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3 years ago

What is a relation and what makes it different from a function? How can you determine the domain and range of a function?

Mathematics

1 answer:

Misha Larkins [42]3 years ago

6 0

Answer:

Note that both relations and functions have domains and ranges. The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range.

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1. To the nearest degree, find the measure of angle A.

Assoli18 [71]

Answer:

(1) Option A is correct , The measure of angle A = 26°

(2) Option D is correct, The measure of angle B =70°

Step-by-step explanation:

(1)

In a right angle triangle figure-1 ,

* Hypotenuse(H) is always opposite the right angle and it is always the longest side of the triangle.

* Adjacent side (B) is the non-hypotenuse side that is next to a given angle A.

* Opposite side(P) is across from a given angle A.

To find the Angle A we use the Cosine ratio:

Cosine ratio states that the ratio of the adjacent side of a right triangle to the hypotenuse.

By definition of cosine ratio we have;

$\cos A = \frac{B}{H}$ ....[1]

In the figure - 1 we have B = 18 in and H = 20 in

substitute these in [1] to find angle A

$\cos A =\frac{18}{20} =\frac{9}{10} = 0.9$

$A = cos^{-1} (0.9)$

⇒ $A \approx 26^{\circ}$

therefore, the measure of angle A is, $26^{\circ}$

(2)P

In figure -2

Find the measure of angle B.

First find the side BC, using Pythagoras theorem;

Pythagoras theorem states that in the right angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Apply Pythagoras theorem in rt. angle ABC;

$AB^2 = AC^2+BC^2$

Substitute the values of AB = 5.1 cm and AC =4.8 cm to solve for BC

$(5.1)^2=(4.8)^2 +BC^2$

$26.01 = 23.04+BC^2$

Simplify:

$BC^2 = 2.97$ or

$BC = \sqrt{2.97} =1.723 cm$

Now, find the angle B, using tangent ratio;

Tangent ratio states that the ratio of the Opposite side of a right triangle to the adjacent side.

$\tan B = \frac{AC}{BC} =\frac{4.8}{1.732} =2.772$

$B = \tan^{-1} (2.772) \approx 70^{\circ}$

Therefore, the measure of angle B is; $70^{\circ}$ .

4 0

3 years ago

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A horse travels an average speed of 12 miles per hour how long does it take a horse to travel 60

olganol [36]

5 hours hun just divide and times and maybe you will find it

8 0

3 years ago

Please help me with this I will make you brainlist if you respond with no links and fully! Do NOT steal points.

inessss [21]

Answer: C. 113.1 cubic centimeters

Step-by-step explanation:

Volume of a sphere= $\frac{4}{3}$ (3.14)(r)^3

Since we know r then just plug in to get 4/3(3.14)(3)^3= 113.1

So the answer is C

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2 years ago

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A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

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

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

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3 years ago

I really need on these cause I really don't know this and I need to understand. please help me please.

lawyer [7]

Answer:

-6m^4-m^3

Step-by-step explanation:

First you move the parenthesis then you group the like terms after you group the like terms you get $m^4-7m^4-m^3$ which is adding the similar elements and after you add similar elements you get -6m^4-m^3. Srry if this makes no sense

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3 years ago

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