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3 years ago

Is 8/15 closest to 0,1/2"or 1

Mathematics

1 answer:

Bumek [7]3 years ago

6 0

8/15 is closest to 1/2

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A car is traveling at a speed of 75 miles per hour and arrives at its final destination in total of 5.25 hours. What is the dist

GuDViN [60]

Answer:

Step-by-step explanation:

8 0

2 years ago

If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

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

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

Please help I don’t get it!!! 3(-x+2)

Dennis_Churaev [7]

Answer:

-3x + 6

Step-by-step explanation:

Distribute the 3 across the parentheses, like you are multiplying. 3 x (-x) = -3x and 3 x 2 = 6. Then write as an expression.

3 0

2 years ago

Read 2 more answers

A shopkeeper fixed the marked price of his radio to make a profit of 30 percentage. allowing rs 30 as a discount then the profit

dusya [7]

Answer:

rs 200

Step-by-step explanation:

Let cost price = x

At 30% profit; marked price of radio is 30% of x = (100% + 30%) = 130%x

Discount = rs 3%

Profit made = 30

Hence,

Marked price - discount = cost price + 30

130%x - 30 = x + 30

1.3x - 30 = x + 30

1.3x - x = 30 + 30

0.3x = 60

Divide both sides by 0.3

0.3x / 0.3 = 60/ 0.3

x =

1.3x / 1.3 = 60 / 1.3

x = 200

Hence, cost price = rs 200

7 0

3 years ago

What is the area of a triangle for one of the legs being 3in and the hypotenuse being 9in

elena55 [62]

The area of a triangle for one of the legs being 3 inches and the hypotenuse being 9 inches is 12.727 square inches

Solution:

Given that to find area of a triangle for one of the legs being 3 inches and the hypotenuse being 9 inches

From given information,

Let "c" = hypotenuse = 9 inches

Let "a" = length of one of the leg of triangle = 3 inches

To find: area of triangle

The area of triangle when hypotenuse and length of one side of triangle is given:

$A = \frac{1}{2} a \sqrt{c^2 - a^2}$

Where, "c" is the length of hypotenuse

"a" is the length of one side of triangle

Substituting the given values we get,

$A = \frac{1}{2} \times 3 \times \sqrt{9^2 - 3^2}$

$A =\frac{1}{2} \times 3 \times \sqrt{81-9}\\\\A =\frac{1}{2} \times 3 \times \sqrt{72}\\\\A =\frac{1}{2} \times 3 \times 8.48528\\\\A = \frac{1}{2} \times 25.45584\\\\A = 12.727$

Thus area of triangle is 12.727 square inches

5 0

3 years ago