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2 years ago

The first three terms of a geometric sequence are as follows.

Mathematics

1 answer:

Rom4ik [11]2 years ago

4 0

-7,14,-28,56,-112

an = a1(r)^n-1

a4 = -7(-2)^4-1

a4 = -7(-2)³

a4 = -7(-8)

a4 = 56

an = a1(r)^n-1

a5 = -7(-2)^5-1

a5 = -7(-2)⁴

a5 = -7(16)

a5 = -112

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2) In 1000 sq. meter of land a farmer cultivated 765 kg of rice with the wastage of 23.5%. I) Find the weight of the wastage. II

LiRa [457]

Answer:

Weight of wastage=179.775kg

weight of rice cultivated= 585.225 kg

percentage of rice cultivated=76.5%

Step-by-step explanation:

Area of land=100 square meters

Cultivated rice=765kg

Wastage=23.5%

1) Weight of the wastage=23.5% of 765kg

=23.5/100 × 765

=17977.5 / 100

=179.775 kg

2) Weight and percentage of rice cultivated.

weight of rice cultivated = 765 kg - 179. 775 kg

= 585.225 kg

percentage of rice cultivated = 100 - 23.5

= 76.5%

3) if area is increased 40 times in size

New area=1000 square meters × 40

=40,000 square meters

Cultivated rice= 765kg × 40

=30,600 kg

Cultivated rice excluding wastage=585.225 kg × 40

=23,409 kg

8 0

2 years ago

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 3x2 − 2x + 1, [0, 2] Yes, it do

expeople1 [14]

Answer:

Yes , function is continuous in [0,2] and is differentiable (0,2) since polynomial function are continuous and differentiable

Step-by-step explanation:

We are given the Function

f(x) = $3x^2 -2x +1$

The two basic hypothesis of the mean valued theorem are

The function should be continuous in [0,2]

The function should be differentiable in (1,2)

upon checking the condition stated above on the given function

f(x) is continuous in the interval [0,2] as the functions is quadratic and we can conclude that from its graph

also the f(x) is differentiable in (0,2)

f'(x) = 6x - 2

Now the function satisfies both the conditions

so applying MVT

6x-2 = f(2) - f(0) / 2-0

6x-2 = 9 - 1 /2

6x-2 = 4

6x=6

x=1

so this is the tangent line for this given function.

4 0

2 years ago

In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 15 boys an

denis-greek [22]

Answer:

There are a total of possible 1820 results.

Step-by-step explanation:

Since there are two competitions, one for boys and one for girls, and we want all the possible results we will calculate the possible combinations for the boys and multiply them by the possible combinations for the girls. This is shown below:

$Boys = \frac{15!}{3!(15 - 3)!} = \frac{15!}{3!12!} = \frac{15*14*13*12!}{3!12!}\\Boys = \frac{15*14*13}{3*2*1}\\Boys = \frac{15*14*13}{3*2*1}\\Boys = 455$