MATHEMATICS HIGH SCHOOL

A weight is attached to to a spring that is fixed to the floor. The equation h=7cos (pi/3 t) models the height, h, in centimeters after t seconds of the weight being stretched and released. Solve for the solution of t and find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round to the nearest hundreth

Answers

Answer 1

Answer:

Answer:

$t=(3)/(\pi)\left(\cos ^(-1)(h)/(7)\right)$

Step-by-step explanation:

The given function is,

$h=7\cos \left((\pi)/(3)t\right)$

$\Rightarrow \cos \left((\pi)/(3)t\right)=(h)/(7)$

$\Rightarrow (\pi)/(3)t=\cos ^(-1)(h)/(7)$

$\Rightarrow t=(3)/(\pi)\left(\cos ^(-1)(h)/(7)\right)$

This is the solution of t.

Now we have to find t when h is 1 cm, 3 cm and 5 cm.

When h=1

$t=(3)/(\pi)\left(\cos ^(-1)(1)/(7)\right)=78.10\ s$

When h=3

$t=(3)/(\pi)\left(\cos ^(-1)(3)/(7)\right)=61.71\ s$

When h=5

$t=(3)/(\pi)\left(\cos ^(-1)(5)/(7)\right)=42.41\ s$

Answer 2

Answer: lets solve for t in the height equation:

h = 7 cos (pi/3 t)
cos (pi/3 t) = h/7
pi/3 t = cos^-1 (h/7)

t = (3/pi) cos^-1 (h/7)

then we substitute:

t = (3/pi) cos^-1 (1/7)
t = 78.1 s

t = (3/pi) cos^-1 (3/7)
t= 61.71

t = (3/pi) cos^-1 (5/7)
t = 42.41

those are the times in seconds respectively.

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Write an integer expression using absolute value symbols to represent the verbal expression.-the absolute value of negative eight-
Enter the correct answer in the box.

Answers

Answer:

$Absolute\ Value = 8$

Step-by-step explanation:

Given

Digit = -8

Required

Determine the absolute value

The absolute value is calculated as follows;

$Absolute\ Value = |Digit|$

Substitute -8 for Digit

$Absolute\ Value = |-8|$

And it returns the positive of its input;

$Absolute\ Value = 8$

Final answer:

The absolute value of negative eight is represented by |-8|. In mathematics, absolute value refers to the distance of a number from zero, disregarding its sign.

Explanation:

The verbal expression 'the absolute value of negative eight' can be written as an integer expression using absolute value symbols as follows: |-8|. The symbol | | denotes the absolute value. Absolute value is a mathematical concept that refers to the non-negative value of an integer, ignoring its sign. Hence, the absolute value of -8 is 8, because 8 is the distance that -8 is from zero on the number line.

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One person can do a certain job in ten minutes, and another person can do the same job in fifteen minutes. How many minutes will they take to do the job together? 4 min 5 min 6 min

Answers

A can do 1 job in 10 min. means 1/10 job per min.
B can do 1/15 job per min.

together A&B can do 1/10+1/15 =1/6 job per min.

1/6 job they spend 1 min
1 spend 1x1/(1/6) = 6 min

Final answer:

The first person completes a job in 10 minutes and the second person completes the same job in 15 minutes. When they work together, they can do the job in 6 minutes.

Explanation:

This question pertains to the concept of rate of work. Work rate is generally described as the amount of work done per unit time. The first person completes the job in ten minutes, so their work rate is 1 job per 10 minutes. The second person completes in fifteen minutes, so their work rate is 1 job per 15 minutes.

When they work together, their rates of work add up. Therefore, the rate at which they complete the work together is (1 job/10 minutes) + (1 job/15 minutes).

Convert these rates to a common denominator (30) to simplify the calculation: (30 jobs/300 minutes)+(20 jobs/300 minutes) equals 50 jobs/300 minutes.

Therefore, together, they can do 50 jobs in 300 minutes. Hence, to do 1 job, they will need 300 minutes / 50 = 6 minutes.

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You have a coin collection of nickels and dimes containing 63 coins. If you have$5.05, how may of each coin do you have?

Answers

Answer: 25 nickels

Step-by-step explanation:

EQUATIONS:

quantity: n + d = 63

value: 5n + 10d = 505

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

Divide thru the 2nd equation by 5 to get:

n + 2d = 101

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

Subtract that from the 1st equation:

-d = -38

d = 38 (# of dimes)

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

Substitute that into n+d=63 to solve for "n":

n + 38 = 63

n = 25 (# of nickels)

F(x)=1\3x^2+3x-18
Please help with steps

Answers

So far, you've only defined f(x). You haven't asked a question.

Okay, it looks like you're going to have to do this on your own (me too lol). I'm guessing you have to make a video also?

At a restaurant the ratio of kids meals sold to adult meals sold was 7:3. Ifthere were 35 kids meals sold, how many adult meals were sold?

Answers

Answer:

Step-by-step explanation:

because 35 divided by 5 is 7 and 15 divided by 15 is 3 making 7:3

hope it helps

Evaluate x0 + y0 for x = 3 and y = 2.

Answers

Answer:

The value of given expression is 2

Step-by-step explanation:

Given: Expression is $x^0+y^0$

To find : Value of expression when x = 3 and y = 2

Consider,

$x^0+y^0$

To find value we put value of x = 3 and y = 2

$\implies 3^0+2^0$

Now we know that value of expression whose power 0 is 1 irrespective of value of base .i.e, $a^0=1$ ∀ a ∈ any no.

⇒ $3^0=1\:and\:2^0=1$

$\implies 3^0+2^0$ = 1 + 1

⇒ 2

Therefore, The value of given expression is 2

Good evening

x^0+y^0 for x=3 and y=2

First thing we need to do is to replace their value

3^0+2^0

Remember: Any number that raised to the zero power equal 1

so now we have

3^0=1 and y^2=1

1+1

= 2

I hope that's help :0

Any Questions /

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