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soldier1979 [14.2K]

3 years ago

14

The function f(t) = 2t2 + 3t - 1 can be used to determine the position of a worm, f(t), in centimeters, after t seconds. Find th

e average rate of change of the function over the interval [3, 6]?

1 answer:

ExtremeBDS [4]3 years ago

7 0

Use (f(6) - f(3))/3 and you'll get your answer :)

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You are constructing triangle ABC given the line segments AB and AC and ∠A. The first thing you do is copy segment AC. Next, you

nikitadnepr [17]

Answer:

copy AB

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Which term does not belong with the other three?

Brrunno [24]

Answer:

The one that does not belong has a different number of dimensions.

Step-by-step explanation:

<u>Given list consists of:</u>

a line segment (AB)
a plane (CDE)
a line (FG)
a ray (HI)

Three of them have one dimension but the plane has two dimensions,

therefore<u> </u>the plane in the list does not belong with the other three.

<u>So correct answer choice is:</u>

The one that does not belong has a different number of dimensions.

6 0

3 years ago

After analyzing a data set using the one-way ANOVA model, the same data are analyzed using the randomized block design ANOVA mod

Contact [7]

Answer: Always equal to

Step-by-step explanation:

A one way analysis of variance refers to the technique that is used in knowing if there's significant difference between two samples means.

Based on the options given, it should be noted that SS (Treatment) in the one-way ANOVA model is always equal to the SS (Treatment) in the randomized block design ANOVA model.

4 0

3 years ago

Find all the complex roots. Write the answer in exponential form.

dezoksy [38]

We have to calculate the fourth roots of this complex number:

$z=9+9\sqrt[]{3}i$

We start by writing this number in exponential form:

$\begin{gathered} r=\sqrt[]{9^2+(9\sqrt[]{3})^2} \\ r=\sqrt[]{81+81\cdot3} \\ r=\sqrt[]{81+243} \\ r=\sqrt[]{324} \\ r=18 \end{gathered}$ $\theta=\arctan (\frac{9\sqrt[]{3}}{9})=\arctan (\sqrt[]{3})=\frac{\pi}{3}$

Then, the exponential form is:

$z=18e^{\frac{\pi}{3}i}$

The formula for the roots of a complex number can be written (in polar form) as:

$z^{\frac{1}{n}}=r^{\frac{1}{n}}\cdot\lbrack\cos (\frac{\theta+2\pi k}{n})+i\cdot\sin (\frac{\theta+2\pi k}{n})\rbrack\text{ for }k=0,1,\ldots,n-1$

Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.

To simplify the calculations, we start by calculating the fourth root of r:

$r^{\frac{1}{4}}=18^{\frac{1}{4}}=\sqrt[4]{18}$

<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>

Then, we calculate the arguments of the trigonometric functions:

$\frac{\theta+2\pi k}{n}=\frac{\frac{\pi}{2}+2\pi k}{4}=\frac{\pi}{8}+\frac{\pi}{2}k=\pi(\frac{1}{8}+\frac{k}{2})$

We can now calculate for each value of k:

$\begin{gathered} k=0\colon \\ z_0=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{0}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{0}{2}))) \\ z_0=\sqrt[4]{18}\cdot(\cos (\frac{\pi}{8})+i\cdot\sin (\frac{\pi}{8}) \\ z_0=\sqrt[4]{18}\cdot e^{i\frac{\pi}{8}} \end{gathered}$ $\begin{gathered} k=1\colon \\ z_1=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{1}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{1}{2}))) \\ z_1=\sqrt[4]{18}\cdot(\cos (\frac{5\pi}{8})+i\cdot\sin (\frac{5\pi}{8})) \\ z_1=\sqrt[4]{18}e^{i\frac{5\pi}{8}} \end{gathered}$ $\begin{gathered} k=2\colon \\ z_2=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{2}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{2}{2}))) \\ z_2=\sqrt[4]{18}\cdot(\cos (\frac{9\pi}{8})+i\cdot\sin (\frac{9\pi}{8})) \\ z_2=\sqrt[4]{18}e^{i\frac{9\pi}{8}} \end{gathered}$ $\begin{gathered} k=3\colon \\ z_3=\sqrt[4]{18}\cdot(\cos (\pi(\frac{1}{8}+\frac{3}{2}))+i\cdot\sin (\pi(\frac{1}{8}+\frac{3}{2}))) \\ z_3=\sqrt[4]{18}\cdot(\cos (\frac{13\pi}{8})+i\cdot\sin (\frac{13\pi}{8})) \\ z_3=\sqrt[4]{18}e^{i\frac{13\pi}{8}} \end{gathered}$

Answer:

The four roots in exponential form are

z0 = 18^(1/4)*e^(i*π/8)

z1 = 18^(1/4)*e^(i*5π/8)

z2 = 18^(1/4)*e^(i*9π/8)

z3 = 18^(1/4)*e^(i*13π/8)

5 0

1 year ago

I am having a conflict with my family what is 7-1×0+3÷3 = ?

ryzh [129]

Follow PEMDAS.

Parenthesis
Exponents
Multiplication & Division
Addition & Subtraction

Alright, do multiplication first, then division. Then, do subtraction then addition.

$7-1*0+3/3= \\ 7-0+3/3= \\ 7 - 0 + 1= \\ 7 + 1 = 8 \\ 7-1*0+3/3 =8$

Hope this helped!

6 0

3 years ago