Question 5: The volume of each cube is given.

Find the domain and range of this relation? (Assume there are arrows at both ends of the relation.)

Radda [10]

Answer:

Domain: ( -∞ , ∞ )
Range: ( -∞ , 4 ]

Step-by-step explanation:

Hi there!

The domain tells us the possible x-values of a function. Because there are arrows at the end of each side, it means the graph is travelling infinitely to both the left and the right side. This means the the domain is all real numbers, meaning that for any value of x, there is a real value for y.

( -∞ , ∞ )

The range tells us the possible y-values of a function. Both sides of the graph are travelling infinitely downwards, starting from 4.

( -∞ , 4 ]

I hope this helps!

5 0

2 years ago

A taxi charges a pick-up fee p!us a charge per mile. Maria paid $15.00 for a 7 mile rode. To my paid $19.50 for a 10 mile ride.

lukranit [14]

Answer:

The y-intercept in coordinate form is (0, 4.5) and represents the taxi pick-up fee. The equation is y=1.5x + 4.5.

Step-by-step explanation:

This question is asking for the slope and y-intercept of a linear equation. A linear equation makes a straight line based on a constant rate of change. For this problem, the cost per mile is the slope, while the independent variable 'x' is the number of miles and the dependent variable 'y' is the total cost. In order to first find slope, you need to use the two points given (7, 15) and (10, 19.5) to set up a change in y / change in x, or (19.5-15)/(10-7) or 4.5/3 which is 1.5. So the slope, or cost per mile is $1.50. To find the y-intercept (b), or the cost of the pick-up fee, simply fill in your equation y=1.5x + b with your other variables and solve for 'b'. So, 15 = (1.5 x7) + b. or 15 = 10.5 +b, subtract 10.5 from both sides of the equation to get b=4.5.

5 0

4 years ago

Find all solutions in the interval [0, 2π). <br> 2 sin2x = sin x

tester [92]

Answer:

The solutions on the given interval are :

$0$

$\pi$

$\cos^{-1}(\frac{1}{4})$

$-\cos^{-1}(\frac{1}{4})+2\pi$

Step-by-step explanation:

We will need the double angle identity $\sin(2x)=2\sin(x)\cos(x)$ .

Let's begin:

$2\sin(2x)=\sin(x)$

Use double angle identity mentioned on left hand side:

$2\cdot 2\sin(x)\cos(x)=\sin(x)$

Simplify a little bit on left side:

$4\sin(x)\cos(x)=\sin(x)$

Subtract $\sin(x)$ on both sides:

$4\sin(x)\cos(x)-\sin(x)=0$

Factor left hand side:

$\sin(x)[4\cos(x)-1]=0$

Set both factors equal to 0 because at least of them has to be 0 in order for the equation to be true:

$\sin(x)=0 \text{ or } 4\cos(x)-1=0$

The first is easy what angles $\theta$ are $y$ -coordinates on the unit circle 0. That happens at $0$ and $\pi$ on the given range of $x$ (this $x$ is not be confused with the $x$ -coordinate).