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Kay [80]
3 years ago
6

A race car travels 400 km in a time of 2 hours. Determine the speed of the race car

Mathematics
1 answer:
Debora [2.8K]3 years ago
6 0

Answer:

200km per hour

3.33km per second

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(x-5y,-3):(1,3y-x) find value of x and y<br>Please help me to solve thiss!!​
11Alexandr11 [23.1K]

Answer:

x=11, y=2

Step-by-step explanation:

We can set 1 equal to x-5y and then solve for x. and y.

x = 5y+1

y = x-1/5

We can use this information and plug back in the values for 3y-x or x-5y.

We can set -3 = 3y-x or 1 = x-5y.

To solve for x using -3 = 3y-x we can swap the values of x and y which would make it -3 = 3(x-1/5)-5(x-1/5)+1.

We can do a bit of algebra which would get us x = 11.

Knowing that y = x-1/5 we can plug in 11 for x. y = 11-1/5.

y=2

x=11, y=2

3 0
1 year ago
Prove for any positive integer n, n^3 +11n is a multiple of 6
suter [353]

There are probably other ways to approach this, but I'll focus on a proof by induction.

The base case is that n = 1. Plugging this into the expression gets us

n^3+11n = 1^3+11(1) = 1+11 = 12

which is a multiple of 6. So that takes care of the base case.

----------------------------------

Now for the inductive step, which is often a tricky thing to grasp if you're not used to it. I recommend keeping at practice to get better familiar with these types of proofs.

The idea is this: assume that k^3+11k is a multiple of 6 for some integer k > 1

Based on that assumption, we need to prove that (k+1)^3+11(k+1) is also a multiple of 6. Note how I've replaced every k with k+1. This is the next value up after k.

If we can show that the (k+1)th case works, based on the assumption, then we've effectively wrapped up the inductive proof. Think of it like a chain of dominoes. One knocks over the other to take care of every case (aka every positive integer n)

-----------------------------------

Let's do a bit of algebra to say

(k+1)^3+11(k+1)

(k^3+3k^2+3k+1) + 11(k+1)

k^3+3k^2+3k+1+11k+11

(k^3+11k) + (3k^2+3k+12)

(k^3+11k) + 3(k^2+k+4)

At this point, we have the k^3+11k as the first group while we have 3(k^2+k+4) as the second group. We already know that k^3+11k is a multiple of 6, so we don't need to worry about it. We just need to show that 3(k^2+k+4) is also a multiple of 6. This means we need to show k^2+k+4 is a multiple of 2, i.e. it's even.

------------------------------------

If k is even, then k = 2m for some integer m

That means k^2+k+4 = (2m)^2+(2m)+4 = 4m^2+2m+4 = 2(m^2+m+2)

We can see that if k is even, then k^2+k+4 is also even.

If k is odd, then k = 2m+1 and

k^2+k+4 = (2m+1)^2+(2m+1)+4 = 4m^2+4m+1+2m+1+4 = 2(2m^2+3m+3)

That shows k^2+k+4 is even when k is odd.

-------------------------------------

In short, the last section shows that k^2+k+4 is always even for any integer

That then points to 3(k^2+k+4) being a multiple of 6

Which then further points to (k^3+11k) + 3(k^2+k+4) being a multiple of 6

It's a lot of work, but we've shown that (k+1)^3+11(k+1) is a multiple of 6 based on the assumption that k^3+11k is a multiple of 6.

This concludes the inductive step and overall the proof is done by this point.

6 0
3 years ago
Read 2 more answers
Please answer ASAP<br> Thank you so much!!!!
anzhelika [568]

Answer:

See below

Step-by-step explanation:

Grade is slope =  rise / run

a) horizontal distance 1400 ft  (run)     vertical distance = 40 ft  (rise)

        40 / 1400 = 2.85%

b)   rise / run  =    805.58 / 13780 = 5.84%

3 0
1 year ago
The pool at "splash around" is open for 14 weeks during the summer. you can swim for $6 a session, or you can buy a membership f
Ratling [72]

Let

x--------> the number of sessions

y-------> the total payment

we know that

without membership:

y=6x --------> equation 1


with membership:

y=100+4x --------> equation 2

using a graph tool------> resolve the system of equations

see the attached figure

the solution is the point (50,300)

that means

For x=50\ sessions

the cost is \$300 in both forms

so

to justify buying the membership

x > 50\ sessions

therefore

<u>the answer is</u>

x > 50\ sessions


3 0
3 years ago
Read 2 more answers
The area of a parallelogram is 8√90 the base is 2√5. What is the<br> height of the parallelogram?
Vsevolod [243]

Step-by-step explanation:

Area of the Parallogram =bh

8√90=2✓5*h

12✓2=h

...................

3 0
3 years ago
Read 2 more answers
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