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2 years ago

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Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the st

atement that could be true for g.

1 answer:

notka56 [123]2 years ago

3 0

Options

(A)g(5) = 12
(B)g(1) = -2
(C)g(2) = 4
(D)g(3) = 18

Answer:

(D)g(3) = 18

Step-by-step explanation:

Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8

Then the following properties must hold

The value(s) of x must be between -1 and 4
The values of g(x) must be between 0 and 18.
g(-1)=2
g(2)=9

We consider the options and state why they are true or otherwise.

<u>Option A: g(5)=12</u>

The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.

<u>Option B: g(1) = -2 </u>

The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.

<u>Option C: g(2) = 4 </u>

The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.

<u>Option D: g(3) = 18</u>

This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.

Therefore, Option D could be true.

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Read 2 more answers

Find the volume of a right circular cone that has a height of 12.5 cm and a base with a circumference of 5.8 cm. Round your answ

BaLLatris [955]

Answer:

$V = 11.2 cm^3$

Step-by-step explanation:

Given

Shape: Right Circular cone

Height, h = 12.5 cm

Base circumference, C = 5.8cm

Required:

Calculate Volume

The volume of a cone is calculated as thus;

Volume, $V = \frac{1}{3}\pi r^2h$

Where V, r and h represent the volume, the radius and the height of the cone respectively

But first we need to calculate the radius of the cone.

Using formula of circumference.

$C = 2\pi r$

We have C to be 5.8cm

By substituting this value;

$5.8 = 2\pi r$

Divide through by $2\pi$

$\frac{5.8}{2\pi} = \frac{2\pi r}{2\pi}$

$r = \frac{5.8}{2\pi}$

$r = \frac{2.9}{\pi}$

Now, we can calculate the volume of the cone

By substituting $r = \frac{2.9}{\pi}$ and h = 12.5 cm;

$V = \frac{1}{3}\pi r^2h$ becomes

$V = \frac{1}{3}\pi * (\frac{2.9}{\pi})^2 * 12.5$

$V = \frac{1}{3}\pi * \frac{8.41}{\pi^2} * 12.5$

$V = \frac{1}{3} * \frac{8.41}{\pi} * 12.5$

Take $\pi$ as 3.14

$V = \frac{1}{3} * \frac{8.41}{3.14} * 12.5$

$V = 11.15976$

$V = 11.2 cm^3$ ---- Approximated

Hence, the volume of the cone is; $V = 11.2 cm^3$

4 0

2 years ago

John's commute to work is 20kmhr while Sheri's commute is 500mmin. Who has the fastest commute to work in mihrif 1.61km=1mi? A S

Andreyy89

Answer:

A) Sheri has the faster commute by 6.2 miles/hr.

Step-by-step explanation:

Given

John's commute to work $=20\ km/hr$

Sheri's commute to work $=500\ m/min$

$1.61\ km = 1\ mile$

John's commute to work in miles per hour = $\frac{20\ km}{1 hr}\times \frac{1\ mile}{1.61\ km}= 12.42\ miles/hr$

Sheri's commute to work in miles per hour = $\frac{500\ m}{1\ min}\times \frac{1\ km}{1000\ m}\times \frac{1\ mile}{1.61\ km}\times \frac{60\ min}{1\ hr}= 18.63\ miles/ hr$

We can see that Sheri has a faster commute.

Difference between the rates = $18.63\ miles/ hr-12.42\ miles/hr=6.21\ miles/hr\approx 6.2\ miles/hr$

∴ Sheri has the faster commute by 6.2 miles/hr.

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