If we know the values of the sine and cosine of x and y, we can find the value of cos(x - y) by using the ____ Formula for Cosine. State the formula: cos(x - y) = ____.

Answer:

[tex]\tan{\theta} = \frac{\sqrt{11}}{11}[/tex]

Step-by-step explanation:

Cosecant:

The cosecant is one divided by the sine. Thus:

[tex]\csc{\theta} = \frac{1}{\sin{\theta}}[/tex]

Tangent is sine divided by cosine, so we first find the sine, then the cosine, to find the tangent.

Sine and cosine:

[tex]\sin{\theta} = \frac{1}{\csc{\theta}} = \frac{1}{2\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{6}[/tex]

[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]

[tex]\cos^{2}{\theta} = 1 - \sin^{2}{\theta}[/tex]

[tex]\cos^{2}{\theta} = 1 - (\frac{\sqrt{3}}{6})^2[/tex]

[tex]\cos^{2}{\theta} = 1 - \frac{3}{36}[/tex]

[tex]\cos^{2}{\theta} = \frac{33}{36}[/tex]

First quadrant, so the cosine is positive. Then

[tex]\cos^{2}{\theta} = \sqrt{\frac{33}{36}} = \frac{\sqrt{33}}{6}[/tex]

Tangent:

Sine divided by cosine. So

[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}} = \frac{\frac{\sqrt{3}}{6}}{\frac{\sqrt{33}}{6}} = \frac{\sqrt{3}}{\sqrt{33}} = \frac{\sqrt{3}}{\sqrt{3}\sqrt{11}} = \frac{1}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{11}}{11}[/tex]

The answer is:

[tex]\tan{\theta} = \frac{\sqrt{11}}{11}[/tex]

Answer:

[tex]=280[/tex] [tex]in^2[/tex]

Step-by-step explanation:

----------------------------------------

Let's find the surface area of the pink rectangular prism first.

[tex]2*10=20+20=40[/tex]

[tex]4*10=40+40=80[/tex]

[tex]4*2=8+8=16[/tex]

[tex]40+80+16=136[/tex]

The surface area for the pink rectangular prism is [tex]136[/tex] [tex]in^2[/tex].

-------------------->>>>>

Now, let's find the surface area of the green rectangular prism.

[tex]4*7=28+28=56[/tex]

[tex]4*7=28+28=56[/tex]

[tex]4*4=16+16=32[/tex]

[tex]56+56+32=144[/tex]

The surface area for the green rectangular prism is 144 [tex]in^2[/tex].

-------------------->>>>>

Now let's add the surface area of both rectangular prisms to find the surface area of the composite figure.

[tex]136+144=[/tex]

[tex]=280[/tex] [tex]in^2[/tex]

----------------------------------------

Hope this is helpful.

9514 1404 393

Answer:

  224 in²

Step-by-step explanation:

There are a couple of ways to go at this. Here, we choose to figure the areas of each of the prisms individually, then subtract the "hidden" area where they are joined together.

The area of a prism is ...

  A = 2(LW +H(L+W))

Pink area:

  A = 2(10·4 +2(10+4)) = 2(40 +28) = 136 . . . square inches

Green area:

  A = 2(7·4 +4(7+4)) = 2(28 +44) = 144 . . . square inches

One 4 in × 7 in face of the green prism meets with a similar area of the pink prism, so the area hidden at that interface is 2(4·7) = 56 square inches. Then the total surface area of the composite figure is ...

  SA = 136 in² +144 in² -56 in² = 224 in²

Answer:

A. GF

Step-by-step explanation:

The shortest side in a triangle is opposite the smallest angle

<d = 180 -52 -61 =67

The smallest angle is 52 so the smallest side is DG

<f = 180 - 48-85 =50

The smallest angle is 48 so the smallest side is FG

The smallest angle is 48 so the smallest side overall is FG (GF)

Answer:

8.9

Step-by-step explanation:

15.71428571-6.8=8.914285714

We round of to one significant figure because its addition n the lowest is 6.8

Answer:

[tex]8\frac{32}{35}[/tex]

Step-by-step explanation:

Answer:

hope it helps you..........

