All categories

3 years ago

I need help with this question

Mathematics

2 answers:

Furkat [3]3 years ago

5 0

Answer:

This question is tying to introduce an idea that

eventually becomes a calculus question ....

(4^2 + 3(4)) - (0^2+3(0))

4 - 0

28 - 0 = 7

Step-by-step explanation:

nika2105 [10]3 years ago

4 0

Answer:

Step-by-step explanation:

1. Approach

The average rate of change can simply be defined as the slope of a line that passes through any two points on a coordinate plane. In this situation, one is given a function, and one is asked to find the rate of change over an interval.

Given function: $f(x)=x^2+3x$

Intervale, $[0, 4]$

This can be done by evaluating the endpoints of the interval by substituting them into the function. Then writing the resulting the form of a point on the coordinate plane ( $x, y$ ). Finally, one can find the slope of the line that passes through the points by using the following slope formula,

$\frac{y_2-y_1}{x_2-x_1}$

Where ( $x_1,y_1$ ) and ( $x_2,y_2$ ) are coordinate points.

2. Find the points

With the function (f(x)), substitute the end points of the itnerval ( [0, 4] ) into the function to generate coordinate points,

$f(x)=x^2+3x$

[ 0, 4 ]

$f(0)=(0)^2+3(0)\\=0 + 0\\ =0$

Point: (0, 0)

$f(4)=(4)^2+3(4)\\= 16 + 12\\ = 28$

Point: (4, 28)

3. Find the average rate of change,

Now substitute the points the formula to find the slope, then simplify to evaluate

$\frac{y_2-y_1}{x_2-x_1}$

(0, 0), (4, 28)

Substitute,

$\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{28-0}{4-0}\\\\=\frac{28}{4}\\\\= 7$

The average rate of change is 7.

You might be interested in

Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B

Vilka [71]

Answer:

66.42°

Step-by-step explanation:

Given:

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

$|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}$

$|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}$

$2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4$

$10\cos{(m\angle{ABC})} = 4$

$\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}$

$m\angle{ABC} = cos^{-1}{(\frac{2}{5})}$

$m\angle{ABC} = 66.4218^{\circ}$

Rounded to two decimal places:

$m\angle{ABC} = 66.42^\circ$

3 0

2 years ago

Please help! Need to confirm my answers.

MariettaO [177]

Answer:

Step-by-step explanation:

Average rate of change is Δy / Δx.

For f(x):

[ f(1) - f(0) ] / (1 - 0)

(1 - 3) / (1 - 0)

-2

For g(x):

[ g(1) - g(0) ] / (1 - 0)

(4 - 3) / (1 - 0)

6 0

3 years ago

Please help! Hurry please!!!!!

Romashka [77]

Its 8:00, because four 15 minutes is 9:00, so when you go back four 15 minutes, its 8:00

7 0

3 years ago

Can you help me with this question?

Rufina [12.5K]

Answer:

16.2

Step-by-step explanation:

The angle internal to the triangle at B is the supplement of the one shown, so is 65°. That is equal to the angle internal to the triangle at D. Since the vertical angles at C are congruent, the two triangles are similar by the AA theorem.

Corresponding sides of similar triangles are proportional, so we can write the proportion shown in the attachment:

BC/FC = DC/AC

BC = FC(DC/AC) = 21.6(7.2/9.6)

BC = 16.2 . . . . matches the first choice

4 0

3 years ago

The dot plot shows the number of pencils each boy has at his desk in class.

Elanso [62]

Answer:

The median is 2

Step-by-step explanation:

Here, we want to get the median for the number of pencils

Firstly, we have to write out the numbers that form the box plot ; we have this as;

1,1,1,2,2,2,2,3,3,5

the median is sum of the 5th and 6th term divided by 2

The 5th term is 2

The 6th term is 2

So the median is;

(2 + 2)/2

= 4/2 = 2

3 0

3 years ago