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gulaghasi [49]
3 years ago
7

Show that the value of cos 30 x tan 60 + sin 30 is an integer

Mathematics
2 answers:
Troyanec [42]3 years ago
7 0

Answer:

ang hirap nang tanong

tatiyna3 years ago
5 0

Answer:

value of cos 30 × tan 60 + sin 30 is an integer...

Step-by-step explanation:

cos 30 =

\frac{ \sqrt{3} }{2}

tan 60 =

\sqrt{3}

sin 30 =

\frac{1}{2}

so, cos 30 × tan 60 + sin 30

\frac{ \sqrt{3} }{2}  \times  \sqrt{3}  +  \frac{1}{2}

=

\frac{3}{2}  +  \frac{1}{2}

=

\frac{4}{2}

=

2

and 2 is an integer , hence we proved that

cos 30 × tan 60 + sin 30 is an integer.

<em>i</em><em> </em><em>hope</em><em> </em><em>it</em><em> </em><em>helped</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em>

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A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marin
sattari [20]

Answer:

Option B. is the answer.

Step-by-step explanation:

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Since coordinates of the point representing rock is (3, 2) and coordinates of the tree are (16, 21) and treasure divides the line joining rock and tree in the ratio of 5:9.

We know the formula to get the coordinates of point P(x, y) joining (a, b) and (c, d) in the ratio of m : n is

P(x, y) = [\frac{(mc+na)}{m+n}, \frac{(md+nb)}{m+n}]

From the given formula,

Coordinates of treasure P = [\frac{((5\times 16)+(9\times 3)}{(5+9)}, \frac{(5\times 21)+(9\times 2)}{(5+9)}]

= [\frac{(80)+(27)}{(14)}, \frac{(105)+(18)}{(14)}]

= [7.64, 8.78]

≈ (7.6, 8.8)

Therefore, Option B will be the answer.

4 0
4 years ago
What is the equation of the line graphed below?
Nastasia [14]

Answer:

Option C is correct.

The equation of line graphed is, y = \frac{1}{2}x

Step-by-step explanation:

Point slope form: The straight of line in the form of :

y-y_1 =m(x-x_1)   ......[1] where m is the slope.

Consider two points from the given graph:

(0, 0) and (2, 1)

First calculate slope:

Slope(m) = \frac{y_2-y_1}{x_2-x_1}

Substitute the given values we have;

m = \frac{1-0}{2-0} = \frac{1}{2}

Substitute the given values m and (0,0) in [1] we have;

y-0 =\frac{1}{2}(x-0)

Simplify:

y = \frac{1}{2}x

therefore, the equation of line graphed is, y = \frac{1}{2}x

4 0
3 years ago
F(x)=-8x+20;5-2[f(-1)]<br>​
Anni [7]

Answer:

Step-by-step explanation:

f(x) = -8x + 20

f(-1) = -8* -1 + 20 = 8+20 =28

5 -  2[f(-1)] = 5 - 2*28 = 5 - 56 = -51

8 0
3 years ago
AD is tangent to circle B at point C. What is the measure of BCA? O 40° O 50° O 90° O 180° ​
blagie [28]

Answer:

C

90

Step-by-step explanation:

B is likely the center, I think. You can't do it otherwise.

The tangent and a radius of a circle meet at 90o

therefore the answer is 90.

All of this could be confirmed with a diagram.

7 0
3 years ago
Wha is the area of this
Korvikt [17]

Octagon, stop sign.

Eight isoscles triangles.   It looks like we're told the side is 9.9 and the height to the side (also called the apothem) is 12.

So each isosceles triangle has area  (1/2)(9.9)(12) and we have eight of them,

area = 8(1/2)(9.9)(12) = 475.2

Answer: 475.2

Usually we wouldn't be told 9.9 -- this is the baby version.  We know each of those isoscles triangles has unique angle 360/8=45 degrees, so the apothem and half the side of the octagon are a right triangle with acute angle 22.5 degrees.

The area of the right triangle with long leg 12, short leg x,

tan 22.5 = x/12 or

x = 12 tan 22.5

Twice that is what we're told is 9.9; let's check:

2x = 24 tan 22.5 = 9.941125496954282

The area of the little right triangle is

(1/2) 12 × 12 tan 22.5

and there are 16 of these

16 (1/2) 12 × 12 tan 22.5 ≈ 477.174

6 0
3 years ago
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