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1 year ago

To the nearest millimeter, a cell phone is 135 mm long and 48 mm wide. What is the ratio of the width to the length

Mathematics

1 answer:

Katena32 [7]1 year ago

6 0

Answer:

48:135

width:length replace width and length with the given value and thats where we get

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Determine the domain of the function (f o g)(x) where f(x)= 3/x+2 and g=5/x.

vitfil [10]

Answer:

The Domain is all real values of x except x = 0 and x = -2.5.

Step-by-step explanation:

I am assuming that f(x) = 3/(x + 2).

(f o g)x is found by substituting 5/x for the x in 3/(x + 2).

(f o g) x = 3/ ( 5/x + 2)

= 3 / ( 5+2x) / x

= 3x / (5 + 2x).

When finding the domain you first check for values of x which make g(x) undefined then values of x which make (f o g)(x) undefined.

x = 0 makes g(x) = 5/0 so it is undefined and x = -2.5 makes g o f undefined also.

7 0

2 years ago

Bus A and Bus B leave the bus depot at 8 am.

LenaWriter [7]

Answer: 10:55

Step-by-step explanation:

Taking statement at face value and the simplest scenario that commencing from 08:00am the buses take a route from depot that returns bus A to depot at 25min intervals while Bus B returns at 35min intervals.

The time the buses will be back at the depot simultaneously will be when:

N(a) * 25mins = N(b) * 35mins

Therefore, when N(b) * 35 is divisible by 25 where N(a) and N(b) are integers.

Multiples of 25 (Bus A) = 25, 50, 75, 100, 125, 150, 175, 200 etc

Multiples of 35 (Bus B) = 35, 70, 105, 140, 175, 210, 245 etc

This shows that after 7 circuits by BUS A and 5 circuits by Bus B, there will be an equal number which is 175 minutes.

So both buses are next at Depot together after 175minutes (2hr 55min) on the clock that is

at 08:00 + 2:55 = 10:55

6 0

2 years ago

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .