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Ivahew [28]
3 years ago
8

A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is give

n by the function h= -16t^2 + 112t + 30 .
How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.



A. 7 s; 30 ft
B. 3.5 s; 366 ft
C. 3.5 s; 618 ft
D. 3.5 s; 226 ft
Mathematics
1 answer:
defon3 years ago
7 0
To determine the time it takes for the maximum height to be achieved, derive the  equation and equate to zero. 
                        h = -16t² + 112t + 30
                       dh / dt = 0 = 2(-16)t + 112
The value of t is 3.5 s. Substitute this value of time to the equation for h,
                         h = -16 x (3.5 s)² + 112 x 3.5 s + 30 = 226 ft
Thus, the answer is letter D. 
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Precalculus
kodGreya [7K]

Answer:

$24.35

Step-by-step explanation:

We will use the compound interest formula provided to solve this problem:

A=P(1+\frac{r}{n} )^{nt}

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

<em />

First, change 1% into a decimal:

1% -> \frac{1}{100} -> 0.01

Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:

A=800(1+\frac{0.01}{12})^{12(3)}

A=824.35

Lastly, subtract <em>A </em>from the principal to get the interest earned:

824.35 - 800 = 24.35

8 0
3 years ago
1/2 cubed? Please help...
Fudgin [204]
1/2 cubed= 1/2 times 1/2 times 1/2
1/2 time 1/2 = 1/4
1/4 times 1/2 = 1/8

A: 1/2 cubed equals 1/8
6 0
3 years ago
Find the probability of throwing a sum of 4 at least 6 times in 9 throws of a pair of fair dice.
lora16 [44]
4/6 with 2 throws left i think.
4 0
3 years ago
La batalla de Inglés y Matemáticas Pregunta: Tenía $ 5.00 Mi mamá me dio $ 10.00 mientras que mi papá me dio $ 30.00. Mi tía y m
nasty-shy [4]

Answer:

$150.00

Step-by-step explanation:

Tenía $ 5.00

Mi mamá me dio $ 10.00 mientras que mi papá me dio $ 30.00.

Esto significa que luego tengo:

5 + 10 + 30 = $ 45.00

 

Mi tía y mi tío me dieron 100.00.

Entonces tuve:

45 + 100 = $ 145.00

Tenía otros $ 5.00.

Esto significa que en conjunto tuve:

145 + 5 = $ 150.00

5 0
3 years ago
judy has a piece of wood that is 4 5/8 feet long. she cuts off 3 feet 6 inches of the wood for a project. how much wood, in feet
Svet_ta [14]

there are 12 inches in 1 foot, so 6 inches is really just half a foot, thus 3'6" is really just 3.5' or 3½ feet.

now, let's convert those mixed fractions to improper fractions and then subtract, bearing in mind our LCD will be 8.

\bf \stackrel{mixed}{4\frac{5}{8}}\implies \cfrac{4\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{45}{8}-\cfrac{7}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)45~~-~~(4)7}{8}}\implies \cfrac{45-28}{8}\implies \cfrac{17}{8}\implies 2\frac{1}{8}

6 0
3 years ago
Read 2 more answers
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