Which function is positive for the entire interval [-3, -2]?

Mathematics

1 answer:

Aleksandr-060686 [28]2 years ago

4 0

Answer:

Answer: A function that is positive in the entire interval [-3, -2] is -x2 - 5x - 5. Let's understand the solution. Explanation: If the function is represented by a downward parabola, then the function must be quadratic and the coefficient of x2 must be negative.

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A chemist is using 336 milliliters of a solution of acid and water. If 19.4 % of the solution is acid, how many milliliters of a

denpristay [2]

Answer:

65.2 milliliters

Step-by-step explanation:

The quantity 336 milliliters is the 100% of the solution. We can represent this information on a table:

Milliliters Percentage of solution

336 ⇔ 100%

we are told that 19.4% of this solution is acid, and we need to know how many milliliters represents this percentage. I will call the number of milliliters of acid on the solution 'x', and updating the last table:

Milliliters Percentage of solution

336 ⇔ 100

x ⇔ 19.4%

We can solve this problem for 'x' using the<u> rule of three</u> which is to multiply the cross quantities on the table (336 by 19.4) and then divide by the remaining amount (100):

x = 336(19.4)/100

x = 6,518.4/100

x = 65.184

which rounding to the nearest tenth is: 65.2 milliliters

8 0

3 years ago

We are given a sequence of five non-zero numbers, where the sum of each term and its neighboring terms is 15 or 25. Find the sum

PSYCHO15rus [73]

We have a sequence that meets the given criteria, and with that information, we want to get the sum of all the terms in the sequence.

We will see that the sum tends to infinity.

So we have 5 terms;

A, B, C, D, E.

We know that the sum of each term and its neighboring terms is 15 or 25.

then:

A + B + C = 15 or 25
B + C + D = 15 or 25
C + D + E = 15 or 25

Now, we want to find the sum of all the terms in the sequence (not only the 5 given).

Then let's assume we write the sum of infinite terms as:

$a_1 + a_2 + a_3 + a_4 + a_5 + a_6 + ...$

Now we group that sum in pairs of 3 consecutive terms, so we get:

$(a_1 + a_2 + a_3) + (a_4 + a_5 + a_6) + ...$

So we will have a sum of infinite of these, and each one of these is equal to 15 or 25 (both positive numbers). So when we sum that infinite times (even if we always have the smaller number, 15) the sum will tend to be infinite.

Then we have:

$(a_1 + a_2 + a_3) + (a_4 + a_5 + a_6) + ... \to \infty$