what is the approximate shadow in feet of the tree in the figure below.​

I assume the series is supposed to be

[tex]\displaystyle\sum_{n=1}^\infty \frac6{n(n+3)}[/tex]

The summand can be expanded into partial fractions:

[tex]\dfrac6{n(n+3)}=\dfrac an+\dfrac b{n+3}[/tex]

[tex]\implies 6=a(n+3)+bn=(a+b)n+3a[/tex]

[tex]\implies\begin{cases}a+b=0\\3a=6\end{cases}\implies a=2,b=-2[/tex]

Then the sum is equivalent to

[tex]\displaystyle2\sum_{n=1}^\infty\left(\frac1n-\frac1{n+3}\right)[/tex]

Consider the N-th partial sum of the series:

2[(1 - 1/4) + (1/2 - 1/5) + (1/3 - 1/6) + (1/4 - 1/7) + (1/5 - 1/8) + …

+ (1/(N - 3) - 1/N) + (1/(N - 2) - 1/(N + 1)) + (1/(N - 1) - 1/(N + 2)) + (1/N - 1/(N + 3))]

Each of the negative terms (in bold) will have a positive counterpart (underlined) that cancel, so the N-th partial sum would be

[tex]\displaystyle\sum_{n=1}^N\frac6{n(n+3)} = 2\left(1+\frac12+\frac13-\frac1{N+1}-\frac1{N+2}-\frac1{N+3}\right)[/tex]

As N approaches infinity, the last three terms in the sum converge to 0, so the original sum converges to

[tex]\displaystyle\sum_{n=1}^\infty \frac6{n(n+3)} = 2\left(1+\frac12+\frac13\right) = \boxed{\frac{11}3}[/tex]

Answer:

the answer for ratio 16 to 14 = 1:3

Step-by-step explanation:

16:48

8:24

4:12

1:3

Answer:

i think it's 52

Step-by-step explanation:

Answer:

add an attachm3nt to make iy clear

Answer:

D.

Step-by-step explanation:

The subtraction property involves subtracting the same number that is subtracted from one side of the equal sign and also subtracting same from the other side of the equal sign

For example: y + 3 = 2

To apply the subtraction property, subtract 3 from each side. Thus:

y + 3 = 2 - 3

From the given equation solved, the subtraction property was not applied in any of the steps shown.

Answer:D.)The addition property of equality was not applied to solve this equation

Answer:

52%

7 more

Step-by-step explanation:

There are 5*5 = 25 boxes in the grid

13 are shaded

13/25 = 13/25 *4/4 = 52/100 = 52% are shaded

We want 80% shaded

80/100

Divide top and bottom by 4

20/25

We need 20 shaded and have 13 shaded

20-13 = 7

We need to shaded 7 more

Answer:

Ellipse

[tex]✔ \: \: : { \sf{ {x}^{2} + {y}^{2} = 1 }}[/tex]

Step-by-step explanation:

[tex]{ \sf{circle : \: {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0}} \\ { \sf{parabola : \: {y}^{2} = 4ax }} \\ { \sf{hyperbola : \: {x}^{2} - {y}^{2} = 1 }}[/tex]

Answer:

cosA = - [tex]\frac{7}{25}[/tex]

Step-by-step explanation:

Using the double angle identity

cos2A = 2cos²A - 1 , then

cosA = 2cos²([tex]\frac{A}{2}[/tex] ) - 1 , that is

cosA = 2 × ([tex]\frac{3}{5}[/tex] )² - 1

        = 2 × [tex]\frac{9}{25}[/tex] - 1

       = [tex]\frac{18}{25}[/tex] - [tex]\frac{25}{25}[/tex]

       = - [tex]\frac{7}{25}[/tex]

Answer:

Me need my points :D                    

Step-by-step explanation:

1.

c² = n²

√c² = √n²

c = n

2.

if

c = 3 + 6 = 9

and

n = 5 + 4 = 9

Answer:

c = ±n

Step-by-step explanation:

Taking the square root of both sides yields

√c² = √n² or c = ±n

c² = n² is a quadratic equation, so we expect that there will be two roots:  one positive and one negative.  

Answer:

g(x) = - ( x^2)

Step-by-step explanation:

opposite of function f

Answer:

60 * -.75 = -45 ... 45 meters below starting point

Step-by-step explanation:

Answer:

16/9

Step-by-step explanation:

(4/3) ^2

(4/3) * (4/3)

First the numerators

4*4 = 16

Then the denominators

3*3 = 9

Numerator over denominator

16/9

[tex]\frac{16}{9}[/tex]

Answer:

Solution given:

[tex](\frac{4}{3})^{2}=\frac{4²}{3²}=\frac{16}{9}[/tex]

Answer:

hi?

