Find TM if BM=7 (Answer quickly)

Suppose that you drop a ball from a window 50 metres above the ground. The ball bounces to 50% of its previous height with each

stich3 [128]

We have been given that you drop a ball from a window 50 metres above the ground. The ball bounces to 50% of its previous height with each bounce. We are asked to find the total distance traveled by up and down from the time it was dropped from the window until the 25th bounce.

We will use sum of geometric sequence formula to solve our given problem.

$S_n=\frac{a\cdot(1-r^n)}{1-r}$ , where,

a = First term of sequence,

r = Common ratio,

n = Number of terms.

For our given problem $a=50$ , $r=50\%=\frac{50}{100}=0.5$ and $n=25$ .

$S_{25}=\frac{50\cdot(1-(0.5)^{25})}{1-0.5}$

$S_{25}=\frac{50\cdot(1-0.0000000298023224)}{0.5}$

$S_{25}=\frac{50\cdot(0.9999999701976776)}{0.5}$

$S_{25}=100\cdot(0.9999999701976776)$

$S_{25}=99.99999701976776\approx 100$

Therefore, the ball will travel 100 meters and option B is the correct choice.

4 0

3 years ago

Which congruence statement says the same thing as ABC=DEF

Oliga [24]

Answer is <span>c.) ACB=DFE

hope that helps

------------------------------------</span>

4 0

2 years ago

If f(x) = x2, which of the following describes the graph of f(x - 1)? A. The graph of f(x - 1) is a horizontal shift of f(x) = x

pantera1 [17]

Answer:

A

Step-by-step explanation:

To understand this, we can look at the vertical & horizontal translations of a parabola of the form $f(x)=x^2$

A vertically translated parabola has the form $f(x)=x^2+k$ , where k is the vertical shift upward when k is positive and vertical shift downward when k is negative.
A horizontally translated parabola has the form $f(x)=(x-a)^2$ , where a is the horizontal shift rightward when a is positive and horizontal shift leftward when a is negative.

When we replace x of the original function with (x-1), we have $f(x)=(x-1)^2$ . According to the rules, this means that the original function is shifted 1 unit right (horizontal shift).

Correct answer is A.

4 0

3 years ago

Read 2 more answers

Please help me with this math problem!! Will give brainliest!! :)

8090 [49]

Answer:

A. 17

B. 16

Step-by-step explanation:

F(5)

5 > 2 so you plug the 5 into 3x+2

F(-2)

-5 < -2 < 2 so you plug the -2 into (x-2)^2

7 0

1 year ago

The function f(x) = 2x2 + 3x + 5, when evaluated, gives a value of 19. What is the function’s input value?

goldenfox [79]

$f(x)=\quad 2{ x }^{ 2 }+3x+5$

Let's called the input 'z'

When we plug 'z' in the function we get ;

$f(z)=\quad 2{ z }^{ 2 }+3z+5$

And we know that, this is equal to 19, so ;

$2{ z }^{ 2 }+3z+5=\quad 19$

Let's rearrange the equation.

$2{ z }^{ 2 }+3z+5=\quad 19\\ \\ 2{ z }^{ 2 }+3z=\quad 19-5\\ \\ 2{ z }^{ 2 }+3z=\quad 14\\ \\ 2{ z }^{ 2 }+3z-14=\quad 0$

So we have a quadratic equation here.

We'll use this formula to solve it :

$\frac { -b\pm \sqrt { { b }^{ 2 }-4ac } }{ 2a }$

The formula is used in equation formed like this :

$a{ x }^{ 2 }+bx+c=0$

In our equation,

a=2 , b=3 and c=-14

Let's plug in the values in the formula to solve,

$a=2\quad b=3\quad c=-14\\ \\ \frac { -3\pm \sqrt { 9-(4\cdot 2\cdot -14) } }{ 4 } \\ \\ \frac { -3\pm \sqrt { 9-(-112) } }{ 4 } \\ \\ \frac { -3\pm \sqrt { 9+112 } }{ 4 } \\ \\ \frac { -3\pm \sqrt { 121 } }{ 4 } \\ \\ \frac { -3\pm 11 }{ 4 }$

So,

$z=\quad \frac { -3+11 }{ 4 } \quad ,\quad \frac { -3-11 }{ 4 } \\ \\ z=\quad \frac { 8 }{ 4 } \quad ,\quad \frac { -14 }{ 4 } \\ \\ z=\quad 2,\quad -\frac { 7 }{ 2 }$

So the input can be both, 2 and $-\frac{7}{2}$

8 0

3 years ago