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3 years ago

9

In indirect variation where y =

1 answer:

vlada-n [284]3 years ago

8 0

Step-by-step explanation:

y=k/x

y=20, x=2

Substitute this first to get "k"

20=k/2

k=40

Value of y when x=10... is now

y= 40/10

y=4.

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Simplify |x| - |-x|.

Verdich [7]

Answer:

0

Step-by-step explanation:

Two cases: if $x\ge0$

$|x| - |-x| = x - x= 0$

Instead if $x$

$|x| -|-x| = -x -(-x)=-x+x=0$

Alternatively you can try to graph both $f(x) = |x|; g(x)=|-x|$ and checking the vertical distance between the two graphs

5 0

3 years ago

The altitude of a triangle is increasing at a rate of 1.500 centimeters/minute while the area of the triangle is increasing at a

puteri [66]

Answer:

The base of the triangle is shrinking at a rate of $\frac{131}{32}$ centimeters per minute.

Step-by-step explanation:

The formula of the area of a triangle is given by the following expression:

$A = \frac{1}{2}\cdot b \cdot h$

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

The base of the triangle is:

$b = \frac{2\cdot A}{h}$

If $A = 98000\,cm^{2}$ and $h = 8000\,cm$ , the base of the triangle is:

$b = \frac{2\cdot (98000\,cm^{2})}{8000\,cm}$

$b = 24.5\,cm$

The rate of change of the area of the triangle in time, measured in minutes, is obtained after differentiating by rule of chain and using deriving rules:

$\frac{dA}{dt} = \frac{1}{2}\cdot h\cdot \frac{db}{dt} + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$

$\frac{dA}{dt} = \frac{1}{2} \cdot \left(h\cdot \frac{db}{dt}+b \cdot \frac{dh}{dt} \right)$

The rate of change of the base of the triangle is now cleared:

$2\cdot \frac{dA}{dt} = h\cdot \frac{db}{dt} + b\cdot \frac{dh}{dt}$

$h\cdot \frac{db}{dt} = 2\cdot \frac{dA}{dt}-b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2\cdot \frac{dA}{dt} - b \cdot \frac{dh}{dt} }{h}$

Given that $\frac{dA}{dt} = 2000\,\frac{cm^{2}}{min}$ , $b = 24.5\,cm$ , $\frac{dh}{dt} = 1500\,\frac{cm}{min}$ and $h = 8000\,cm$ , the rate of change of the base of the triangle is:

$\frac{db}{dt} = \frac{2\cdot \left(2000\,\frac{cm^{2}}{min} \right)-(24.5\,cm)\cdot \left(1500\,\frac{cm}{min} \right)}{8000\,cm}$

$\frac{db}{dt} = -\frac{131}{32}\,\frac{cm}{min}$

The base of the triangle is shrinking at a rate of $\frac{131}{32}$ centimeters per minute.

5 0

3 years ago

Juliana is x years old. Her sister is 2 years older than her. Her mother is 3 times as old as her sister. Her Uncle Rich is 5 ye

s2008m [1.1K]

X=Juliana's age
r=Rich's age

(x+2)+(x*3)+5=R

You can solve it from there

8 0

3 years ago

Read 2 more answers

The following table provides a probability distribution for the random variable y. Y f(y) 1 0. 20 5 0. 30 6 0. 40 9 0. 10 (a) co

Vitek1552 [10]

The probability distribution table is used to represent individual probabilities

The value of E(y) is 5.0

<h3>How to compute e(y)?</h3>

The value of e(y) is calculated using the following expected value formula

$E(y) = \sum y * P(y)$

So, we have:

$E(y) = 1 * 0.20 + 5 * 0.30 + 6 * 0.40 + 9 * 0.10$

Evaluate

$E(y) = 5.0$

Hence, the value of E(y) is 5.0

Read more about probability distribution tables at:

brainly.com/question/9385303

3 0

2 years ago

A cylinder has a radius of 5 and height of 3. what is the volume

Ratling [72]

Answer: Volume of the cylinder is 75π or 235.62 cm³

Volume of cylinder =πr²h

where r is radius and h is height.

Here given radius = 5 and height = 3

Using the formula: πr²h

: π * 5² * 3

: π * 5 * 5 * 3

: 75π or 235.62 cm³

8 0

3 years ago

Read 2 more answers