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podryga [215]
2 years ago
5

if it is p miles from home to school how many round trips can be made if your car gets q miles per gallon of gasoline and there

are 5 gallons of gas in its tank
Mathematics
1 answer:
Bumek [7]2 years ago
3 0
5 is less than or equal to (2q)/p
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For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of
Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is (-1)^{k+1}(\frac{1}{2^{k}}).

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as (-1)^{k+1}(\frac{1}{2^{k}}).

where k is from 1 to 10.

By the given expression sequence will be \frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......

In this sequence first term "a" = \frac{1}{2}

and common ratio in each successive term to the previous term is 'r' = \frac{\frac{(-1)}{4}}{\frac{1}{2} }

r = -\frac{1}{2}

Since the sequence is infinite and the formula to calculate the sum is represented by

S=\frac{a}{1-r} [Here r is less than 1]

S=\frac{\frac{1}{2} }{1+\frac{1}{2}}

S=\frac{\frac{1}{2}}{\frac{3}{2} }

S = \frac{1}{3}

Now we are sure that the sum of infinite terms is \frac{1}{3}.

Therefore, sum of 10 terms will not exceed \frac{1}{3}

Now sum of first two terms = \frac{1}{2}-\frac{1}{4}=\frac{1}{4}

Now we are sure that sum of first 10 terms lie between \frac{1}{4} and \frac{1}{3}

Since \frac{1}{2}>\frac{1}{3}

Therefore, Sum of first 10 terms will lie between \frac{1}{4} and \frac{1}{2}.

Option D will be the answer.

3 0
3 years ago
5 plus 2 times 10 equals
Goryan [66]
The answer is 70.
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2 years ago
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Which set of coefficients of the terms in the expansion of the binomial (x+y)^3 is correct ?
BigorU [14]
We are technically FOILing this out... with a power of 3.

(x+y)(x+y)(x+y)

So we can first factor out the first two "x+y"s.

( x^{2} +2xy + y^{2} ), multiplied by the last "x+y".

x^{3} +3 x^{2} y +3x y^{2} + y^{3}

Coefficients are the number that comes in front of a variable. 

In this case, 1 comes in front of x^{3}, 3 comes in front of x^{2} y, 3 comes in front of x y^{2}, and 1 comes in front of y^{3}.

Thus: 1, 3, 3, 1.
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