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3 years ago

What’s the area of an circle with the diameter 14cm

Mathematics

2 answers:

ryzh [129]3 years ago

3 0

153.86 is the answer because the formula is Pi times radius squared. So, the equation would be 3.14X7^2=3.14X49=153.86

Artemon [7]3 years ago

3 0

153.93cm2 is what I got for my answer

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Two birds sit at the top of two different trees. The distance between the first bed and a birdwatcher on the ground is 34 feet t

stira [4]

Answer:

Step-by-step explanation:

The given triangle is a right angle triangle.

The distance between the first bed and the bird watcher on the ground represents the opposite side of the right angle triangle.

The distance between the birdwatcher and the second bird is 47 feet. This represents the hypotenuse of the right angle triangle. To determine the angle of depression, x degrees, we would apply the Sine trigonometric ratio which is expressed as

Sin θ = opposite side/hypotenuse

Sin x = 34/47 = 0.723

x = Sin^-1(0.723)

x = 46.3 degrees to the nearest tenth.

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3 years ago

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Rina8888 [55]

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2 years ago

Find the length of the altitude to the hypotenuse. Round the answer to the nearest tenth, if needed.

SVEN [57.7K]

To solve this, it might be easier to draw it out (see the picture below). I split it into two triangles and used trig functions to find the altitude. I used the big triangle to find theta, and the used theta to find the side of the altitude. *remember that sine= opposite/hypotenuse*

8 0

3 years ago

find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8)

frutty [35]

Answer:

cosФ = $\frac{1}{\sqrt{65}}$ , sinФ = $-\frac{8}{\sqrt{65}}$ , tanФ = -8, secФ = $\sqrt{65}$ , cscФ = $-\frac{\sqrt{65}}{8}$ , cotФ = $-\frac{1}{8}$

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

cosФ = $\frac{x}{r}$
sinФ = $\frac{y}{r}$
tanФ = $\frac{y}{x}$
secФ = $\frac{r}{x}$
cscФ = $\frac{r}{y}$
cotФ = $\frac{x}{y}$

Where r = $\sqrt{x^{2}+y^{2} }$ (the length of the terminal side from the origin to point (x, y)

You should find the quadrant of (x, y) to adjust the sign of each function

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = $\sqrt{x^{2}+y^{2} }$

∵ x = 1 and y = -8

∴ r = $\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}$

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = $\frac{x}{r}$

∴ cosФ = $\frac{1}{\sqrt{65}}$

∵ sinФ = $\frac{y}{r}$

∴ sinФ = $-\frac{8}{\sqrt{65}}$

∵ tanФ = $\frac{y}{x}$

∴ tanФ = $-\frac{8}{1}$ = -8

∵ secФ = $\frac{r}{x}$

∴ secФ = $\frac{\sqrt{65}}{1}$ = $\sqrt{65}$

∵ cscФ = $\frac{r}{y}$

∴ cscФ = $-\frac{\sqrt{65}}{8}$

∵ cotФ = $\frac{x}{y}$

∴ cotФ = $-\frac{1}{8}$

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3 years ago

A person creates a game in which a person pays $5.00 to play. Then, they draw a single card from a standard shuffled deck of car

valkas [14]

Answer:

Step-by-step explanation:

The expected value is the probability of an event multiplied by the number of times the event happens. And if there is more than 1 event, the expected value is the sum of those.

There are 52 cards in a deck.

There are 12 face cards in a deck. (gain 10)

There are 4 ace in a deck. (gain 20)

Any other card is 36 of them. (lose 5)

The probability of face card is 12/52

The probability of ace is 4/52

The probability of any other card is 36/52

Thus the expected values is:

(12/52)(10) + (4/52)(20) + (36/52)(-5) = $0.38

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3 years ago

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