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sladkih [1.3K]
2 years ago
7

You and a friend are running on treadmills. you run 0.5 mile every 3 minutes and your friend runs 2 miles every 14 minutes. you

both start and stop running at the same time and run a whole number of miles. what is the least possible number of miles you and your friend can run?
Mathematics
2 answers:
Natali5045456 [20]2 years ago
4 0
I run 1 mile every 6 minutes.
My friend runs 1 mile every 7 minutes.
Lowest Common Multiple:  LCM ( 6, 7 ) = 42 minutes.
Me : 42 : 6 = 7 miles
My friend : 42 : 7 = 6 miles. 

rosijanka [135]2 years ago
4 0
Start by finding how long it takes each to run 1 mile.

You: 0.5 mile every 3 minutes => 1 mile every 6 minutes

Your friend 2 miles every 14 minutes => 1 mile every 7 minutes

Now you have to calculate the minimum common multiple of 6 and 7.

For that you need to factor both numbers and take common and non common factors raised to their highest exponent:

6 = 3*2
7 = 7

Then the minimum common multiple is 2*3*7=42.

Now divide the time 42 by the humber of minutes each of you take to run 1 mile

you: 42 minutes / 6 minutes per mile = 7 miles
your friend 42 minutes / 7 minutes per mile = 6 miles.

You can run 7 miles and your friend 6 miles in the same time.

Answer: 7 and 6

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yes and yes.

you're told ∠A=∠B. this means angle A and B are equal. so the value you get for cos A will be the same as the value you'll get for cos B

also, the value you get for tan A will be the same as the value you'll get for tan B


if that doesn't make sense you could also draw the triangle and solve for A and B.

you're told it's a right angled triangle meaning one of the angles = 90

you're told that C is that angle so if C is a right angle, angle C=90

the sum of all the angles in a triangle = 180

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angle A+ angle B + 90 = 180

angle A+ angle B = 180 - 90

angle A+ angle B = 90

  • A and B could be any value but you're told angle A = angle B

        angle A+ angle B = 90

        you can divide 90 by 2 because A and B are equal. that will give you 45 for A and 45 for B

or

  • angle A+ angle B = 90

        since angle A = angle B,

1. you can substitute angle A with angle B like this

  angle B+ angle B = 90

  2 angle B = 90

  angle B = 90/2

  angle B=45; ∴ angle A is also 45 ( because angle A= angle B)

2. or you could substitute angle B with angle A

   angle A+ angle A = 90

2 angle A = 90

  angle A = 90/2

  angle A =45; ∴ angle B is also 45 ( because angle A= angle B)


Now you know what A and B are,

sin A = sin 45; sin B = sin 45

sin 45 = sin 45

tan A = tan 45; tan B = tan 45

tan 45 = tan 45

7 0
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Question 5: 10 pts
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6.7i + 7.4j

Step-by-step explanation:

if the angle starts from the East (direction of positive x-axis)

then the y (j) component is 10*sin(42) = 6.7

and x (i) component is 10*cos(42) = 7.4

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2 years ago
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Oksi-84 [34.3K]
7) Certainly there is a typo in the statement, just see that the expression of item (ii) is different from that of item (i). Probably the correct expression is: 2x^2-4x+5. With this consideration, we can continue.

(i) Let E the expression that we are analyzing:

E=2x^2-4x+5\\\\ E=2x^2-4x+2-2+5\\\\ E=2(x^2-2x+1)-2+5\\\\ E=2(x-1)^2+3

Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.

(ii) Manipulating the expression:

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8) Let E the expression that we want to calculate:

E=(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)+1\\\\ E-1=(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)

Multiplying by (2-1) in the both sides:

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