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2 years ago

What is the arc length of ab if the angle degree is 60 and the radius is 8 cm

Mathematics

1 answer:

Elis [28]2 years ago

5 0

Answer:

8cm

Step-by-step explanation:

Formula

l=2rsintita/2

l=2*8sin60/2

l=16sin30

l=8cm

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Find the values of x and y. Pls helpI’m helpless at math

Svetradugi [14.3K]

Answer:

x = 1

$y=\frac{\sqrt{3}}{2}$

Step-by-step explanation:

From the given right-angle triangle

The angle = ∠60°

The adjacent to the angle ∠60° is 1/2.

The opposite to the angle ∠60° is y.

The hypotenuse = x

<u>Determining the value of x:</u>

Using the trigonometric ratio

cos 60° = adjacent / hypotenuse

substituting adjacent = 1/2 and hypotenuse = x

$cos\:60^{\circ }=\:\:\frac{\frac{1}{2}}{x}$

$\cos \left(60^{\circ \:}\right)=\frac{1}{2x}$

$\frac{1}{2}=\frac{1}{2x}$ ∵ cos (60°) = 1/2

$2x=2$

Dividing both sides by 2

$\frac{2x}{2}=\frac{2}{2}$

Simplify

$x=1$

Thus, the value of hypotenuse x is:

x = 1

<u>Determining the value of y:</u>

Using the trigonometric ratio

sin 60° = opposite / hypotenuse

As we have already determined the value of hypotenuse x = 1

substituting opposite = y and hypotenuse = 1

sin 60° = y/1

y = 1 × sin 60°

$y=\frac{\sqrt{3}}{2}$ ∵ $\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}$

Therefore, the value of y is:

$y=\frac{\sqrt{3}}{2}$

Summary:

x = 1

$y=\frac{\sqrt{3}}{2}$

5 0

2 years ago

Given that u =< 2,12 >, and z =< -7,5 >

swat32

Using the dot product:

For any vector x, we have

||x|| = √(x • x)

This means that

||w|| = √(w • w)

… = √((u + z) • (u + z))

… = √((u • u) + (u • z) + (z • u) + (z • z))

… = √(||u||² + 2 (u • z) + ||z||²)

We have

u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37

z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74

u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46

and so

||w|| = √((2√37)² + 2•46 + (√74)²)

… = √(4•37 + 2•46 + 74)

… = √314 ≈ 17.720

Alternatively, without mentioning the dot product,

w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩

and so

||w|| = √((-5)² + 17²) = √314 ≈ 17.720

7 0

2 years ago

If f(x)=4x^2+5x, what is f(a+4)

Firlakuza [10]

I think it might be 20 I don't really know that one

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3 years ago

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Two lemon creams plus four fudge cookies have 450 calories. Four lemon creams plus two fudge cookies have 420 calories. How man

Gnoma [55]

Answer:

Each fudge cookie has 80 calories.

Each lemon cream has 65 calories.

Step-by-step explanation:

We will let $\ell$ represent the calories in lemon creams and $f$ represent the calories in fudge cookies.

Two lemon creams and four fudge cookies together have 450 calories. So, we can write the following equation:

$2\ell+4f=450$

And four lemon creams plus two fudge cookies together have 420 calories. So, we can write the following equation:

$4\ell+2f=420$

We now have a system of equations. We can solve this by elimination.

For the first equation, we can multiply both sides by -2. This way, the $\ell$ will cancel when we add the two equations together.

So, the first equation becomes:

$-4\ell-8f=-900$

Add this to the second equation. Hence:

$(-4\ell+4\ell)+(-8f+2f)=(-900+420)$

Simplify:

$-6f=-480$

Divide both sides by -6. Hence:

$f=80$

So, there are 80 calories in one cookie.

We can use the first equation again to find the amount of calories in one cream. We have:

$2\ell+4f=450$

Substituting 80 for $f$ yields:

$2\ell+320=450$

Then it follows that:

$\ell=65$

So, there are 65 calories in each lemon cream.

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2 years ago

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Is it ture equivalent decimals are decimals that have the same value

tester [92]

Yes that statement is true

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2 years ago