Questions 6-9 <br>Math 8

Write the ratios for sin X, cos X, and tan X. Use the / for a fraction.

fgiga [73]

Answer:

Step-by-step explanation:

From the right triangle attached in the picture,

sine ratio for the angle X,

$\text{sinX}=\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$=\frac{YZ}{XZ}$

$=\frac{21}{29}$

cosine ratio for the angle X,

$\text{cosX}=\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

$=\frac{XY}{XZ}$

$=\frac{20}{29}$

tang ratio for the angle X,

$\text{tanX}=\frac{\text{Opposite side}}{\text{Adjacent side}}$

$=\frac{21}{20}$

3 0

3 years ago

Determinar a posição da reta r, de equação 2x-3y+5=0, em relação à reta s, de equação 4x-6y-1=0

My name is Ann [436]

Answer:

$2x - 3y = - 5 - - - (a) \\ 4x - 6y = 1 - - - (b) \\ no \: answers$

5 0

3 years ago

Determine whether each of these functions from Z to Z is one-to-one. a) f(n) = n - 1 b) f(n) = n2 + 1 c) f(n) = nº d) f(n) = [n/

sesenic [268]

Answer: The correct option is

(a) f(n) = n - 1.

Step-by-step explanation: We are given to determine whether the given functions are one-to-one or not.

We know that a function y = f(x) is one-to-one if and only if

f(x) = f(y) ⇔ x = y.

That is, any two distinct elements cannot have the same image.

(a) The given function is

$f(n)=n-1.$

Let us consider that

$f(n_1)=f(n_2)\\\\\Rightarrow n_1-1=n_2-1\\\\\Rightarrow n_1=n_2.$

Similarly,

$n_1=n_2\\\\\Rightarrow n_1-1=n_2-1\\\\\Rightarrow f(n_1)=f(n_2).$

So, this function is one-to-one.

(b) The given function is

$f(n)=n^2+1.$

Let us consider that

$f(n_1)=f(n_2)\\\\\Rightarrow n_1^2+1=n_2^2+1\\\\\Rightarrow n_1^2=n_2^2\\\\\Rightarrow n_1=\pm n_2.$

That is, there may be two unequal elements having same image.

For example, f(-1)=(-1)²+1=1+1=2, f(1)=(1)²+1=1+1=2.

It implies that f(-1)=f(1) but 1 ≠ -1.

So, the given function is not one-to-one.

(c) The given function is

$f(n)=n^0.$

Here, the image of all the elements is 1.

For example, $f(2)=2^0=1,~~f(3)=3^0=1.$

f(2)=f(3) but 2≠3.

So, more than one element is having the same image and so the function cannot be one-to-one.

(d) The given function is

$f(n)=\left[\dfrac{n}{2}\right].$

Here, we see that

$f(2)=\left[\dfrac{2}{2}\right]=[1]=1,\\\\\\f(3)=\left[\dfrac{3}{2}\right]=[1.5]=1.$

So, f(2)=f(3) but 2≠3.

So, the given function is not one-to-one.

Thus, the correct option is (a).

5 0

4 years ago

A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is a 90%

xxMikexx [17]

Answer:

1. How many will be infected next week

From the information, there are 1000 mice in the lab.

200 mice are infected. It is expected that 90% of the mice are expected to overcome the infection and 40% uninfected mice will be infected.

If 200 mice are infected, then number of uninfected mice is:

= 1000 - 200 = 800

90% of infected mice get cured. Out of 200 mice who are infected, the number of mice getting cures is:

N(E) = P(E)×N(S)

= 0.90*200

= 180

The number of mice still infected is 200 - 180 = 20

Out of 800 uninfected mice, 40% will get infected. Number of infected mice is:

N(E) = P(E) * N(S)

= 0.40 * 800

= 320

Total number of infected mice is 320 + 20 = 340 . Thus, the number of infected mice next week is 340

2. How many will be infected in 3 weeks

After three week, the number of infected mice is 340. Therefore, the number of uninfected mice is 1000 - 340 = 660

Now, out of 340 mice, it is expected that 90% will recover. This indicates that 10% will remain infected. Then the number of infected mice is

N(E) = P(E) * N(S)

= 0.10 * 340

= 34

Out of 660 mice, 40% will be infected. The number of mice becoming infected is

N(E) = P(E) * N(S)

= 0.40 * 660

= 264

Total number of infected mice is 264 + 34 =298. Thus, the number of infected mice after two weeks is 298.

5 0

3 years ago

A block is pushed from four sides with forces of different magnitude, as shown in the diagram below. N = North, W = West, S = So

iVinArrow [24]

Answer:

odian quien alas saludos algo tuyo el ella el el el

8 0

3 years ago

Questions 6-9 Math 8