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Kobotan [32]
3 years ago
5

What is the sum of the first six terms of the geometric series 4 − 12 36 − . . . ?

Mathematics
1 answer:
Anastasy [175]3 years ago
4 0
The formula to use for the sum of n terms is as follows:
S_{n}=\frac{a(1-r^{n})}{1-r}
r = -3, n = 6.
S_{6}=\frac{4(1-(-3)^{6})}{1-(-3)}=-728
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Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hy
vladimir1956 [14]

Answer:

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

we know that

In the right triangle XYZ

cos(Y)=\frac{ZY}{XY} ---> adjacent side divided by the hypotenuse

substitute the values

cos(30\°)=\frac{ZY}{4}

Remember that

cos(30\°)=\frac{\sqrt{3}}{2}

so

substitute

\frac{\sqrt{3}}{2}=\frac{ZY}{4}

ZY=(4)\frac{\sqrt{3}}{2}

ZY=2\sqrt{3}\ units

step 2

sin(Y)=\frac{XZ}{XY} --> opposite side divided by the hypotenuse

substitute the values

sin(30\°)=\frac{XZ}{4}

Remember that

sin(30\°)=\frac{1}{2}

so

\frac{1}{2}=\frac{XZ}{4}

XZ=2\ units

step 3

tan(Y)=\frac{XZ}{ZY} --> opposite side divided by adjacent side

substitute the values

tan(Y)=\frac{2}{2\sqrt{3}}

tan(Y)=\frac{1}{\sqrt{3}}

Simplify

tan(Y)=\frac{\sqrt{3}}{3}

so

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

7 0
3 years ago
Read 2 more answers
M(x)=−(x−5) 2 +25m, left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, minus, 5, right parenthesis, squ
Aleksandr [31]

Answer:

25

Step-by-step explanation:

Given the function that represents the amount of mosquitoes as;

M(x) = -(x-5)² + 25

To get the maximum mosquitoes possible, we need to first find x;

At the maximum dM/dx = 0

dM//dx = -2(x-5)

0 = -2(x-5)

-2(x-5) = 0

-2x + 10 = 0

-2x = -10

x = 10/2

x = 5

Substitute x = 5 into the function;

M(5) = −(5−5)² +25

M(5) = 0+25

M(5) = 25

Hence the maximum number of mosquitoes is 25

8 0
3 years ago
4. Which of the following indicates the multiplication property of equality when solving Vz= 5?
tiny-mole [99]

Answer:

D. 21.

Step-by-step explanation:

The general form of the equation of a circle is:

(x - a)^2 + (y - b)^2 = r^2  where r is the radius.

Comparing:

(x + 5)^2 + (y + 7)^2 = 21^2

So r^2 = 21^2

making r = √21^2

= 21.

plz make me brainliest

3 0
3 years ago
which will have a higher effective interest rate a payday loan for $1700 that is due in 16 days with a fee of $100, or a payday
Fantom [35]
1700 that is due in 14 days with a fee of 100$ because it’s a shorter time period
7 0
3 years ago
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Mila [183]
U can multiply on some answers but some are trick questions
8 0
3 years ago
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