Select each interval where the graph is increasing.

Mathematics

2 answers:

olya-2409 [2.1K]2 years ago

8 0

- 3 and 2 are the answers because at each of those points the graph line is rising.

Tresset [83]2 years ago

3 0

The increases at -3, and 2

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The area of the region under the curve of the function f(x) = 5x + 7 on the interval [1, b] is 88 square units, where b > 1.

djverab [1.8K]

We are given the area of the region under the curve of the function f(x) = 5x + 7 with an interval [1, b] which is 88 square units where b > 1

We need to find the integral of the function f(x) = 5x + 7 with the limits 1 and b

5/2 x^2 + 7x (limits: 1, b)

substitute the limits:

5/2 (1^2) + 7 (1) - 5/2 b^2 + 7b = 0

solve for b

Then after solving for b, this would be your interval input with 1: [1, b].<span />

4 0

2 years ago

Read 2 more answers

Enter the explicit rule for the sequence

Softa [21]

Let's take a look at the first few numbers in the sequence based on the given rule:

$a_{1}=6\\ a_{2}= \frac{1}{4}(6)\\ a_3= \frac{1}{4}\big( \frac{1}{4}\big)6= \big(\frac{1}{4}\big)^2(6)\\ a_{4}= \frac{1}{4} \big(\frac{1}{4}\big)^26= \big(\frac{1}{4}\big)^3(6)$

Inspecting this pattern it seems like the power $\frac{1}{4}$ is being raised to is always one less than the number of the sequence, so if we were on the nth number in the sequence, that part of the expression would be $\big(\frac{1}{4} \big)^{n-1}$ . We also know that we'll be multiplying whatever we get from that by 6, so we can write the full explicit rule for our sequence as

$a_n=6\big( \frac{1}{4} \big)^{n-1}$

Where $a_n$ is the nth number in our sequence.