How many seconds are there in 203060708030506040 hours?

The first and second terms of a linear sequence (A.p) are 3 and 8 respectively. Please determine the least Number of terms of Ap

Alla [95]

Answer:

To rewrite your question, you are looking for the smallest that fulfills the inequality:

∑=1>250

First, we must find the sequence in explicit form. We can think of it as a line we are trying to get the slope-intercept form of. We have the points (1, 3) and (2, 8). Therefore, the slope is 8−32−1=51=5 . Now we just need the y-intercept. We can find it through substitution:

=5+

In order to solve for , we can plug in one of the points that we were already given. I will choose the point (1, 3). Note that this point just means that when =1 , =3 .

3=5(1)+

3=5+

=−2

Now for the original question.

∑=1(5−2)>250

((5(1)−2)+(5()−2)2)>250

(5+12)>250

522+12>250

2+15>100

2+15+1100>100+1100

(+110)2>100+1100

(+110)2>10001100

+110>±10001100‾‾‾‾‾‾‾√

+110>±11010001‾‾‾‾‾‾√

>−110±11010001‾‾‾‾‾‾√

Since we are looking for the smallest value, we will subtract for the plus or minus sign.

>−110−11010001‾‾‾‾‾‾√≈−10

Since that is negative, we will have to add instead.

>−110+11010001‾‾‾‾‾‾√≈9.9

Therefore, the smallest integer that makes sense and satisfies the inequality is 10.

So, the first 10 numbers must be added.

Honestly, it would have been quicker just to brute-force this.

Step-by-step explanation:

Have a good day

8 0

3 years ago

The side lengths of a triangle are 5, 8, and 12. Is this a right triangle?

katovenus [111]

Answer:

no

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

I NEED HELP!! please show all work

PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

$4^{5x} = 3^{x-2}$

$\implies \log 4^{5x} = \log 3^{x-2}$

Drop the exponents:

$\implies 5x \log 4 = (x-2) \log 3$

Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing x to the left side and factor out x :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

$\implies x (5 \log 4 - \log 3) = - 2 \log 3$

Solve for x by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

5 0

3 years ago

X + y = 152, 8.5x + 12y = 1,656 How many hats were sold?

Elodia [21]

Answer:

x = 48 and y = 104

Step-by-step explanation:

Given equations are:

$x+y = 152\\8.5x+12y=1656$

From equation 1:

$x = 152-y$

Putting the value of y in equation 2

$8.5(152-y)+12y = 1656\\1292-8.5y+12y = 1656\\3.5y+1292 = 1656\\3.5y = 1656-1292\\3.5y = 364\\\frac{3.5y}{3.5} = \frac{364}{3.5}\\y = 104$

Now we have to put the value of y in one of the equation to find the value of x

Putting y = 104 in the first equation

$x+y = 152\\x+ 104 = 152\\x = 152-104\\x = 48$

Hence,

The solution of the system of equations is x = 48 and y = 104

The value of variable which was assumed for number of hats, is the total number of hats.

6 0

3 years ago

Walter walked 15.5 block from his house to work. It took him 35 minutes. What is his rate in blocks per hour

Sonbull [250]

For this case we first calculate the rate in blocks per minutes.
rate = (15.5) / (35) = 0.443 blocks per minutes.
Then, we can go to blocks per hour.
Remember: 1h = 60min.
rate = 0.443 * (1/60) = 0.00738 blocks per hour.
answer
his rate in blocks per hour is 0.00738 blocks per hour.

6 0

3 years ago

How many seconds are there in 203060708030506040 hours?​

How many seconds are there in 203060708030506040 hours?