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2 years ago

Fill in the blank with the correct word to describe this expression: n + 4 , the blank of a number and four)

Mathematics

1 answer:

gulaghasi [49]2 years ago

8 0

Answer:

There is a plus sign between the n and 4. This cannot be reduced any further. So the answer that should go into the blank is Sum

Step-by-step explanation:

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A baseball is hit and its height is given by h = 29.4t – 4. 9t^2, where h is the

ioda

Answer:

44.1m

Step-by-step explanation:

we are given a quadratic function which represents the height and time of a baseball

$\displaystyle h = 29.4t - 4.9 {t}^{2}$

we want to figure out maximum height of

the baseball

since the given function is a quadratic function so we have a parabola

which means figuring out the maximum height is the same thing as figuring out the maximum y coordinate (vertex)

to do so we can use some special formulas

recall that,

$\displaystyle \rm t= \frac{ - b}{ 2a}$

$\displaystyle H_{\text{max}}=f(t)$

notice that, our given function is not in standard form i.e

$\displaystyle f(x) = a {x}^{2} + bx + c$

let's make it so

$\displaystyle h = - 4.9 {t}^{2} + 29.4t$

therefore we got

our a is -4.9 and b is 29.4

so substitute:

$\displaystyle\rm t= \frac{ -( 29.4)}{ 2 \cdot - 4.9}$

remove parentheses and change its sign:

$\displaystyle\rm t= \frac{ -29.4}{ 2 \cdot - 4.9}$

simplify multiplication:

$\displaystyle\rm t= \frac{ -29.4}{ - 9.8}$

simplify division:

$\displaystyle \: t = 3$

so we have figured out the time when the baseball will reach the maximum height

now we have to figure out the height

to do so

substitute the got value of time to our given function

$\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot {3}^2$

simplify square:

$\displaystyle H_{\text{max}}=29.4\cdot 3-4.9\cdot 9$

simplify mutilation:

$\displaystyle H_{\text{max}}=88.2-44.1$

simplify substraction:

$\displaystyle H_{\text{max}}=44.1$

hence,

the maximum height of the baseball is 44.1 metres

4 0

3 years ago

Read 2 more answers

Ex 7) Imagine a mile-long bar of metal such as the rail along railroad tracks. Suppose that the rail is anchored on both ends an

Fantom [35]

9514 1404 393

Answer:

about 44.5 feet

Step-by-step explanation:

We can write relations for the height of the rail as a function of initial length and expanded length, but the solution cannot be found algebraically. A graphical solution or iterative solution is possible.

Referring to the figure in the second attachment, we can write a relation between the angle value α and the height of the circular arc as ...

h = c·tan(α) . . . . . . where c = half the initial rail length

Then the length of the expanded rail is ...

s = r(2α) = (c/sin(2α)(2α) . . . . . . where s = half the expanded rail length

Rearranging this last equation, we have ...

sin(2α)/(2α) = c/s

It is this equation that must be solved iteratively. We find the solution to be ...

α ≈ 0.0168538794049 radians

So, the height of the circular arc is ...

h = 2640.5·tan(0.0168538794049) ≈ 44.4984550191 . . . feet

The rail will bow upward by about 44.5 feet.

_____

Additional comments

Note that s and c in the diagram are half the lengths of the arc and the chord, respectively. The ratio of half-lengths is the same as the ratio of full lengths: c/s = 2640/2640.5 = 5280/5281.

We don't know the precise shape the arc will take, but we suspect is is not a circular arc. It seems likely to be a catenary, or something similar.

We used Newton's method iteration to refine the estimate of the angle from that shown on the graph. The iterator used is x' = x -f(x)/f'(x), where x' is the next guess based on the previous guess of x. Only a few iterations are required obtain an angle value to full calculator precision.

3 0

3 years ago

Two Step Equations 9=5- 9/3

Alex787 [66]

9=5 -y/3
-5
3=-y/3
cross multiply
1=-y
y=-1

6 0

3 years ago

A high school sewing club has 11 members. In how many different ways can they choose a president and vice president?

lorasvet [3.4K]

Since the order matters Person A and B can be chosen as AB (A pres B vice pres) or BA (B president A Vice president)

When the order matters we are talking about permutations. How many permutations of 11 taken 2 at a time are there.
It can be written like this 11nPr 2
It means start at 11 and multiply by the next lower number
11 x 10 = 110 ways they can choose.
Extension of the concept:
If there had been three positions President, Vice President, and Treasurer
then it would be 11nPr3 or 11 x 10 x 9
Once again the answer to your problem is 110.

6 0

3 years ago

Read 2 more answers

What is the factor of 4x subtracted from 28 ?

jolli1 [7]

Answer:

I think its (2x+4)(2x+7)

4 0

3 years ago