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3 years ago

12) Find the sum, S7 for the geometric series {1 + 5 + 25 + - + 15625).

Mathematics

2 answers:

zhenek [66]3 years ago

7 0

Understanding:

The sum of a geometric series is, $a+ar+ar^2+ar^3+...$ , with a being the start point and r is the common ratio. We can also use the following formula to make life easier $S_n=a\frac{1-r^n}{1-r}$ , a is your start point, r is the common ratio, and n is the number of terms, which in our case is S7.

Solution:

Our start point is 1, $a=1$ ,

The common ratio is 5, $r=5$ ,

And finally, the number of terms is 7, $n=7$ .

$S_n=a\frac{1-r^n}{1-r} \\=(1)\frac{1-(5)^{(7)}}{1-(5)} \\=\frac{1-78125}{1-5} \\=\frac{-78124}{-4}\\=19531$

The answer is [A] 19531.

Nonamiya [84]3 years ago

5 0

Answer:

Step-by-step explanation:

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nataly862011 [7]

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3 years ago

Help me I need help fast it is due soon!

Arte-miy333 [17]

Answer:

400 square meters

Step-by-step explanation:

We can first solve this problem with each unit representing 1 centimeter, and then scale up at the very end. The shape that we have a parallelogram. The base is 8 cm, and the height is 2 cm. The formula for the area of a parallelogram is just $bh$ , so the area of the parallelogram is 16 square centimeters. However, now we scale up. Since each centimeter correlates to 5 meters, each little box will correlate to 25 square meters. Therefore, $16 \cdot 25 = \boxed{400}$ square meters is our answer

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3 years ago

At what point does the curve have maximum curvature? Y = 4ex (x, y) = what happens to the curvature as x → ∞? Κ(x) approaches as

MAXImum [283]

Answer-

At $x= \frac{1}{2304e^4-16e^2}$ the curve has maximum curvature.

Solution-

The formula for curvature =

$K(x)=\frac{{y}''}{(1+({y}')^2)^{\frac{3}{2}}}$

Here,

$y=4e^{x}$

Then,

${y}' = 4e^{x} \ and \ {y}''=4e^{x}$

Putting the values,

$K(x)=\frac{{4e^{x}}}{(1+(4e^{x})^2)^{\frac{3}{2}}} = \frac{{4e^{x}}}{(1+16e^{2x})^{\frac{3}{2}}}$

Now, in order to get the max curvature value, we have to calculate the first derivative of this function and then to get where its value is max, we have to equate it to 0.

${k}'(x) = \frac{(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})}{(1+16e^{2x} )^{2}}$

Now, equating this to 0

$(1+16e^{2x})^{\frac{3}{2} } (4e^{x})-(4e^{x})(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x}) =0$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}-(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{3}{2}}=(\frac{3}{2}(1+e^{2x})^{\frac{1}{2}})(32e^{2x})$

$\Rightarrow (1+16e^{2x})^{\frac{1}{2}}=48e^{2x}$

$\Rightarrow (1+16e^{2x})}=48^2e^{2x}=2304e^{2x}$

$\Rightarrow 2304e^{2x}-16e^{2x}-1=0$

Solving this eq,

we get $x= \frac{1}{2304e^4-16e^2}$

∴ At $x= \frac{1}{2304e^4-16e^2}$ the curvature is maximum.

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3 years ago

Which expression represents the phrase the sum of twice a number and 7

bixtya [17]

Answer:

2n+7

Step-by-step explanation:

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3 years ago

The ANOVA procedure is a statistical approach for determining whether or not the means of:______.

Mandarinka [93]

Answer:

a. two or more samples are equal.

Step-by-step explanation:

ANOVA (Analysis of Variance) is a statistical procedure that could be used to compare two or more population means are equal.

Remember, the means referred to here is the expected value or average value of a set of numbers, which is calculated by summing the values in a given set divided by the number of values. Also, put simply, the analysis of variance is a measure of how much differences exist out a data set.

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3 years ago