Answer:
a. A(x) = (1/2)x(9 -x^2)
b. x > 0 . . . or . . . 0 < x < 3 (see below)
c. A(2) = 5
d. x = √3; A(√3) = 3√3
Step-by-step explanation:
a. The area is computed in the usual way, as half the product of the base and height of the triangle. Here, the base is x, and the height is y, so the area is ...
A(x) = (1/2)(x)(y)
A(x) = (1/2)(x)(9-x^2)
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b. The problem statement defines two of the triangle vertices only for x > 0. However, we note that for x > 3, the y-coordinate of one of the vertices is negative. Straightforward application of the area formula in Part A will result in negative areas for x > 3, so a reasonable domain might be (0, 3).
On the other hand, the geometrical concept of a line segment and of a triangle does not admit negative line lengths. Hence the area for a triangle with its vertex below the x-axis (green in the figure) will also be considered to be positive. In that event, the domain of A(x) = (1/2)(x)|9 -x^2| will be (0, ∞).
__
c. A(2) = (1/2)(2)(9 -2^2) = 5
The area is 5 when x=2.
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d. On the interval (0, 3), the value of x that maximizes area is x=√3. If we consider the domain to be all positive real numbers, then there is no maximum area (blue dashed curve on the graph).
Answer:
P(0,0) = 2/12 times 1/11 = 1/66
Step-by-step explanation:
For probability questions, think of each event happening separately, it makes the maths easier to understand. For example, in this question, do not think of the two boys taking a fruit at the same time - that makes the maths complicated
.
Let Daniel take a fruit first, then Sean can take a fruit. There are two parts to consider.
P
r
o
b
a
b
i
l
i
t
y
=
number of desirable outcomes
total number of possible outcomes
For Daniel: there are 12 different pieces of fruit in the bowl, he just takes one without choosing a specific fruit. (random)
The chance that Daniel takes an orange is
2
12
Of the 12 pieces of fruit. 2 are oranges.
Now Sean: the numbers of fruit in the bowl have changed. There are now only 11 pieces of fruit in the bowl, and only 1 is an orange.
The chance that Sean takes an orange is
1
11
Answer:
−16(2−−5)
Step-by-step explanation:
hay un factor común entre estos números, por lo que simplemente −16t2+16t+80 divida y reutilice y luego reciba−162+16+80 llegar
−16(2−−5)
Answer:
no
Step-by-step explanation:
2 is just 2
This question is incomplete
Complete Question
Kiran buys supplies for the school’s greenhouse. He buys bags of fertilizer and
packages of soil. He pays $5 for each bag of fertilizer and $2 for each package of soil,
and spends a total of $90. The equation
5f + 2p = 90 describes this relationship.
If Kiran solves the equation for p, which equation would result?
A. 2p = 90 − 5f
B. p = 5f − 90
/2
C. p = 45 − 2.5f
D. p =
85
f
/2
Answer:
A. 2p = 90 − 5f
Step-by-step explanation:
The equation
5f + 2p = 90 describes this relationship.
We are to solve for p, this means to make p the subject of the formula , hence:
5f + 2p = 90
Subtract 5f from both sides.
5f - 5f + 2p = 90 - 5f
2p = 90 - 5f
Divide both side by 2
2p/2 = 90 - 5f/2
p = 90 - 5f/ 2
If Kiran solves the equation for p, the equation that would result is
2p = 90 − 5f
.
Further simplified to :
p = 90 - 5f/ 2
Option A is correct.
