What's the new volume of the new box?

You bike 1 mile the first day of your training, 1.3 miles the second day, 1.9 miles the third day, and 3.1 miles the fourth d

JulsSmile [24]

Answer:

19.9 miles

Step-by-step explanation:

In this problem we have:

$d_1=1 mi$ is the distance travelled during the 1st day

$d_2=1.3 mi$ is the distance travelled during the 2nd day

$d_3=1.9 mi$ is the distance travelled during the 3rd day

$d_4=3.1 mi$ is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

$d_2-d_1=0.3\\d_3-d_2=2\cdot 0.3 = 0.6\\d_4-d_3=2\cdot 0.6 = 1.2$

Which can be rewritten using the general formula:

$d_{n+1}-d_n=2(d_n-d_{n-1})$

This means that

$d_{n+1}=d_n+2(d_n-d_{n-1})$

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

$d_1=1\\d_2=1.3\\d_3=1.9\\d_4=3.1\\d_5=3.1+2\cdot 1.2=5.5\\d_6=5.5+2\cdot 2.4=10.3\\d_7=10.3+2\cdot 4.8=19.9 mi$

So, the distance travelled on the 7th day is 19.9 miles.

7 0

2 years ago

Given the following 2 equations, state whether these equations are parallel, perpendicular, or neither.

stiks02 [169]

Answer:

Neither

Explanation:

The slope-intercept form of the equation of a line is generally given as;

$y=mx+b$

where m = the slope of the line

b = the y-intercept of the line

Two lines are said to be parallel if they have the same slope. Looking at the two given equations below, we see that the slope of the 1st one, 5/7, is different from the slope of the 2nd one, 7/5;

$\begin{gathered} y=\frac{5}{7}x+14 \\ y=\frac{7}{5}x-20 \end{gathered}$

Two lines are said to be perpendicular if their slopes are negative reciprocals of each other, let's go ahead and compare their slopes;

$\begin{gathered} m_1=\frac{5}{7} \\ m_2=\frac{7}{5} \\ \therefore m_2=\frac{1}{m_1_{}} \end{gathered}$

So the two lines are not perpendicular to each other. It, therefore, means that the correct answer will be Neither.

3 0

4 months ago

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year; 4 years.

Mekhanik [1.2K]

Answer: $2880

Step-by-step explanation:

I = P • r • t

I = 12000 • 0.06 • 1460/365 (I used 1340/365 because there are 365 days in a year. 4 years = 1460)

I = 2880

8 0

2 years ago

Y+5<br> ——=0 solve for y<br> X-1

Ira Lisetskai [31]

Answer:

y = -5

Step-by-step explanation:

see the pic for the steps . .

5 0

2 years ago

Identify the congruent triangles in the figure.

Komok [63]

Answer:

The answer would be HFG = KIJ (A)

If we know that the opposite and the adjacent side of the triangle are congruent, then the hypotenuse is congruent too. Therefor, A is correct as we know the opposite side and the adjacent side are congruent.

5 0

2 years ago