Step-by-step explanation:

Answer:

KM = 10.68

K = 55 degrees

M = 35 degrees

Step-by-step explanation:

Firstly, we can use Pythagoras’ theorem to calculate the length of the hypotenuse which is KM

Mathematically, this is the sum of the squares of the two other sides KL and LM according to Pythagoras’ theorem

Thus, we have it that;

KM^2 = KL^2 + LM^2

KM^2 = 6.2^2 + 8.7^2

KM^2 = 114.13

KM = √(114.13)

KM = 10.68

We have two angles to calculate

Let us start with the angle at vertex K

The opposite side to is is the length LM which is 8.7

The adjacent side to it is the length 6.2

Mathematically, the relationship between the two can be calculated using the Tan ; as the Tan of an angle is the ratio of the length of the opposite to that of the adjacent

thus;

Tan K = 8.7/6.2

K = arc Tan (8.7/6.2)

K = 54.5 which is 55 degrees

since we have a right angle , we only have to subtract he measure of angle K from 90 to get the measure of M

M = 90-55 = 35 degrees

Answer:

The answer is correct

Step-by-step explanation:

3(x + 4) + 2 = 2 + 5(x – 4)

3x + 12 + 2 = 2 + 5x - 20

3x + 14 = 5x - 18

-2x = -32

x = 16

Answer:

0.047619

P.S. do you need to round?

Answer:

[tex]\frac{1}{21}[/tex]

Step-by-step explanation:

Answer: [tex]25\ mph[/tex]

Step-by-step explanation:

Given

Jane took 3 hours

First she rode 48 miles with let say with [tex]x[/tex] mph

then she rode 15 miles with speed [tex](x+5)[/tex] mph

Equate the time in each ride and equate it to total time

[tex]\Rightarrow 3=\dfrac{48}{x}+\dfrac{15}{x+5}\\\\\Rightarrow 3x(x+5)=48(x+5)+15x\\\\\Rightarrow 3x^2+15x=48x+48\times 5+15x\\\\\Rightarrow 3x^2-48x-240=0\\\\\Rightarrow (x-20)(x+4)=0\\\\\text{Neglecting the negative value as speed cannot be negative}\\\\\Rightarrow x=20\ mph[/tex]

So, her along the summit is [tex]x+5=25\ mph[/tex]

Answer:

2 and 5 is the gcf and lcm is 360

Step-by-step explanation:

Answer:

GCF is 120 and LCM is 1440

Step-by-step explanation:

-To find the GCF, take a look at the orange section(the intersection) and multiply all the numbers in there. 2^3x3x5=120

-To find the LCM, multiply all the numbers in the entire venn diagram. 2^5x3^2x5=1440

The result shows that Brittany is faster than Natalie because she moved faster than her. Therefore, Brittany is (43.64 - 21.5) = 22.14mph faster than Natalie.

The average speed can be calculated by dividing the distance moved by the time taken. That is;

Average speed = Distance/time

According to this question, Brittany and Natalie start cycling together from their home to school, which is 14.4 miles away.

However, Natalie takes 40 minutes to reach school and Brittany reaches 20 minutes after Natalie.

First, we calculate the average speed of each individual as follows:

This shows that Brittany is faster than Natalie because she moved faster than her. Therefore, Brittany is (43.64 - 21.5) = 22.14mph.

Learn more about average speed at: https://brainly.com/question/12322912

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Answer:

6s - 300 > 210 is the answer.

Answer:

yikes

Step-by-step explanation:

honestly I would help if I could.

The function represented by graph g(x) is

g(x) = 3x² / (x² - 9)

Option A is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

g(x) = 3x² / (x² - 9)

This can be written as,

g(x) = 3x² / (x - 3)(x + 3)

This is a rational function.

This can be graphed as the given graph.

