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3 years ago

If you can figure this out I will give you Brainliest and 5 stars ⭐️

Mathematics

1 answer:

hram777 [196]3 years ago

4 0

Answer:

The y-intercept is $b=0$

The y-intercept represents the initial quantity of gas in the canister which is zero.

Step-by-step explanation:

The y-intercept is where the graph of the straight line touches the y-axis.

From the graph, the y-intercept is the origin (0,0).

Recall that the slope intercept form of a straight line is $y=mx+b$ , where $b=0$ is the y-intercept in this case.

Since the graph represents the amount of gasoline in a canister after Joshua begins to fill it at the gas station pump, the y-intercept means the initial gallons of gas in the canister is zero.

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Use the summation formulas to rewrite the expression without the summation notation. summation_k = 1^n 12k(k - 1) / n^3 Use the

kvasek [131]

Answer:

$Sum=4*[\frac{n^2-1}{n^2}]$

For n=10:

Sum=3.96

For n=100:

Sum=3.9996

For n=1000:

Sum=3.999996

For n= 10000:

Sum=3.99999996

Step-by-step explanation:

Formula:

$\sum_{k=1}^n \frac{12k(k-1)}{n^3}$

Rearranging the above formula:

$\sum_{k=1}^n \frac{12}{n^3}*k(k-1)\\\sum_{k=1}^n \frac{12}{n^3}*(k^2-k)$ Eq (1)

According to summation formula:

$\sum_{k=1}^n\ k= \frac{n(n+1)}{2}\\ \sum_{k=1}^n\ k^2= \frac{n(n+1)(2n+1)}{6}\\$

Putt these in Eq (1), and we will get:

$=\frac{12}{n^3}[\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}]\\Taking\ n\ as\ common\\=n*\frac{12}{n^3}[\frac{(n+1)(2n+1)}{6}-\frac{(n+1)}{2}] \\=\frac{12}{n^2}*[\frac{(n+1)(2n+1)}{6}]-\frac{12}{n^2}*[\frac{(n+1)}{2}] \\=\frac{2*(n+1)(2n+1)}{n^2}-\frac{6(n+1)}{n^2}\\$

Taking $2(n+1)$ as common:

$=2(n+1)*\frac{2n+1-3}{n^2} \\=(2n+2)*\frac{2n-2}{n^2}\\=\frac{4n^2-4}{n^2}$

After more simplifying,

$Sum=4*[\frac{n^2-1}{n^2}]$

Now ,for n=10:

$Sum=4[\frac{(10^{2})-1}{10^{2}}]\\Sum=3.96$

For n=100:

$Sum=4[\frac{(100^{2})-1}{100^{2}}]\\Sum=3.9996$

For n=1000

$Sum=4[\frac{(1000^{2})-1}{1000^{2}}]\\Sum=3.999996$

For n=10000:

$Sum=4[\frac{(10000^{2})-1}{10000^{2}}]\\Sum=3.99999996$

4 0

3 years ago

Circle theorems please help

suter [353]

Answer:

n = 28°

Step-by-step explanation:

The angle at the centre is twice the angle on the circle subtended on the same arc.

Also angles subtended on the same arc are congruent , thus

m = n

Then

35 + m = $\frac{1}{2}$ (98 + n ) ← multiply both sides by 2 to clear the fraction

70 + 2m = 98 + n , but since m = n, then

70 + 2m = 98 + m ( subtract m from both sides )

70 + m = 98 ( subtract 70 from both sides )

m = 14 and n = 28

6 0

2 years ago

Help me find the measures

Ronch [10]

Angle B=118 degrees
angle D=118 degrees
angles C=62 degrees
angle A=62 degrees
angle G=118 degrees
angle K=62 degrees
angle P=62 degrees
angle L=62 degrees
angle N=118 degrees
angle M=118 degrees
angle W=62 degrees
angle I=118 degrees
angle F=62 degrees
angle J=62 degrees
angle E=49 degrees
angle H=118 degrees
angle R=53 degrees
angle U=71 degrees
angle T=109 degrees
angle V=109 degrees
angle S=35.5
angle Q=35.5

7 0

3 years ago

Find the missing angle<br> measures marked with<br> question marks.

slavikrds [6]

Answer:

First one- The ? across from 70 degrees is 70 degrees, and the ones on the side are both 110 degrees.

The second one- The one across 53 degrees is 53 degrees and the ones are the side are both 127 degrees.

Step-by-step explanation:

Take the shown angle and subract that by 180 degrees to get your answer for the missing angles. And the one across from the shown angle is the same number.

Hope this helped im not sure if its right though.

6 0

3 years ago

Is 2/3 greater than 3/5

Zinaida [17]

Yes because the larger the bottom number the smaller the amount. :)

8 0

3 years ago

Read 2 more answers