Answer:

1) Yes, it is a right angle triangle

2)Yes, it is a right angle triangle

3) No, they are not similar.

Step-by-step explanation:

Dimension of triangle A = 48, 55 & 73

Dimension of triangle B = 36, 77 & 85

For any of the triangles to be a right angled one, then;

c = √(a² + b²)

Where a,b & c are side dimensions of a triangle.

Thus;

Triangle A: c = √(48² + 55²)

c = √5329

c = 73

This tallies with what we are given and so it is a right angled triangle.

Triangle B: c = √(36² + 77²)

c = √(7225)

c = 85

Similar to the third side dimension of 85, thus it is true.

For Triangle A & B to be similar, the ratio of the 3 corresponding sides must be in a whole number ratio.

Thus, we have;

48/36 = 1.5

55/77 = 5/7

73/85 = 73/85

Since the ratios are not similar, then we can say that the triangles are not similar.

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  x ≈ 9.3

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(50°) = 6/x

Solving for x gives ...

  x = 6/cos(50°) ≈ 9.3343

  x ≈ 9.3

__

There is no 'c' to find the value of.

Answer:

x ≈ 9.3

Step-by-step explanation:

Since , this is right triangle, we can use trigonometry functions;

cos θ = Adjacent side / Hypotenuse

Where, θ = 50°

Solve for x

cos 50° = 6 / x

Multiply both side by x

cos 50° × x = 6 / x × x

cos 50° × x = 6

divide cos50° by both sides

cos 50° / cos 50° × x = 6 / cos 50°

x = 6 / cos 50°

x ≈ 9.33434296

Nearest tenth :- x ≈ 9.3

Answer:

The answer in each numeral is:

Step-by-step explanation:

To obtain the result in each case, you must replace the variable (n) by the value that appears in the second case, I'll explain it with the first exercise:

As you can see, in the second doesn't appear f(n), but f(4), that means you must replace the "n" in the equation by 4, if we do this, we obtain:

The first answer is 28, now we'll continue with the next exercises:

In this form, you can prove the answers are: 28, -19, -33, and -9 respectively.

Answer:

x = 5q - 15

Step-by-step explanation:

[tex]\frac{7}{7q+21}=\frac{x}{5q^{2}-45}\\\\\frac{7}{7(q+3)}=\frac{x}{5 (q^{2} -9)}\\\\frac{1}{q+3}=\frac{x}{5*(q^{2}-3^{2})}\\\\\frac{1}{q+3}=\frac{x}{5(q+3)(q-3)}\\\\\frac{1}{q+3}*5*(q+3)(q-3)=x\\\\5(q-3)=x\\\\x= 5q-15[/tex]

Answer:

(a)=50%(b)=2.1and(c)=16.1

Step-by-step explanation:

Hope this helps

Answer:

One leg: 3

So, the hypo: 2*3 = 6

And the third is according to the formula for right angle triangles: a^2 + b^ = c^2

So: √9+36= c

6.7 to get an exact number round it: 7

Answer:

sides are √3 ft,2√3 ft,3 ft

Step-by-step explanation:

let one leg=x

length of hypotenuse=2x

third side=3 ft

(2x)²=x²+3²

4x²-x²=9

3x²=9

x²=9/3=3

x=√3 ft

hypotenuse=2√3 ft

Answer:

58

Step-by-step explanation:

58/3 gives a remainder of 1

58/4 gives a remainder of 2

58/5 gives a remainder of 3

Answer:

[tex]m =-4[/tex]

Step-by-step explanation:

Given

[tex]p(m-3 , -6) = p(-7 , -6)[/tex]

Required

Find m

[tex]p(m-3 , -6) = p(-7 , -6)[/tex]

By comparison:

[tex]m-3 = -7[/tex]

Add 3 to both sides

[tex]m = -7+3[/tex]

[tex]m =-4[/tex]

Answer:

