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2 years ago

If the expression (2ya)4 is equivalent to 16y8 , what is the value of A.

1 answer:

7 0

If you meant:

(2ya)^4=16y^8 raise the left side to the power of four

16y^4*a^4=16y^8 divide both sides by 16y^4

a^4=y^4 take the quartic root of both sides

a=±y

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Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m

VLD [36.1K]

<h2>Answer:</h2>

The average speed of car is:

0.75 miles per minutes.

The equation of line is:

$n=\dfrac{3}{4}t$

<h2>Step-by-step solution:</h2>

The table that describes the time and number of miles marked is given by:

Time Miles

0 0

4 3

8 6

Clearly we could observe that with the increase in time by every 4 minutes the number of mile increases by 3.

i.e. the average speed is calculated as the ratio of change in miles to the change in time.

Hence,

$Average\ Speed=\dfrac{3-0}{4-0}\\\\\\i.e.\\\\\\Average\ Speed=\dfrac{3}{4}=0.75$

Hence, the average speed=0.75 miles per minutes.

Also we will find the equation of the lines that related the miles and time by using the two-point formula.

i.e. any line passing through (a,b) and (c,d) is calculated by using the formula:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here (a,b)=(0,0) and (c,d)=(4,3)

i.e. the equation is given by:

$n-0=\dfrac{3-0}{4-0}\times (t-0)\\\\i.e.\\\\n=\dfrac{3}{4}t$

6 0

2 years ago

Read 2 more answers

Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At x = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at x = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at x = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

4 0

2 years ago

On september 8, 2004, the genesis spacecraft crashed in the utah desert because its parachute did not open. the 210-kg capsule h

maw [93]

311km/h = 86.389 m/s
Initial KE 
= 0.5 * 210 * 86.389^2 J 

work done by force of ground 
= F * 0.81 J 

0.5 * 210 * 86.389^2 = 0.81 F 

F = 967433.58 N 

capsule's weight W= 210 * 9.81 = 2060.1 N 

F = 469.6 times capsule weight ---answer

6 0

2 years ago

Arrivals at a fast-food restaurant follow a poisson distribution with a mean arrival rate of 16 customers per hour. what is the

maks197457 [2]

Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour. In the study of statistics and probability, the Poisson distribution is a widely-used discrete probability distribution. Using the formula, it was determined that 0.0661 is the probability that in the next hour there will be exactly 12 arrivals.

8 0

2 years ago

Customer: "I see that the amount I owe has been reduced from $90.00 to $75.00." Employee: "Yes, the discount has saved you _____

dusya [7]

Answer:

15 dollers or 22.5%

Step-by-step explanation:

thank you i hope this helps

3 0

2 years ago

Read 2 more answers