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2 years ago

If cos 60° = 1/2 and sin 60º = root 3/2 find cos 240° and sin 240".

Mathematics

1 answer:

Vesnalui [34]2 years ago

7 0

Answer:

cos 240 deg = -1/2 and sin 240 = - root(3)/2

Step-by-step explanation:

if cos 60° = 1/2 and sin 60º = root 3/2 find cos 240° and sin 240".

we know that cos 240 = cos (60 + 180) = - cos 60 = - 1/2

cosine is negative when the angle is in the 3rd quadrant

sin 240 = sin (60 + 180) = - root(3) /2

sine is also negative in the 3rd quadrant.

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Recall that the volume of a sphere is given by the formula V = 4/3pi to the 3rd

Kisachek [45]

9514 1404 393

Answer:

1. (256/3)π ft³

2. 33.49 ft³

Step-by-step explanation:

1. Put 4 ft into the formula where r is, then simplify.

V = (4/3)π(4 ft)³ = (256/3)π ft³

2. The radius is half the diameter, so is 2 ft. Put that in the formula, along with the value for π, and do the arithmetic.

V = (4/3)(3.14)(2 ft)³ ≈ 33.49 ft³

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2 years ago

To complete this component you will need to insert parentheses in Expression 2 to change the order of operations so the expressi

Alika [10]

Given:

The expression is $5+4\times 2+6-2\times 2-1$ .

To find:

The position of parentheses inserted in the expression to get the value 19

Step-by-step explanation:

We have,

$5+4\times 2+6-2\times 2-1$

Now,

$(5+4)\times 2+6-2\times 2-1=9\times 2+6-4-1$

$(5+4)\times 2+6-2\times 2-1=18+6-5$

$(5+4)\times 2+6-2\times 2-1=18+1$

$(5+4)\times 2+6-2\times 2-1=19$

There are more ways to apply the parenthesis, but we do not get 19.

$5+4*\left(2+6\right)-2*2-1=32\neq 19$

$5+4*2+\left(6-2\right)*2-1=20\neq 19$

$5+4*2+6-2*\left(2-1\right)=17\neq 19$

And many more possibilities.

Therefore, the expression after inserting the parentheses is $(5+4)\times 2+6-2\times 2-1$ .

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2 years ago

6 qts equals ? pints 8 qts equals ? gallons and 48 fl oz equals ? cups

nikdorinn [45]

6 quarts equals 12 pints
8 quarts equals 2 gallons
48 fl oz equals 6 cups

8 0

3 years ago

Read 2 more answers

What is 5,820,000,000 written in scientific notation?

Ksenya-84 [330]

Answer:

Step-by-step explanation:

the decimal would have to move 9 times from the zero position to get to between 5 and 8.

so 5.82 x 10^9

5 0

2 years ago

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Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5

zmey [24]

Differentiate both sides of the equation of the circle with respect to $x$ , treating $y=y(x)$ as a function of $x$ :

$x^2+y^2=5\implies2x+2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac xy$

This gives the slope of any line tangent to the circle at the point $(x,y)$ .

Rewriting the given line in slope-intercept form tells us its slope is

$x=2y+5\implies y=\dfrac12x-\dfrac52\implies\mathrm{slope}=\dfrac12$

In order for this line to be tangent to the circle, it must intersect the circle at the point $(x,y)$ such that

$-\dfrac xy=\dfrac12\implies y=-2x$

In the equation of the circle, we have

$x^2+(-2x)^2=5x^2=5\implies x=\pm1\implies y=\mp2$

If $x=-1$ , then $-1=2y+5\implies y=-3\neq2$ , so we omit this case.

If $x=1$ , then $1=2y+5\implies y=-2$ , as expected. Therefore $x=2y+5$ is a tangent line to the circle $x^2+y^2=5$ at the point (1, -2).

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3 years ago

Read 2 more answers