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2 years ago

Please help!! i don’t understand how to do this.

Mathematics

1 answer:

ser-zykov [4K]2 years ago

3 0

Answer:

C= 5/9 * (F -32)

Move 5/9 to the left which makes it 9/5

9/5 * C = (F -32)

Move the -32 to the left

9/5 * C +32 = F or to make it read left to right

Fahrenheit = 9/5 * Celsius + 32

Step-by-step explanation:

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums

gtnhenbr [62]

I'm guessing the sum is supposed to be

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}$

Split the summand into partial fractions:

$\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}$

$1=a(5k+4)+b(5k-1)$

If $k=-\frac45$ , then

$1=b(-4-1)\implies b=-\frac15$

If $k=\frac15$ , then

$1=a(1+4)\implies a=\frac15$

This means

$\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}$

Consider the $n$ th partial sum of the series:

$S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)$

The sum telescopes so that

$S_n=\dfrac2{14}-\dfrac2{5n+4}$

and as $n\to\infty$ , the second term vanishes and leaves us with

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17$

7 0

3 years ago

3<3x+6<24<br><br>i keep getting 1 < x < 6<br>but the answer says -1 < x < 6

lara [203]

3 < 3x+6
-3<3x
-1<x

3x+6<24
3x<18
x<6

-1<x<6 the book is right

6 0

3 years ago

I need some help please

Veronika [31]

The definition of the tangent function tells you
tan(angle) = (300 ft) / (distance to mountain)
This equation can be rearranged to
(distance to mountain) = (300 ft) / tan(angle)

For the far end of the river,
distance to far end = (300 ft) / tan(24°) ≈ 673.8 ft

For the near end of the river
distance to near end = (300 ft) / tan(40°) ≈ 357.5 ft

Then the width of the river can be calculated by finding the difference of these distances:
width of river = distance to far end - distance to near end
width of river = 673.8 ft - 357.5 ft
width of river = 316.3 ft

The appropriate answer choice is
316 ft.

8 0

3 years ago

-4x - 6y = 6<br> 4x + 6y = -4

Sloan [31]

Step-by-step explanation:

$-4x - 6y = 6$

$4x + 6y = -4$

To solve a system of equations, we can add the two equations and solve for one of the remaining variables -- let's try to eliminate the $x$ variable when we add the two equations together.

Right now, there's a $-4x$ term in the first equation, and a $4x$ term in the second equation, so if we add those together, we'll be able to eliminate the $x$ variable altogether and solve for $y$ .

However, when we also have a $-6y$ term in the first equation and $6y$ term in the second equation, so adding these together will also eliminate the $y$ term, leaving a $0$ on the left-hand side of the equation.

If we add the two numbers on the right side of the equation, we get $-2$ , which does not equal $0$ , meaning there are no solutions to this system of equations.