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4 years ago

8k + 2m=3m +k solve for k

Mathematics

2 answers:

Veronika [31]4 years ago

5 0

Answer: k= One- seventh of m.

Step-by-step explanation:

Given equation : 8k + 2m=3m +k ,where k and m are variables

To solve for k, Subtract 2m from both sides,we get

⇒8k+2m-2m=3m-2m+k

Simplify

⇒ 8k=m+k

Subtract k from both sides, we get

⇒ 8k-k=m+k-k

Simplify

⇒ 7k=m

Divide 7 from both the sides, we get

⇒ k=1/7m

⇒ k=one-seventh of m...........>here is the answer.

spin [16.1K]4 years ago

4 0

The answer is K=M/7. That is the answer I got taking the quiz on ed.

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A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial pos

jeka57 [31]

Part A - The average value of v(t) over the interval (0, π/2) is 6/π

Part B - The displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

<h3>Part A: Find the average value of v(t) on the interval (0, π/2)</h3>

The average value of a function f(t) over the interval (a,b) is

$f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx$

So, since velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval (0, π/2) is given by

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt$

Since v(t) = 3cost, we have

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}$

So, the average value of v(t) over the interval (0, π/2) is 6/π

<h3>Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?</h3>

To find the displacement of the yo-yo, we need to find its position.

So, its position x = ∫v(t)dt

= ∫3cos(t)dt

= 3∫cos(t)dt

= 3sint + C

Given that at t = 0, x = 3. so

x = 3sint + C

3 = 3sin0 + C

3 = 0 + C

C = 3

So, x(t) = 3sint + 3

So, its displacement from time t = 0 to time t = π is

Δx = x(π) - x(0)

= 3sinπ + 3 - (3sin0 + 3)

= 3 × 0 + 3 - 0 - 3

= 0 + 3 - 3

= 0 + 0

= 0 m

So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m

<h3>Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)</h3>

The total distance the yo-yo travels from time t = 0 to time t = π is given by

$x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6$

So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

Learn more about average value of a function here:

brainly.com/question/15870615

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4 0

1 year ago

only 93% of the airplane parts being examined pass inspection. what is the probability that the next 5 parts examined will all p

DedPeter [7]

Answer:

Question 4 pts Only 93% of the airplane parts being examined pass Inspection: What is the probabllity that the next 5 parts examined will all pass inspection? (Write your probability a5 decimal rounded to the nearest thousandth or third decimal place):

Step-by-step explanation:

in order for us to find this probability here. What we're going to need to do is first ask ourselves if we were to just randomly select five parts, does one passing or felling affect the next one passing your fellow. And it really wouldn't um because one passing doesn't really say the next word should pass. And so because of that we know that this is going to be an independent event and if we have an independent event that's just really going to be where we multiply the probabilities of each live, it's occurring by themselves. So in this case it's just going to be the probability of one of them passing times 0.3 times the probability of the second one passing times. The probability of the third passing times. The fourth passing At times the 5th passing For just 0.93 Raised to the 5th power. So this is going to be the exact answer but they want it to three decimal places Which is going to be 0.6 956. So we round to three decimal so we have six and then we have five. So we would round it up To about 6.96. So this is going to be our probability or if you want you can change this into a decimal of 69.6%. But normally we would receive it as this decimal here. So either of these um would be good answers for what we have here

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3 years ago

All figures below are regular, which figure has point symmetry (I.e. rotational symmetry of 180)?

kenny6666 [7]

Answer:

Step-by-step explanation:

After rotation the hexagon 180° you will have the same image that you started with.

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2 years ago

Complete the table

djverab [1.8K]

I think the equation is y=5+2x

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3 years ago

10 + 5 + 5 ( 10 + 10 )

Shalnov [3]

Answer:

The answer is 115 you do parentheses first and multiply 5 by the number in the parentheses and then add

Step-by-step explanation:

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3 years ago