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4 years ago

Will mark brainliest. Find cos(a-(π/4)), if cos(a)= -(1/3)

Mathematics

1 answer:

grigory [225]4 years ago

6 0

Answer:

Step-by-step explanation:

$cos(\frac{-1}{3}-\frac{\pi }{4})$

$cos(\frac{-4}{12}-\frac{3\pi }{12})$

$cos(\frac{-13.42}{12})$ = 0.44 <- rounded to the nearest hundredth

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Find the centroid of the quarter of the unit circle lying in the third quadrant.

asambeis [7]

As you know that Centroid is the point of any curve ,Starting from a line segment it's centroid is it's mid point, want to say that centroid means the point where the curve is balanced such that if at that point if you put anything it will remain balanced in all directions, whether it is a one dimensional figure,two dimensional figure,or three dimensional figure.For a circle it's center is the Centroid.

Now coming to your question

Centroid of the quarter of the unit circle lying in the third quadrant.

Circle being a two dimensional figure. The equation of circle is

$x^2+y^2=1\\$

Applying the rule of integration i.e from (-1,0) to (0,-1). i.e from $x_{1}=-1 \text{ to } x_{2} =0 \text{ and } y_{1}=0\text{ to } y_{2} =-1$ -----[∵ we have to find centroid of a circle lying in the third quadrant.]

$x^2+ y^2=1\\y^2=1-x^2\\y=\sqrt{1-x^{2}}$

Applying the formula of centroid i.e

$\bar{x}=\frac{1}{A}\int_{a}^{b}xy\text{ dx }\\\bar{y}=\frac{1}{2A}\int_{a}^{b}y^{2}\text{ dx }\\ \text{ or }\\\bar{y}=\frac{1}{A}\int_{a}^{b}yx\text{ dy }$

where A is the area of circle which is $\pi r^{2}$ .

Area of unit circle=π

Area of Quadrant of a circle=π/4

$\bar{x}=\frac{4}{\pi}\int_{-1}^{0}x\sqrt{1-x^2}\text{ dx }$

put, (1-x²)=t

differentiating both sides

-2 x dx = dt

x dx= - (dt/2)

Also when , x= -1, t=0 and when x=0 then t=1

$\bar{x}=-\frac{4}{3\pi}\int_{0}^{1}\sqrt{t}\text{ dt }}$

$\bar{x}=-\frac{4}{3\pi}{ t ^ \frac{3}{2}}_{0}^{1}$

x coordinate= $\bar{x} =-\frac{4}{3\pi}$

Now finding the y -cordinate by using the above formula

$\bar{y}=\frac{2}{\pi }\int_{0}^{-1}y^{2}\text{ dx }$

$\bar{y}=\frac{2}{\pi}\int\limits^{-1}_{0} {1-x^2} \, dx$

$\bar{y}=\frac{2}{\pi }[x-\frac{x^3}{3}]_{0}^{-1}$

$\bar{y}=-\frac{4}{3\pi}\\centroid(-\frac{4}{3\pi},-\frac{4}{3\pi})$

5 0

4 years ago

What is the value of x in circle c

sladkih [1.3K]

The value of X in the circle C is 1.6 (The 6 is repeated! )

5 0

4 years ago

For two independent events, A and B, P(A)equals . 3 andP(B)equals . 2 . a. Find P(Aintersect B). b. Find P(A|B). c. Find

Gnoma [55]

Answer:

a) 0.06

b) 0.3

c) 0.44

Step-by-step explanation:

We are given the following in the question:

A and B are two independent events.

P(A) = 0.3

P(B) = 0.2

a) P(A intersect B)

$P(A\cap B) = P(A)\times P(B) = 0.3\times 0.2 = 0.06$

b) P(A|B)

$P(A|B) = \dfrac{P(A\cap B)}{P(B)} = \dfrac{0.06}{0.2} = 0.3$

c) P(A union B)

$P(A\cup B) = P(A) + P(B) - P(A\cap B)\\P(A\cup B) = 0.3 + 0.2 - 0.06 = 0.44$

3 0

3 years ago

A safety regulation states that the maximum angle of elevation for a rescue ladder is 72º. A fire department's longest

Svetradugi [14.3K]

Answer:

110sin(72°) feet

Step-by-step explanation:

In the right triangle with the 110 ft ladder as the hypotenuse, the side opposite the 72° angle represents the maximum height the ladder will reach. The definition of the sine function tells you ...

Sin = Opposite/Hypotenuse

so the Opposite side will be ...

ladder height = (110 ft)sin(72°)

6 0

3 years ago

5/18 + 4/9 (fractions)

Airida [17]

Answer:

$\frac{13}{18}$