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aliya0001 [1]
1 year ago
12

The size of a population of fish in a pond ismodeled by the function P, where P(t) givesthe number of fish and t gives the numbe

ryears after the first year of introduction of thefish to the pond for 0 < t < 10. The graphof the function P and the line tangent to P att= 4 are shown above. Which of thefollowing gives the best estimate for theinstantaneous rate of change of P at t=4?

Mathematics
1 answer:
Goryan [66]1 year ago
7 0
<h2>Answer:</h2>

The slope of the line joining (3.9, P(3.9)) and (4.1, P(4.1)). Option D is correct.

<h2>Explanations:</h2>

Instantaneous rate of change is the measure of slope of a curve at a given instant.

From the given diagram, we can see that there is a line drawn tangential to the curve. The x-axis (time) for the slope of the curve must lie within the range of the tangential line.

Sine the range of time for the tangential line is between around t = 3 and t = 5, hence the x-axis for the slope must lie within this range.

From the given option, the only coordinate points that lie within the range is (3.9, P(3.9)) and (4.1, P(4.1))

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Oil leaked from a tank at a rate of r(t) liters per hour. the rate decreased as time passed, and values of the rate at two hour
Galina-37 [17]
The given data is
t, h:            0     2     4     6     8   10
r(t), L/h:   8.6  7.9  6.8  6.4  5.7  5.3

The lower and upper estimates for the total amount that leaked may be computed as the Left and Right Riemann sums.

The shape of the graph of r versus will determine which of the two sums yields an upper or lower sum.
The plot of the graph is shown below.

The Left Riemann sum is
Sl = 2*(8.6+7.9+6.8+6.4+5.7) = 70.8 L

The Right Riemann sum is
Sr = 2*(7.9+6.8+6.4+5.7+5.3) = 64.2 L

Answer:
The lower estimate for oil leakage is 64.2 L
The upper estimate for oil leakage is 70.8 L

4 0
3 years ago
Read 2 more answers
Which equation is in point-slope form for the given point and slope?
faust18 [17]

Answer: y-7 = 4(x+3), choice B

============================================

Point slope form is generally

y-y1 = m(x-x1)

we have m as the slope and (x1,y1) as the point this line goes through. In this case,

m = 4

(x1,y1) = (-3,7) so x1 = -3 and y1 = 7

So,

y-y1 = m(x-x1)

y - 7 = 4(x - (-3))

y - 7 = 4(x + 3)

which is why choice B is the answer

6 0
3 years ago
Read 2 more answers
Find the measure of angle of GDE
nikdorinn [45]
I would think it is a 90 degree angle, sorry if I’m wrong.
3 0
3 years ago
Which of the following symbols results in a true number sentence when placed in the blank?
torisob [31]
The term is used as means of asking students to write down equations using simple mathematical symbols (numerals, the four basic mathematical operators, equality symbol)[5]. Sometimes boxes or shapes are used to indicate unknown values. As such number sentences are used to introduce students to notions of structure and algebra prior to a more formal treatment of these concepts.

A number sentence without unknowns is equivalent to a logical proposition expressed using the notation of arithmetic.

[edit] Examples
A valid number sentence that is true: 3 + 7 = 10.

A valid number sentence that is false: 7 + 9 = 17.

A valid number sentence using a 'less than' symbol: 3 + 6 < 10.

An example from a lesson plan:

Some students will use a direct computational approach. They will carry out the addition 26 + 39 = 65, put 65 = 23 + □, and then find that □ = 42.[6] (wikipedia)

<span>I hope this is helpful!
</span>
5 0
3 years ago
Does anybody know the answer???
Romashka [77]
Rotation: a b
Translation:e j
Reflection over a horizontal line: g f
Reflection over a vertical line: c e
Rotation then reflection: a h
Rotation then translation: a d


I’m sorry if this isn’t right
4 0
3 years ago
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