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3 years ago

What are the domain and range of this function

Mathematics

1 answer:

belka [17]3 years ago

3 0

$f(x)=\sqrt{x-7}+9\\\\\text{the domain:}\\x-7\geq0\to x\geq7\\\\\text{the range:}\\\sqrt{x-7}\geq0\ \text{therefore}\ \sqrt{x-7}+9\geq9\\\\y\geq9$

$Answer:\\domain:\ x\geq7\\range:\ y\geq9$

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Two thirds of the parade vehicles were vintage vehicles and 1⁄3 of the vintage vehicles were motorcycles. What fraction of the t

Liula [17]

Answer:the fraction of the total parade vehicles that are motorcycles is 2/9

Step-by-step explanation:

Let x represent the total number of parade vehicles.

Two thirds of the parade vehicles were vintage vehicles. This means that the total number of vintage vehicles would be

2/3 × x = 2x/3

1⁄3 of the vintage vehicles were motorcycles. This means that the total number of motorcycles would be

1/3 × 2x/3 = 2x/9

Therefore, the fraction of the total parade vehicles that are motorcycles would be

2x/9/x = 2/9

5 0

2 years ago

Find the value of the length x rounded to 1 DP.

bagirrra123 [75]

Length of x is 98.2 m

Step-by-step explanation:

Step 1:

Use the trigonometric ratio tan 27° to find the common side of both the right angled triangles.

tan 27° = opposite side/adjacent side = opposite side/9

∴ Opposite side = 9 tan 27° = 9 × - 3.27 = -29.46 m

Step 2:

Use this side and trigonometric ratio cosine to find the value of x.

cos 49° = adjacent side/x = -29.46/x

∴ x = -29.46/cos 49° = -29.46/0.30

= 98.2 m (negative value neglected)

5 0

2 years ago

Read 2 more answers

Determine the quadrant when the terminal side of the angle lies according to the following conditions: cos (t) < 0, csc (t) &

Bess [88]

Answer:

The angle is in the second quadrant.

Step-by-step explanation:

The cosecant of an angle is the same as the reciprocal of the sine of that angle. In other words, as long as $\sin (t) \ne 0$ ,

$\displaystyle \csc t = \frac{1}{\sin t}$ .

Therefore, $\csc(t) > 0$ is equivalent to $\sin (t) > 0$ .

Consider a unit circle centered at the origin. If the terminal side of angle $t$ intersects the unit circle at point $(x,\, y)$ , then

$\cos (t) = x$ , and
$\sin(t) = y$ .

For angle $t$ ,

$x = \cos(t) < 0$ , meaning that the intersection is to the left of the $y$ -axis.
$y = \sin(t) > 0$ , meaning that the intersection is above the $x$ -axis.