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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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Adrian just got hired for a new job and will make $66,000 in his first year. Adrian was told that he can expect to get raises of

Ann [662]

Answer:

Adrian would make $196000 in his 26th year working.

Step-by-step explanation:

Adrian salary in first year = $66,000

As Adrian is expected to get raises of $5,000 every year going forward.

Here is the sequence of Adrian's raises:

5,000, 10000, 15000, 20000, 25000 .....

As the common difference between consecutive terms is constant.

d = 10000 - 5,000 = 5,000 ⇒ d = 15000 - 10000 = 5,000

So, Adrian's raises is in Arithmetic sequence.

a₁ = 5,000

n = 26

$\ a_{n}=a_{1}+(n-1)d$

Put n = 26 to get the total amount of salary raises in Adrian's 26th year.

$\ a_{26}=5000+(26-1)5000$

$\ a_{26}=5000+(25)5000$

$\ a_{26}=5000+125000$

$\ a_{26}=130000$

Total raises amount after 26th year = $130000

Adding total raises after 26th year to the initial salary would let us figure out the total salary Adrian would make in his 26th year.

So,

Total Salary after 26th year = initial salary + total raises of 26 years

= 66000 + 130000

= $196000

So, Adrian would make $196000 in his 26th year working.

Keywords: arithmetic sequence, salary, raises, common difference

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6 0

3 years ago

Triangle QRS is similar to triangle TUV. Using the image below, prove that lines RS and UV have the same slope. You must show al

N76 [4]

Explanation:

Lines will have same slope if they make the same angle with respect to the vertical or horizontal

The similarity statement ∆QRS ~ ∆TUV tells you that ∠R ≅ ∠U.

Angle R is the angle measured clockwise from vertical segment RQ to segment RS. Angle U is the angle measured clockwise from vertical segment UT to segment UV.

Segments RS and UV both make the same angle with a vertical segment, so have the same slope.

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2 years ago

David proved the Law of Cosines with reference to ∆ABC using a different method. Arrange the steps of his proof in the correct s

irinina [24]

image of solution attached below