Simplify: 3x3 (4x4 + 3y)

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

janice invests a total of 8000 in two different accounts. the first account returns 5%, while the second account returns 8%. if

Zinaida [17]

Answer:

"She invested $2500 in 5% account and $5500 in 8% account"

Step-by-step explanation:

Let the amount invested in 5% account be "x"

So, the amount invested in 8% account would be "8000 - x"

Interest amount is the percentage multiplied by amount invested. So

Interest of 5% account = 5% of x = 0.05x

Interest of 8% account = 8 % of 8000 - x = 0.08(8000 - x)

Total interest is the sum of these 2 expressions that EQUATES to 565 (given). Let's solve for x:

$0.05x + 0.08(8000 - x) = 565\\0.05x+640-0.08x=565\\0.03x=75\\x=2500$

and thus,

"8000 - x" = 8000 - 2500 = 5500

Hence,

She invested $2500 in 5% account and $5500 in 8% account

6 0

3 years ago

Which expressions are equivalent to ? Check all that apply.

GrogVix [38]

Answer:

6.2+8.7+8.9x

Step-by-step explanation:

For expressions to be equivalent, they must simplify to the same lowest form. 8.9x+6.2+8.7 simplifies to 8.9x +14.9.

Each of the expressions below must simplify to 8.9x + 14.9 to be equivalent.

9x+6+9 = 9x + 15 NO

3.9+6.2+8.7x = 8.7x + 10.1 NO

3.7+8.9+6.2 = 18.8 NO

6.2+8.7+8.9 = 23.8 NO

6.2+8.7+8.9x = 8.9x + 14.9 YES

3.9+6.2x+8.7 = 6.2x + 12.6 NO

3.9x+8.7+6.2 = 3.9x + 14.9 NO

8 0

3 years ago

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Solve for the missing piece. Round answer to the nearest tenth when necessary.

galina1969 [7]

Answer:

21.0

Step-by-step explanation:

SOHCAHTOA

In this case you would be using TOA

tan (x) = opposite/ adjacent

tan (51) = x / 17

x = 17 tan (51)

x = 20.9932

x= 21.0

4 0

3 years ago

Delia spent 45 minutes working on her book report. She finished the report at 6:10 p.m. at what time did Delia start working on

inna [77]

All you have to do is subtract 45 from 6:10. Which is 5:65pm she started

7 0

3 years ago

Read 2 more answers