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Katena32 [7]
3 years ago
8

Roger and Natalie travel in similar cars. Roger's car drives the two miles to school in 7.5 minutes. Natalie drives the same dis

tance in the opposite direction but in only 6.5 minutes. What is true of their velocities?
Mathematics
2 answers:
slava [35]3 years ago
8 0

Answer:

Natalie's velocity is greater in magnitude than Roger's velocity.

Step-by-step explanation:

Roger and Natalie both are travelling two miles.  

The cars by which they both of them travel are also similar.

Assuming that they are both obeying traffic laws :  

Time taken by Roger to travel 2 miles = 7.5 minutes

Time take by Natalie to travel 2 miles = 6.5 minutes

Now, since the time taken by Natalie to cover 2 miles is less than that of Roger so, The velocity of Natalie is greater than that of Roger.

Also, it is given that Roger and Natalie are traveling in opposite directions so we have to also consider the magnitude in this case.

Because it might be possible that Roger is travelling 2 miles uphill then in that case the velocity of Roger will be greater than that of Natalie.

Hence, Natalie's velocity is greater in magnitude than Roger's velocity.

Ipatiy [6.2K]3 years ago
4 0

Natalie’s velocity is greater in magnitude than Roger’s velocity.

i took the test and it was right :)

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The population of a place increased to 54,000 in 2003 at a rate of 5% per annum. what would
svlad2 [7]

Answer:

The population in 2005 is 59,535 people.

Step-by-step explanation:

Annum means annually or yearly. We assume the rate has been consistent. To calculate percentage, take the percent in decimal form. 5% is 0.05 (like 17% is 0.17, and 50% 0.5). 5% is actually 5 hundredths of a number. Multiply this by the number you want the percentage of. 54,000*0.05=2,700. This is how much the population grows from 2003 to 2004.

There is a very common mistake people make after this, which is simply doubling that number and adding to the population. This is incorrect because if it grows 5% yearly, the yearly population CHANGES. The question would change if it were 2004 to 2005. Ask your teacher for clarification if this sounds wrong (if it is, do what I said above, the answer would be 59,400 people).

So, the population in 2004 is 54,000+2,700=56,700. Now, find 5% of the population in 2004 using the same method as before. 56,700*0.05=2,835. Add the growth to the pervious population. 56,700+2,835=59,535.

The population in 2005 is 59,535 people.

7 0
2 years ago
HELP PLZ ILL GIVE BRAINLIEST
svet-max [94.6K]

Step-by-step explanation:

m<G=m<H

180-20= 160°

160/2=80°

m<G= 80°

4 0
2 years ago
The area of a rectangle is
ANEK [815]
Area = length x width
length = 3 x width - 5

i.e. 50 = w(3w - 5)
3w^2 - 5w - 50 = 0
(3w + 10)(w - 5) = 0
w = -10/3 or w = 5
but width cannot be negative, hence
width = 5 yd
Length = 3 x 5 - 5 = 15 - 5 = 10 yd
8 0
3 years ago
Consider the function V=g(x), where g(x) =x(6-2x)(8-2x), with x being the length of a cutout in cm and V being the volume of an
Andrej [43]

Answer:

The maximum volume of the open box is 24.26 cm³

Step-by-step explanation:

The volume of the box is given as V=g(x), where g(x)=x(6-2x)(8-2x) and 0\le x\le3.

Expand the function to obtain:

g(x)=4x^3-28x^2+48x

Differentiate  wrt  x to obtain:

g'(x)=12x^2-56x+48

To find the point where the maximum value occurs, we solve

g'(x)=0

\implies 12x^2-56x+48=0

\implies x=1.13,x=3.54

Discard x=3.54 because it is not within the given domain.

Apply the second derivative test to confirm the maximum critical point.

g''(x)=24x-56, g''(1.13)=24(1.13)-56=-28.88\:

This means the maximum volume occurs at x=1.13.

Substitute x=1.13 into g(x)=x(6-2x)(8-2x) to get the maximum volume.

g(1.13)=1.13(6-2\times1.13)(8-2\times1.13)=24.26

The maximum volume of the open box is 24.26 cm³

See attachment for graph.

6 0
3 years ago
Find the value of given expression<br><br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B29%20-%204%7D%20" id="TexFormula1" titl
Dafna11 [192]
So 29-4 =25... which is a perfect square

Answer= +/- 5
3 0
3 years ago
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