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2 years ago

Can the statement be written as a biconditional statement and why?????

Mathematics

1 answer:

Gwar [14]2 years ago

5 0

No. Writing it as a biconditional would mean that "If a number is odd, then it is a prime number" is also true. The original statement is true, but the converse is false.

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Look at the triangle show on the right. The Pythagorean Theorem states that the sum of the squares of the legs of a right triang

Vladimir [108]

Answer:

$cos^2\theta + sin^2\theta = 1$

Step-by-step explanation:

Given

$(\frac{b}{r})^2 + (\frac{a}{r})^2$

Required

Use the expression to prove a trigonometry identity

The given expression is not complete until it is written as:

$(\frac{b}{r})^2 + (\frac{a}{r})^2 = (\frac{r}{r})^2$

Going by the Pythagoras theorem, we can assume the following.

a = Opposite
b = Adjacent
r = Hypothenuse

So, we have:

$Sin\theta = \frac{a}{r}$

$Cos\theta = \frac{b}{r}$

Having said that:

The expression can be further simplified as:

$(\frac{b}{r})^2 + (\frac{a}{r})^2 = 1$

Substitute values for sin and cos

$(\frac{b}{r})^2 + (\frac{a}{r})^2 = 1$ becomes

$cos^2\theta + sin^2\theta = 1$

3 0

3 years ago

What is 2x-3=4(x-5)? And also what is 2x squared=50?

Ierofanga [76]

2x - 3 = 4(x - 5)
2x - 3 = 4x - 20
4x - 2x = 20 - 3
2x = 17
x = 8 1/2

2x² = 50
x² = 25
x = $\pm$ √25
x = $\pm$ 5

6 0

2 years ago

Two times the sum of nine and a number is the opposite of 9.

marshall27 [118]

18 that question is confusing so I guessed sorry dude

8 0

2 years ago

How many different ways can 25 students line up for lunch?

zheka24 [161]

$25!=15,511,210,043,330,985,984,000,000$

7 0

2 years ago

Read 2 more answers

A spring has natural length 20 cm. Compare the work W1 done in stretching the spring from 20 cm to 30 cm with the work W2 done i

sashaice [31]

Answer:

W1 = W2 = 50k Joules (assuming W1 and W2 have the same force constant, k)

W1 - W2 = 0

Step-by-step explanation:

Work done in stretching a spring is given by 1/2ke^2

Where, k is force constant and e is extension

e1 = 30cm - 20cm = 10cm

W1 = 1/2k(e1)^2 = 1/2×k×10^2 = 50k Joules

e2 = 40cm - 30cm = 10cm

W2 = 1/2k(e2)^2 = 1/2×k×10^2 = 50k Joules

W1 = W2 = 50k Joules provided W1 and W2 have equal force constant

Therefore, W1 - W2 = 0

7 0

2 years ago