-2x^3+x^2+5x-5

Step-by-step explanation:

f(x) = 4 - 2x – 2x^3

g(x) = x² + 7x-9

f(x) + g(x)=4 - 2x – 2x^3+ x² + 7x-9

Combine like  terms

f(x) + g(x) = -2x^3+x^2+5x-5

Answer:

7/19

Step-by-step explanation:

7/19=square root of 11=22-3 19

Answer:

q5 is 4

q6 is 72

Step-by-step explanation:

yan na po ..sana maktulong sau

Answer:

gfs

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Answer:

Interval Notation:

(6,∞)

Inequality Form:

x>6

there ya go

Answer:

cscθ = 5/4, secθ = 5/3

Step-by-step explanation:

First, let's view the drawing that I have attached, with the dot in the bottom left representing the origin. We know that cosecant and secant are the reciprocals of sin and cos respectively, and in order to find sin and cos, we must find the opposite, adjacent, and hypotenuse sides. The hypotenuse is opposite the right angle, equal to √(8²+6²) = 10

Next, we can find sin and cos of θ . sinθ = 8/10=4/5, making cscθ the reciprocal of 4/5, or 5/4

Similarly, cosθ = 6/10=3/5, and secθ = 5/3

Answer:

option A

Step-by-step explanation:

take 45 degree as reference angle

using sin rule

sin 45 = opposite / hypotenuse

[tex]\frac{1}{\sqrt{2} }[/tex] = s/[tex]8\sqrt{2}[/tex]

[tex]\frac{1}{\sqrt{2} } *8\sqrt{2}[/tex] = s

root 2 and root 2 gets cancel

8 = s

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Pick a point (such as K, L, or M). Count one grid square to the left and 7 up. That is its new location.

Answer:

Option A:

x^2 + (y - 2)^2 = 9

Step-by-step explanation:

We know that the equation for a circle centered in the point (a, b) and of radius R is given by:

(x - a)^2 + (y - b)^2 = R^2

So the first thing we need to find is the center of the circle.

We can see that the center is at:

x = 0

y = 2

Then the center is at the point (0, 2)

Now we want our circle to pass through point 2, located at a distance of 2 units from the radius of the first circle.

So the distance between the center and point 2 is 2 units plus the radius of the smaller circle:

And the radius of the smaller circle is one unit.

Then, the radius of a circle centered at (0, 2) that passes through point 2 is:

R = 1 + 2 = 3

Then we have a circle centered at (0, 2) and of radius R = 3

Replacing these in the equation for a circle we get:

(x - 0)^2 + (y - 2)^2 = 3^2

x^2 + (y - 2)^2 = 9

The correct option is A

Answer:

ans: ln (5/8) , ln5 - ln8

Step-by-step explanation:

8e^x -5 = 0

e^x = 5/8

x = ln (5/8)

x = ln5 - ln8

Answer:

Set of alternative optimal solution : 0 ≤ z ≤ 1.5

Hence There will be an infinite set of Alternative optimal solution

Step-by-step explanation:

considering Cx1 = 4

∴ C = 4 / x1

Cx2 = 6

∴ 4x2 - 6x1  = 0

2x2 - 3x1 = 0 ------ ( 1 )

considering Cx3 = 6

C = 6/x3

Cx4 = 3

∴ (6/x3) x4 - 3 = 0

= 2x4 - x3 = 0 ---- ( 2 )

attached below is the remaining part of the solution

set of alternative optimal solution : 0 ≤ z ≤ 1.5

There will be an infinite set of Alternative optimal solution

Answer:B

Step-by-step explanation:

This is the only possible answer trust me

Answer:

segments LJ and LI are congruent

Step-by-step explanation:

look for the little lines (tick marks)

similar marks mean congruent to each other

The two congruent segments in the figure are LJ and LI.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

An included angle is found between two sides that are under consideration. Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

In the figure, the two segments marked are LI and LJ these two segments are congruent to each other. Congruency means the shape and the size of the segments will be equal to each other.

To know more about congruency follow

https://brainly.com/question/2938476

#SPJ2

Answer:

the answer to this question is 36.86989°