integration of $\dfrac{1-\cos 2x}{1+\cos 2x}$ .

Let us consider,

$I=\int \dfrac{1-\cos 2x}{1+\cos 2x}dx$

$I=\int \dfrac{2\sin^2x}{2\cos^2x}dx$ $[\because 1+\cos 2x=2\cos^2x,1-\cos 2x=2\sin^2x]$

$I=\int \dfrac{\sin^2x}{\cos^2x}dx$

$I=\int \tan^2xdx$ $\left[\because \tan \theta =\dfrac{\sin \theta}{\cos \theta}\right]$

It can be written as:

$I=\int (\sec^2x-1)dx$ $[\because 1+\tan^2 \theta =\sec^2 \theta]$

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3 years ago

A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.

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The monthly payment amount is $860.25.

Step-by-step explanation:

Step 1; The bank offers an amount of $195,000 with an APR of 5.3%. This means that the family must pay 5.3% of the $195,000 every year for 30 years. To calculate we must determine how much 5.3% of $195,000 is. To do that we make 5.3% a fraction by dividing it by 100 and multiplying it with the amount.

5.3% of $195,000 = $\frac{5.3}{100}$ × $195,000 = 0.053 × $195,000 = $10,335 per year.

Payment owed for 30 years = Payment owed a year × 30

= $10,335 per year × 30 = $310,050 for 30 years.

Step 2; To find the monthly payments we need to know how many months are in a 30 year period. Months in 30 years = 30 × 12 months = 360 months. The monthly payment is, therefore, payment owed in 30 years divided by the months in that 30 year period.

Monthly payment = $10,335 / 360 = $ 861.25.

So the family must pay a monthly payment of $861.25 for 30 years.

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