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Rufina [12.5K]
1 year ago
9

A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air h = −162 + 24t + 16.

How long will it take the gymnast to reach the ground?
Mathematics
1 answer:
dimulka [17.4K]1 year ago
5 0
That is when h=0
so assuming yo meant
h(t)=-16t²+24t+16
solve for t such that h(t)=0
because when height=0, the gymnast hits the ground

so
0=-16t²+24t+16
using math (imma complete the square
0=-16(t²-3/2t)+16
0=-16(t²-3/2t+9/16-9/16)+16
0=-16((t-3/4)²-9/16)+16
0=-16(t-3/4)²+9+16
0=-16(t-3/4)²+25
-25=-16(t-3/4)²
25/16=(t-3/4)²
sqrt both sides
+/-5/4=t-3/4
3/4+/-5/4=t
if we do plus (because minus would give us negative height)
8/4=t
2=t
it takes 2 seconds
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Answer:

24.39mL of the solution would be given per hour.

Step-by-step explanation:

This problem can be solved by direct rule of three, in which there are a direct relationship between the measures, which means that the rule of three is a cross multiplication.

The first step to solve this problem is to see how many mg of the solution is administered per hour.

Each minute, 200 ug are administered. 1mg has 1000ug, so

1mg - 1000 ug

xmg - 200 ug

1000x = 200

x = \frac{200}{1000}

x = 0.2mg

In each minute, 0.2 mg are administered. Each hour has 60 minutes. How many mg are administered in 60 minutes?

1 minute - 0.2 mg

60 minutes - x mg

x = 60*0.2

x = 12mg

In an hour, 12 mg of the drug is administered. In 250 mL, there is 123 mg of the drug. How many ml are there in 12 mg of the drug.

123mg - 250mL

12 mg - xmL

123x = 250*12

x = \frac{250*12}{123}

x = 24.39mL

24.39mL of the solution would be given per hour.

7 0
1 year ago
A mouse traveled a total distance of 3/24 of a mile in a maze over the past three hours the mouse travel the same distance each
alexgriva [62]

Answer:

Total distance mouse traveled in 3 hours = \frac{3}{24} of a mile

The mouse traveled the same distance in each hour. So in order to find the distance covered in 1 hour we have to divide the distance covered in 3 hours by 3. This will give us the distance that the mouse traveled in one hour.

So, the distance traveled in one hour will be = \frac{3}{24} \div 3 = \frac{3}{24} \times \frac{1}{3} =\frac{1}{24} of a mile

The error which Matt made was that he divided only the denominator of the expression by 3, this probably was a calculation error.

Correct conclusion will be: Mouse travel 1/24 of a mile each hour

8 0
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Lelu [443]
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3 0
1 year ago
Read 2 more answers
Jeremy rides his bike at a rate of 15 miles per hour. Below is a table that represents the number of hours and miles Kevin rides
TiliK225 [7]

The correct answer would be, Jeremy rides at a greater speed than Kevin.

Step-by-step explanation:

Jeremy rides at a rate of 15 miles per hour

Kevin rides at a rate given in the table

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And X be the number of hours

Then for Jeremy:

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(46-23)/(4-2)

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So for Kevin, Y = 11.5 x

So when Jeremy's and Kevin's rates are compared,

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which means Jeremy rides at a greater speed.  

Learn more about Time and Distance problem at:

brainly.com/question/3581191

#LearnWithBrainly

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This is an example of a distribution property. In a distribution property, the number outside the parenthesis is distributed to all the terms inside it by multiplication. So the answer here is:

<span>The 4 will be multiplied to each term inside the parentheses.

</span>

5 0
2 years ago
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