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2 years ago

A trapezoidal sum is an underestimate when the function is.

Mathematics

1 answer:

Elis [28]2 years ago

3 0

Answer: Concave down

Explanation:

An example is shown below. We have the concave down parabola $y = -x^2+7$ marked in red. The trapezoidal sum is in blue. The three trapezoids combine to something just a bit smaller than the true area under the curve from x = -2 to x = 1. Therefore, this trapezoidal sum is an underestimate of the true area under the curve.

Every part of each trapezoid is completely below the red curve. In other words, no part of the blue pieces spill above the parabola.

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Please help ASAP. The question is down below. thank you

ira [324]

Answer:

(1,1) minimum point

Step-by-step explanation:

The point on curve of parabola where curve changes direction is referred as the vertex of parabola.

In the given direction we can see that as the curve starts increasing from negative sides of x, first the value of y is decreasing,

then at a point which is v-shaped point(ti-point), there the value of y becomes minimum,

but after that the value of y starts increasing as value of x is increasing .

Thus, at tip -point , we can say that the parabola has changed direction.

and hence tip-point is the vertex.

while carefully looking at we can see that

value of x is 1 and y also is 1

thus vertex is (1,1).

By minimum/maximum point it means, value of x for which the value of y is minimum or maximum.

Here , the value of y at x = 1 is 1 which is minimum, it is clear from this graph that beyond this point,

at every point of curve value of y is greater than one,

Thus, option d is correct choice (1,1) minimum point

Also, remember if parabola is u shaped as shown

vertex is minimum point.

if parabola is inverted u shaped, vertex is maximum point.

3 0

3 years ago

Find the area of the circle with the given radius or diameter. Use pi = 3.14. r = 6

svetoff [14.1K]

The answer is 113.1. Hope this helps

3 0

3 years ago

Read 2 more answers

A restaurant sells taco salads for $4 each and churros

Darina [25.2K]

Answer:

4$ = 6pcs churros and 1.5$= 14 pcs taco salads

Step-by-step explanation:

7 0

3 years ago

The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours

ella [17]

Answer:

137

Step-by-step explanation:

Use the model A = Pe^(kt), where P is the initial number and k is the growth constant. Then, in case 1,

300 = Pe^(k*3)

and in case 2,

4000 = Pe^(k*10). We need to find P and e^k.

300 = Pe^(k*3) can be rewritten as (300/P) = [e^k]^3, which in turn may be solved for e^k:

∛(300/P) = e^k

Now we go back to 4000 = Pe^(k*10) and rewrite it as (4000/P) = [e^k]^10. Substituting ∛(300/P) for e^k, we obtain:

(4000/P) = (300/P )^(10/3)

which must now be solved for P. Raising both sides by the power of 3, we get:

(4000/P)^3 = (300/P)^10. Therefore,

4000^3 300^10

------------- = -------------

P^3 P^10

which reduces to:

4000^3 300^10

------------- = -------------

1 P^7

------------ = -----------

4000^3 300^10

or:

300^10

P^7 = ---------------- = 9.226*10^13 = 92.26*10^12

4000^3

Taking the 7th root of both sides results in P = (92.26*10^12)^(1/7), or

P = 137.26

The initial number of bacteria was 137.

7 0

3 years ago

0=x2+4x-5 using zero product property

Elenna [48]

Answer:

x=1,-5x=1,−5

Step-by-step explanation:

0=(x−1)(x+5)

2 Switch sides.

(x-1)(x+5)=0(x−1)(x+5)=0

3 Solve for xx.

x=1,-5x=1,−5

4 0

3 years ago