The rate of change of the parabola on the interval [0, 4] is 0.
How to get the average rate of change?For any function f(x), we define the rate of change on an interval [a, b] as:
R = (f(b) - f(a))/(b - a)
Here we want to get the rate of change on the interval [0, 4], and we know that the graph has the points:
(0, 4), (2, -4), (4, 4)
Then:
f(0) = 4
f(4) = 4
Replacing that in the rate of change formula we get:
R = ( f(4) - f(0))/(4 - 0)
R = (4 - 4)/4 = 0
The rate of change on that interval is 0.
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An isosceles triangle with congruent sides of length
49.3 inches has a perimeter of 121.7 inches Find the
length of the base.
The length of the base is 22.1
An isosceles triangle with congruent sides of length 49.3 inches has a perimeter of 121.7 inches
An triangle is said to be isosceles if two sides of the trainagle have same length.
The two sides of this triangle is congurent that is they have same length = 49.3
perimeter of a triangle is the summation of all three sides.
Perimeter = length + base + length
121.7 = 49.3 + base + 49.3
base = 121.7 - 99.6
base = 22.1
Therefore, the length of the base is 22.1
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Juan and Malia make money by walking neighborhood pets. During a conversation about their work, they realize that they are both walking the same total number of pets, even though Juan walks pets in groups of 9 and Malia walks pets in groups of 3. What is the smallest total number of pets each could be walking?
The smallest total number of pets each could be walking is 2.
Given:
Juan and Malia make money by walking neighborhood pets. During a conversation about their work, they realize that they are both walking the same total number of pets, even though Juan walks pets in groups of 9 and Malia walks pets in groups of 3.
from the given statements:
Juan pets groups = 9
Malia pets groups = 3
so they both can same total number of pets is maximum 3.
so minimum number for each is 1.
Total = 1+1
= 2
Therefore The smallest total number of pets each could be walking is 2.
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find the value of b/a if a+1/b-1=5/1 and a-1/b+1=1/1
Answer:
1/2
Step-by-step explanation:
You want the value of b/a when (a+1)/(b-1)=5/1 and (a-1)/(b+1)=1/1.
SolutionThe latter equation tells you ...
a -1 = b +1
b = a -2
Then the first equation tells you ...
a +1 = 5(b -1)
a +1 = 5(a -2 -1) substitute for b
a +1 = 5a -15 . . . . eliminate parentheses
16 = 4a . . . . . . . . add 15 -a
4 = a . . . . . . . . . divide by 4
b = a -2 = 4 -2 = 2 . . . . find the value of b
b/a = 2/4 . . . . . . . . . . find the desired ratio
b/a = 1/2
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The percentage error is 0.67%
What is Linear approximation ?
A linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.
The formula is
L(x) = f(a) + f'(a) (x - a)
Given,
y = sin(2x)
Δx = 0.1 at x = 0
y'(x) = dy/dx = 2 cos 2x
As, x = 0
y'(0) = 2 cos 0
we know, cos 0 = 1
y'(0) = 2
Δy = y'(x) * Δx
= y'(0) * Δx
= 2 * 0.1
Δy = 0.2 (Approx value)
Exact value of Δy = sin(2 * 0.1) - sin 0
= sin(0.2) - 0
= 0.19867
% error = [ (Exact value - Approx value) / Exact value ] * 100
= [ (0.2 - 0.19867) / 0.19867 ] * 100
= 0.66945 or 0.67%
Hence, the percentage error is 0.67%
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Wha is the y intercept of the line given by the equation below y=4x - 6
in a class of 50 student 35 are girls what is the probability that a student selected at random is a boy
Helen had $330 in her savings account when Vince
opened a savings account with zero
dollars.
Helen deposited $30
into her account each week for x week;
Vince deposited $50 into his account
each week for x weeks.
The accounts did not earn
interest.
Which inequality represents this situation when the amount of money in Helen's account wa
greater than the amount of money in Vince's account?
Answer:
Step-by-step explanation:
50x < 330 + 30x
explain what a,h, and k do to transform the parent absolute function y=|x| to the function y= a|x|…
The a ,h and k values affect the parent absolute function ,by altering the the size , causing horizontal and vertical movements respectively.
How do the a , h and k values affect the function?a )a values
a values affect the size of the graphed parent absolute function and they have a scalar factor.When a is greater than 1 , we have a vertical stretch (Taller appearance )and a horizontal compression (Thinner appearance).When a is between 0 and 1 , we have a vertical compression( Shorter appearance) and a horizontal stretch ( wider appearance).b ) h values
h values cause left or right movement of the graph, which is known as the horizontal shift or translation.When h is negative, the graph moves right.When h is positive , the graph moves left.c ) k values
k values cause up and down movement ,which is known as the vertical shift or translation.When k is negative, the graph moves down.When k is positive , the graph moves up.To learn more about parent absolute function, refer:
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Write the given expression as an algebraic expression in x. tan(2 sin^-1(x))
The trigonometric ratio tan(2 sin⁻¹(x)) is expressed as 2sec(x)
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
In the question given, we have;
tan(2 sin⁻¹(x))
tan = sin / cos
sin/cos(2 * 1/sin x)
The expression becomes 2/cosx or 2cos⁻¹(x)
But cos⁻¹ = sec
tan(2 sin⁻¹(x)) = 2sec(x)
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What is 4x6x26x376x466 equal to
Q12) 150 Chinese Yuan is about $21 US dollars. How much (in US dollars) will an item cost in 700 Chinese Yuan?
Answer:
Step-by-step explanation:
Set up the equation:
21/150=x/700
Cross multiply 150*x and 21*700
14700=150x
Divide each side by 150
98=x