Thus,

The function represented by g(x) graph is

g(x) = 3x² / (x² - 9)

Learn more about functions here:

https://brainly.com/question/28533782

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Answer:

(12+3x)x

Step-by-step explanation:

the other 3 can be simplified into 15x, but (12+3x)x = 12x+3x^2

Answer:

6 ≈ 27.78C

7 = 219.2F

8 = 20C

9 = 116.6F

Step-by-step explanation:

6. From the formula C/5 = (F-32)/9

     We get C/5 = (82-32)/9

     C = (50/9)*5

     C ≈ 27.78

7. From the formula C/5 = (F-32)/9

     We get 104/5 = (F-32)/9

     F-32 = 104/5 * 9

     F-32 = 187.2

     F = 219.2

8. From the formula C/5 = (F-32)/9

    We get C/5 = (68-32)/9

     C/5 = 36/9

     C/5 = 4

     C = 5 * 4

     C = 20

9. From the formula C/5 = (F-32)/9

    We get C/5 = (F-32)/9

     47/5 = (F-32)/9

     (47/5)*9 = (F-32)

     84.6 = F-32

     F = 84.6 + 32

     F = 116.6

Formula Used

Temperture Conversion

C/5 = (F-32)/9 = R/4 = (K-273)/5

C - Celcius, F - Fahrenheit, R - Rankine, K - Kelvin

Note

Please use the correct subject next time

6) 82°F to C°

Formula

(82°F − 32) × 5/9 = 27.78°C

82°F=27.78°C

7) 10°C to °F

Formula

(104°C × 9/5) + 32 =219.2°F

104°C =219.2°F

8) 68°F to C°

Formula

(68°F − 32) × 5/9 = 20°C

68°F=20°C

9) 47°C to °F

Formula

(47°C × 9/5) + 32 = 116.6°F

47°C =116.6°F

Answer:b

Step-by-step explanation:

Answer:

3 or 6/2

Step-by-step explanation:

4--2 (you add there is a subtraction of a negative) over or divided by 3-1

Answer:

[tex]slope = \frac{y2 - y1}{x2 - x1} \\ = \frac{4 - - 2}{3 - 1} \\ = \frac{6}{2} = 3 \\ thank \: you[/tex]

Answer:

[tex]12.2\text{ ft}[/tex]

Step-by-step explanation:

In any right triangles, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared ([tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side).

In this case, the length we're solving for is the hypotenuse of the triangle and the two legs of the triangle are 7 and 10. Therefore, we have:

[tex]7^2+10^2=c^2,\\49+100=c^2,\\c^2=149,\\c=\sqrt{149},\\c\approx \boxed{12.2\text{ ft}}[/tex]

9514 1404 393

Answer:

  a) (1.75 +1.00d)/4 < (3.50 +1.50d)/5

  b) 3.70

Step-by-step explanation:

a) You want ...

   classic cost < XL cost

Using the given expressions for the costs, the inequality is ...

  (1.75 +1.00d)/4 < (3.50 +1.50d)/5

__

b) For a 10-mile ride, the XL cost is ...

  (3.50 +1.50(10))/5 = (3.50 +15.00)/5 = 18.50/5 = 3.70

Each passenger in a group of 5 friends pays $3.70 for the 10-mile ride.

_____

Additional comment

Each expression can be divided out to give ...

  classic cost per person = $0.4375 +0.25d

  XL cost per person = $0.70 +0.30d

Comparing these, we see there is no positive value of d that will make the XL cost per person be less than the classic cost per person. Both the initial fee and the per-mile cost are lower for the classic.

[tex] \tt \huge \leadsto \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} + \sqrt{3} } [/tex]

[tex] \tt \huge \leadsto \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} + \sqrt{3}} \times \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} - \sqrt{3} } [/tex]

[tex] \tt \huge \leadsto \frac{7 - 3}{ (\sqrt{7 })^{2} - ( \sqrt{3})^{2} } [/tex]

[tex] \tt \huge \leadsto \frac{4}{7 - 3} [/tex]

[tex] \tt \huge \leadsto\frac{4}{4} [/tex]

[tex]\tt\huge\leadsto{1}[/tex]

Answer:

Step-by-step explanation:

To rationalize the denominator multiply the numerator and denominator by the conjugate of √7 + √3 = √7- √3

[tex]\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}=\frac{(\sqrt{7}-\sqrt{3})(\sqrt{7}-\sqrt{3})}{(\sqrt{7}+\sqrt{3})(\sqrt{7}-\sqrt{3})}\\\\\\= \frac{(\sqrt{7}-\sqrt{3})^{2}}{(\sqrt{7})^{2}-(\sqrt{3})^{2}}\\\\\\= \frac{(\sqrt{7})^{2}-2*(\sqrt{7})*(\sqrt{3})+(\sqrt{3})^{2})}{7-3}\\\\=\frac{7-2\sqrt{21}+3}{4}\\\\=\frac{10-2\sqrt{21}}{4}\\\\=\frac{2(5-\sqrt{21})}{4}\\\\=\frac{5-\sqrt{21}}{2}[/tex]