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1 year ago

Part 1 -Sample roller coasters warm up:

Mathematics

1 answer:

Ann [662]1 year ago

3 0

Answer:

Step-by-step explanation:

h(t) = 0.3t -t +21t , t=time and h=height

at t=0 the hight is h=0

h(0) = 0.3*0 -0 +21*0 = 0

It makes sense that at the time 0 seconds when the rollercoaster did not leave the hight is 0 feet.

for t=10 substitute t with 10

h(10) = 0.3*10 -10 +21*10 = 3 -10 +210 = 203

3. see graph

4. the rollercoaster is going up

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Complete the table of values

Agata [3.3K]

Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, $3^{-2} =
\frac{1}{3^{2} }$ .
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, $(\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} }$ .
3) The zero exponent rule says that any number raised to zero is 1. For example, $3^{0} = 1$ .


Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is $y = 4^{-x}$ . The x-values are:
1) x = 0
Plug this into $y = 4^{-x}$ to find letter a:
$y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1$

2) x = 2
Plug this into $y = 4^{-x}$ to find letter b:
$y = 4^{-x}\\ 
y = 4^{-2}\\ 
y = \frac{1}{4^{2}} \\ 
y= \frac{1}{16}$

3) x = 4
Plug this into $y = 4^{-x}$ to find letter c:
$y = 4^{-x}\\ 
y = 4^{-4}\\ 
y = \frac{1}{4^{4}} \\ 
y= \frac{1}{256}$


Problem 2
The x-values are in the left column. The title of the right column tells you that the function is $y = (\frac{2}{3})^x$ . The x-values are:
1) x = 0
Plug this into $y = (\frac{2}{3})^x$ to find letter d:
$y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1$

2) x = 2
Plug this into $y = (\frac{2}{3})^x$ to find letter e:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9}$

3) x = 4
Plug this into $y = (\frac{2}{3})^x$ to find letter f:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}$

-------

Answers:
a = 1
b = $\frac{1}{16}$ 
c = $\frac{1}{256}$
d = 1
e = $\frac{4}{9}$
f = $\frac{16}{81}$

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2 years ago

Use the figure below to estimate the indicated derivatives, or state that they do not exist. If a derivative does not exist, ent

tatiyna

F(x)=3x/2 for 0≤x≤2
.....=6 - 3x/2 for 2<x≤4 
g(x) = -x/4 + 1 for 0≤x≤4 and g'(x)=-1/4 
so h(x)= f(g(x)) = (3/2)(-¼x+1)=-3x/8 + 3/2 for 0≤x≤2 
for x=1, h'(x)=-3/8 so h'(1)=-3/8 

When x=2, g(2)=1/2 so h'(2)=g'(2)f '(1/2)= -(1/4)(3/2)=-3/8 

When x=3, h(x)=6 - (3/2)(1 - x/4) = 9/2 +3x/8 
h'(x)=3/8 so h'(3) = 3/8

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2 years ago

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each stu

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If one is to choose among given choices and the order is not important, we use the concept of combination. First, we calculate for the sample space or number available since there is a total number of 12 electives and a student may choose 2 out of them.
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What is the domain and range of the equation y=500(1.08)^x

Marina CMI [18]

(x) is an element of a real number. This means it could be an integer, fraction or irrational number.

* As x approaches infinity, y approaches infinity.

* As x approaches minus infinity, y approaches 0.

-------------

Domain:

(x) is an element of a real number

Range:

y>0

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2 years ago