MATHEMATICS MIDDLE SCHOOL

The equation that models the height above or below equilibrium in inches, h, of a spring over time in seconds, t, is h = -15 cos(2pi/5 t). At which times will the spring be at a height of 8 in. above equilibrium? Select two of the following, make two selections.

Answers

Answer 1

Answer:

Answer:

1.7 seconds, and

3.3 seconds

Step-by-step explanation:

We simply need to plug in 8 into h and solve for t:

$h=-15Cos((2\pi)/(5)t)\n8=-15Cos((2\pi)/(5)t)\n-(8)/(15)=Cos((2\pi)/(5)t)\n(2\pi)/(5)t=Cos^(-1)(-(8)/(15))\n(2\pi)/(5)t=2.13\nt=(2.13)/((2\pi)/(5))\nt=1.70$

Since cosine is negative in the 3rd quadrant as well, we need to figure out the 3rd quadrant equivalent of 2.13 radians.

First, π - 2.13 radians = 1.01 radians.

Then, we add 1.01 to π radians, so we get 4.15 radians

Solving from the last part, we have:

$t=(4.15)/((2\pi)/(5))\nt=3.3$

also, t = 3.30 seconds

*Note: we put the calculator mode in radians when solving

So, t = 1.7 seconds & 3.30 seconds

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Thomas has a box with four black color bottles and eight gray color bottles. Two bottles are drawn without replacement from the box. What is the probability that both of the bottles are gray

Answers

The probability that the bottles pulled out are gray is a 8:4 chance. Reduced that would be 1:2. so 1/2 chance that both are gray

Please someone can help me with #3. Thanks

Answers

You plug in 8 for the r's and you'll get 8 plus 8 divide by 2 times 4 then youll get 8+4 times 4. Then you'll get 8+16 and it --24

r + r ÷ 2 × 4 when r = 8.

8 + 8 ÷ 2 × 4
8 + ___ × 4
8 + ___
___

Lets solve for the missing.

8 + 8 ÷ 2 × 4
8 ÷ 2 = 4
8 + 4 × 4
4 × 4 = 16
8 + 16
8+16 = 24

SO:-

8 + 8 ÷ 2 × 4
8 + _4_ × 4
8 + _16__
_24__

So, r + r ÷ 2 × 4 when r = 8 is 24.

Hope I helped ya!! xD

How many eighths in one half

Answers

4/8 = 1/2 so it is four eigths in one half. 4/8 simplified is 1/2

lets think about that.....
what is half of eight???
four, so in one half there would be four-eighths.

4 1
8 = 2

i hope i helped

John is 6 years older than Keisha. Together their ages equal four times Keisha's age. How old is each?

Answers

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Age of John = m

Age of Keisha = n

m = 6 + n

m + n = 4n

m = 9

n = 3

The age of John is 9

The age of Keisha is 3

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let the age of John = m

Let the age of Keisha = n

Now,

John is 6 yearsolder than Keisha.

This means,

m = 6 + n _____(1)

Together their ages equal fourtimesKeisha's age.

This means,

m + n = 4n _____(2)

From (1) and (2) we get,

6 + n + n = 4n

6 + 2n = 4n

6 = 4n - 2n

6 = 2n

n = 3

Now,

m = 6 + n

m = 6 + 3

m = 9

Thus,

The age of John is 9

The age of Keisha is 3

Learn more about expressions here:

brainly.com/question/3118662

#SPJ2

J = K+6
K + J = 4K

Replace J in the second equation
K + (K + 6) = 4K
K + K + 6 = 4K
2K + 6 = 4K
Subtract 2K from each side
6 = 2K
Divide both sides by 2
K=3

So, Keisha is 3 and therefore John is 9 because 3 + 6=9

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Answers

I would say for every 1 brownie, there are 5 cookies.

Yes cheetah is correct.She would have 1 brownie and 5 cookies,She would have 20 groups.

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Answers

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