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2 years ago

3.

Mathematics

2 answers:

katen-ka-za [31]2 years ago

7 0

Answer:

Option B will be your answer

Step-by-step explanation:

B. The balloon starts at a height of 500 ft and rises at a rate of 150 ft.

hope it helps ^_^

d1i1m1o1n [39]2 years ago

6 0

Answer:

the answer is C

Step-by-step explanation:

It shows the line starts at 0.05 a d to get to 3 it has to raise upb150 ft

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For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant

nirvana33 [79]

Answer:

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of $y$ with respect to $x$ over the interval by definition of secant line:

$r = \frac{y(b) -y(a)}{b-a}$ (1)

Where:

$a$ , $b$ - Lower and upper bounds of the interval.

$y(a)$ , $y(b)$ - Function exaluated at lower and upper bounds of the interval.

If we know that $y = 3\cdot x^{2}$ , $a = 3$ and $b = 6$ , then the average rate of change of $y$ with respect to $x$ over the interval is:

$r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}$

$r = 27$

The average rate of change of $y$ with respect to $x$ over the interval $[3,6]$ is 27.

b) The instantaneous rate of change can be determined by the following definition:

$y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}$ (2)

Where:

$h$ - Change rate.

$y(x)$ , $y(x+h)$ - Function evaluated at $x$ and $x+h$ .

If we know that $x = 3$ and $y = 3\cdot x^{2}$ , then the instantaneous rate of change of $y$ with respect to $x$ is:

$y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}$

$y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h$

$y' = 6\cdot x$

$y' = 6\cdot (3)$

$y' = 18$

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

5 0

2 years ago

Can you help me with this!!!!!!!!!

alexira [117]

a. The first variable is x and the second variable is y.

b. The equations are $x+y=12$ and $x-y=8.$

Step-by-step explanation:

Step 1:

The first step is to define the variables. The variables can be any two symbols, letters, characters, etc.

Here let the first variable be x and the let the second variable be y.

So the variables are defined as x and y.

Step 2:

The sum of the given variables is 12.

The first variable + the second variable = 12,

$x+y=12.$

The difference between the two variables is 4.

The first variable - the second variable = 4.

$x-y=4.$

Step 3:

If we add both the equations we get, $2x =16, x= 8$ and $y=4.$

x = 8 and y = 4.

4 0

2 years ago

How do you find X and Y? 4y + 5z = 60 5x + 3y = 60 4x + 3z = 60

oee [108]

Answer:

1. y=5 x=8

2. x=9 y=5

3. x=12 z=4

Step-by-step explanation:

1. 4(5)+5(8)=60

2. 5(9)+3(5)=60

3. 4(12)+3(4)=60

6 0

2 years ago

3x - 6 = 2 - 5x how do i get x

Elanso [62]

Answer:

x=0.875

Step-by-step explanation:

3x-6=2-5x

Add 6 on both sides (6+2)

2x=8-5x

Add 5x on both sides

7x=8

Divide 7 from both sides

x=0.875

4 0

3 years ago

In a recent survey, 40 percent indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of twelve

worty [1.4K]

Answer:

4 people name chocolate

Step-by-step explanation:

Let's first understand the given information.

The survey shows that 40 percent of a finite number of people name chocolate as their favorite flavor of ice cream. Because the survey is reporting a percentage, then 40% means that from 100 people 40 people name chocolate, while the others name a different type of flavor.

Dividing the total of people (100) by the ones who name chocolate (40) then we have:

100/40 = 2.5

Through the above equation we are actually expressing the following:

Total people = 2.5 * (people who name chocolate flavor)

Using this equation if we have now 12 people:

12 = 2.5 * (people who name chocolate flavor)

12/2.5 = (people who name chocolate flavor)

4.8 = people who chose chocolate flavor

Because we can't have 0.8 of a person, then if we have a sample of 12 people, we will expect that 4 of them name chocolate.

5 0

3 years ago