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patriot [66]
2 years ago
15

y is directly proportional to x^3. it is known that =5 for a particular value of x. find the value of y when this value of y whe

n this value of x is multplied by 1/2.​
Mathematics
1 answer:
alina1380 [7]2 years ago
5 0

Answer:

The value of y when the value of x is multiplied by \frac{1}{2} is \frac{5}{8}.

Step-by-step explanation:

According to the statement, we have the following relationship:

y = k\cdot x^{3} (1)

Where:

x - Independent variable.

y - Dependent variable.

k - Proportionality constant.

We can eliminate the proportionality constant by constructing the following relationship:

\frac{y_{2}}{y_{1}} = \left(\frac{x_{2}}{x_{1}} \right)^{3}

If we know that y_{1} = y, y_{2} = 5, x_{2} = x_{o} and x_{1} = \frac{1}{2}\cdot x_{o}, then the value of y when the value of x is multiplied by \frac{1}{2} is:

\frac{5}{y} = \left(\frac{x_{o}}{\frac{1}{2}\cdot x_{o} } \right)^{3}

\frac{5}{y} = 8

y = \frac{5}{8}

The value of y when the value of x is multiplied by \frac{1}{2} is \frac{5}{8}.

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sleet_krkn [62]
The answer is A because the “hops” are jumping over two spaces which equals 2/10 simplified to 1/5. and since the number line stops at 2 it’d be 2 and not 1. If you do the keep change flip method for answer option one you get 10.
5 0
3 years ago
A person invest $10,000 into a bank the bank pays 4.75% interest compounded semi annually. To the nearest 10th of a year, how lo
Mama L [17]

Answer:

T is 13.9 years to the nearest 10th of a year

Step-by-step explanation:

In this question, we are to calculate the number of years at which someone who invests a particular amount will have a particular amount based on compound interest.

To calculate the number of years, what we do is to use the compound interest formula.

Mathematically,

A = P(1+ r/n) ^nt

Where A is the final amount after compounding all interests which is $19,200 according to the question

P is the initial amount invested which is $10,000 according to the question

r is the rate which is 4.75% according to the question = 4.75/100 = 0.0475

n is the number of times per year in which interest is compounded. This is 2 as interest is compounded semi-annually

t= ?

we plug these values;

19200 = 10,000(1+0.0475/2)^2t

divide through by 10,000

1.92 = (1+0.02375)^2t

1.92 = (1.02375)^2t

We find the log of both sides

log 1.92 = log [(1.02375)^2t)

log 1.92 = 2tlog 1.02375

2t = log 1.92/log 1.02375

2t = 27.79

t = 27.79/2

t = 13.89 years

The question asks to give answer to the nearest tenth of a year and thus t = 13.9 years

7 0
3 years ago
Please help me answer this <br><br> Explain you’re answer <br><br> Will give braisnlt
choli [55]

Answer:

Concept: Math Analysis

  1. So we want the cost of a 8 × 10
  2. Notice the price distribution
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3 0
2 years ago
Create an expression to represent the following<br><br> (picture is included below)
zheka24 [161]

Answer:

7) x + 0.09x, where x is the price of the car

8) x + 0.05x where x is the price of clothing

9) It will take michael about 9.14 minutes to eat 32 cookies.

Step-by-step explanation:

7) 9% of x is the same as 0.09x, so you can write this:

x + 0.09x, where x is the price of the car

8) same thing for this one

x + 0.05x where x is the price of clothing

9) michael can eat cookies at a rate of 21 cookies per 6 minutes, or \frac{21}{6}

Because he will be eating them at the same pace, you can write an equation and solve for the variable:

\frac{21}{6} = \frac{32}{y}

cross multiply the proportion:

21 × y = 32 × 6

solve:

21y = 192

y ≈ 9.14

It will take michael about 9.14 minutes to eat 32 cookies.

This works because they both simplify to 3.5 cookies per minute

\frac{21}{6} = 3.5

\frac{32}{9.14} = 3.5

6 0
3 years ago
Someone please help me asap need answers to all 8 problems and If possible explain how you got them
sattari [20]

Answer:

1.C=10cm

3.b=12cm

5.x=5cm

6.x=8mm

Step-by-step explanation:

a2 + b2 =c2

82 + 62=c2

64 +36 =c2

[100=c2]    Square root

c=10cm  

8 0
3 years ago
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