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Mathematics

2 answers:

Grace [21]3 years ago

3 0

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zloy xaker [14]3 years ago

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A balloon is rising at a constant speed of 5 ftys. A boy is cycling along a straight road at a speed of 15 ftys. When he passes

Ket [755]

Answer:

13 ft/s

Step-by-step explanation:

t seconds after the boy passes under the balloon the distance between them is ...

d = √((15t)² +(45+5t)²) = √(250t² +450t +2025)

The rate of change of d with respect to t is ...

dd/dt = (500t +450)/(2√(250t² +450t +2025)) = (50t +45)/√(10t² +18t +81)

At t=3, this derivative evaluates to ...

dd/dt = (50·3 +45)/√(90+54+81) = 195/15 = 13

The distance between the boy and the balloon is increasing at the rate of 13 ft per second.

_____

The boy is moving horizontally at 15 ft/s, so his position relative to the spot under the balloon is 15t feet after t seconds.

The balloon starts at 45 feet above the boy and is moving upward at 5 ft/s, so its vertical distance from the spot under the balloon is 45+5t feet after t seconds.

The straight-line distance between the boy and the balloon is found as the hypotenuse of a right triangle with legs 15t and (45+5t). Using the Pythagorean theorem, that distance is ...

d = √((15t)² + (45+5t)²)

7 0

3 years ago

What is the equation in point-slope form that represents the line going through (1,3) and (4,6)

Darya [45]

We have the slope m = (6-3)/(4-1) = 3/3 = 1;
Then, y - 3 = 1·( x - 1);
finally, y = x + 2.

3 0

3 years ago

Which function is undefined for x = 0? y=3√x-2 y=√x-2 y=3√x+2 y=√x=2

Andre45 [30]

For this case, we must indicate which of the given functions is not defined for $x = 0$

By definition, we know that:

$f (x) = \sqrt {x}$ has a domain from 0 to infinity.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. For it to be defined, the term within the root must be positive.

Thus, we observe that:

$y = \sqrt {x-2}$ is not defined, the term inside the root is negative when $x = 0$ .

While $y = \sqrt {x + 2}$ if it is defined for $x = 0.$

$f(x)=\sqrt[3]{x}$ , your domain is given by all real numbers.

Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. In the same way, its domain will be given by the real numbers, independently of the sign of the term inside the root.

So, we have:

$y = \sqrt [3] {x-2}$ with x = 0: $y = \sqrt [3] {- 2}$ is defined.