Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like t
2 answers:
Answer:
i) 3.25x ≤ 26.50
ii) Omar can buy 8 bracelets.
Step-by-step explanation:
Omar has a gift card for $40.00.
Omar bought a hat for $13.50
The remaining amount he has = $40.00 - $13.50 = $26.50
He would like to buy souvenir bracelets for his friends.
Each cost = $3.25
Let "x" be the number of bracelets can buy.
3.25x ≤ 26.50
Now we have to solve the inequality.
Dividing both sides by 3.25, we get
x ≤ 8.15
The bracelets cannot be in decimal form.
So we have to round off to nearest whole number.
x ≤ 8
Therefore, Omar can buy 8 bracelets.
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We are given an equation:
This is an equation of a circle. General form of a circle equation is:
Where:
a = x coordinate of a center
b = y coordinate of a center
r = radius of a circle
Motion detector can detect person anywhere within a boundary. The greatest distance at which detector can detect is at the edge of a circle. That distance, between detector and edge of circle, is equal to radius.
From the equation we have:
The greatest distance at which person can be detected is 4ft.
This is an equation of a circle. General form of a circle equation is:
Where:
a = x coordinate of a center
b = y coordinate of a center
r = radius of a circle
Motion detector can detect person anywhere within a boundary. The greatest distance at which detector can detect is at the edge of a circle. That distance, between detector and edge of circle, is equal to radius.
From the equation we have:
The greatest distance at which person can be detected is 4ft.
Answer:
maximum: y = 1
minimum: y = 0.
Step-by-step explanation:
Here we have the function:
y = f(x) = √(1 + x^2 - 2x)
we want to find the minimum and maximum in the segment [0, 1]
First, we evaluate in the endpoints, which are 0 and 1.
f(0) =√(1 + 0^2 - 2*0) = 1
f(1) = √(1 + 1^2 - 2*1) = 0
Now let's look at the critical points (the zeros of the first derivate)
To derivate our function, we can use the chain rule:
f(x) = h(g(x))
then
f'(x) = h'(g(x))*g(x)
Here we can define:
h(x) = √x
g(x) = 1 + x^2 - 2x
Then:
f(x) = h(g(x))
f'(x) = 1/2*( 1 + x^2 - 2x)*(2x - 2)
f'(x) = (1 + x^2 - 2x)*(x - 1)
f'(x) = x^3 - 3x^2 + x - 1
this function does not have any zero in the segment [0, 1] (you can look it in the image below)
Thus, the function does not have critical points in the segment.
Then the maximum and minimum are given by the endpoints.
The maximum is 1 (when x = 0)
the minimum is 0 (when x = 1)
