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3 years ago

6

CAN SOMEONE HELP ME OUT PLEASE!!! A baker makes 3 sponge cakes following the recipe exactly.How much more sugar does the baker u

se than flour to make 3 sponge cakes

1 answer:

Reptile [31]3 years ago

3 0

L.5 more sugar than flower

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A town in east Texas received 25 inches of rain in two weeks. If it kept raining at this rate for a 31−day month, how much rain

Likurg_2 [28]

25 in of rain in 2 weeks.

there are 14 days in 2 weeks

25/14 = 1.785 in per day

1.785 x 31 = 55.335 in. of rain

55.335 in of rain is your answer

hope this helps

7 0

3 years ago

Read 2 more answers

Determine the above sequence converges or diverges. If the sequence converges determine its limit

marshall27 [118]

Answer:

This series is convergent. The partial sums of this series converge to $\displaystyle \frac{2}{3}$ .

Step-by-step explanation:

The $n$ th partial sum of a series is the sum of its first $n\!\!$ terms. In symbols, if $a_n$ denote the $n\!$ th term of the original series, the $\! n$ th partial sum of this series would be:

$\begin{aligned} S_n &= \sum\limits_{k = 1}^{n} a_k \\ &= a_1 + a_2 + \cdots + a_{k}\end{aligned}$ .

A series is convergent if the limit of its partial sums, $\displaystyle \lim\limits_{n \to \infty} S_{n}$ , exists (should be a finite number.)

In this question, the $n$ th term of this original series is:

$\displaystyle a_{n} = \frac{{(-1)}^{n+1}}{{2}^{n}}$ .

The first thing to notice is the ${(-1)}^{n+1}$ in the expression for the $n$ th term of this series. Because of this expression, signs of consecutive terms of this series would alternate between positive and negative. This series is considered an alternating series.

One useful property of alternating series is that it would be relatively easy to find out if the series is convergent (in other words, whether $\displaystyle \lim\limits_{n \to \infty} S_{n}$ exists.)

If $\lbrace a_n \rbrace$ is an alternating series (signs of consecutive terms alternate,) it would be convergent (that is: the partial sum limit $\displaystyle \lim\limits_{n \to \infty} S_{n}$ exists) as long as $\lim\limits_{n \to \infty} |a_{n}| = 0$ .

For the alternating series in this question, indeed:

$\begin{aligned}\lim\limits_{n \to \infty} |a_n| &= \lim\limits_{n \to \infty} \left|\frac{{(-1)}^{n+1}}{{2}^{n}}\right| = \lim\limits_{n \to \infty} {\left(\frac{1}{2}\right)}^{n} =0\end{aligned}$ .

Therefore, this series is indeed convergent. However, this conclusion doesn't give the exact value of $\displaystyle \lim\limits_{n \to \infty} S_{n}$ . The exact value of that limit needs to be found in other ways.

Notice that $\lbrace a_n \rbrace$ is a geometric series with the first term is $a_0 = (-1)$ while the common ratio is $r = (- 1/ 2)$ . Apply the formula for the sum of geometric series to find an expression for $S_n$ :

$\begin{aligned}S_n &= \frac{a_0 \cdot \left(1 - r^{n}\right)}{1 - r} \\ &= \frac{\displaystyle (-1) \cdot \left(1 - {(-1 / 2)}^{n}\right)}{1 - (-1/2)} \\ &= \frac{-1 + {(-1 / 2)}^{n}}{3/2} = -\frac{2}{3} + \frac{2}{3} \cdot {\left(-\frac{1}{2}\right)}^{n}\end{aligned}$ .

Evaluate the limit $\displaystyle \lim\limits_{n \to \infty} S_{n}$ :

$\begin{aligned} \lim\limits_{n \to \infty} S_{n} &= \lim\limits_{n \to \infty} \left(-\frac{2}{3} + \frac{2}{3} \cdot {\left(-\frac{1}{2}\right)}^{n}\right) \\ &= -\frac{2}{3} + \frac{2}{3} \cdot \underbrace{\lim\limits_{n \to \infty} \left[{\left(-\frac{1}{2}\right)}^{n} \right] }_{0}= -\frac{2}{3}\end{aligned}}_$ .

Therefore, the partial sum of this series converges to $\displaystyle \left(- \frac{2}{3}\right)$ .

8 0

3 years ago

When amy exercises in her fitness for 1 hour she burns a total of 475calories if she burns 9 calories a minute jogging on the tr

Alex73 [517]

Answer:

26 minutes on the bicycle

Step-by-step explanation:

Let t and b represent the number of minutes on the treadmill and bicycle, respectively. The problem statement tells us two ways to relate these values.

t + b = 60 . . . . . Amy exercises a total of 60 minutes (1 hour)

9t +6.5b = 475 . . . . . she burns a total of 475 calories

Since we want to find the value of "b", we can use the first equation to write an expression that will substitute for t.

t = 60 -b

9(60 -b) +6.5b = 475

540 -2.5b = 475 . . . . . . simpify

-2.5b = -65 . . . . . . . . . . subtract 540

b = 26 . . . . . . . . . . . . . . . divide by -2.5 (equivalently, multiply by -2/5)

Amy spends 26 minutes exercising on the bicycle.

5 0

4 years ago

X^2-5x-36/x-2 ÷(x^2-18x+81)

mamaluj [8]

The answer is 76520^

6 0

3 years ago

Mr. Jones wants to buy 6 tickets to a play. Each ticket costs $10. Mr. Jones has $45 in his pocket.

lawyer [7]

Answer:

He needs $15 more

Step-by-step explanation:

since each ticket costs $10 dollars, and there is 6 tickets, we need to multiply 10 x 6 to get the total cost of all tickets

10 x 6 = $60

To find how much more money he needs to buy all tickets, we need to subtract $45 from the total cost of tickets, which is $60

$60 - $45 = $15

Hope you understand this explanation!

8 0

3 years ago