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2 years ago

Convert 14.75 to its equivalent fraction expressed in lowest terms

Mathematics

1 answer:

stellarik [79]2 years ago

6 0

Either its 14 and 3 4ths or 59 4ths. its depends on what fractions it wants it in. hope this makes sense!

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The floor of a canyon has an elevation of −14.5−14.5 feet. Erosion causes the elevation to change by −1.5−1.5 feet per year. How

Alona [7]

The canyon starts at an elevation of (-14.5). After each year, the elevation drops by (-1.5). The equation that could be written for this, then, would be (-14.5 - 1.5x = -31). First, we could add 14.5 to both sides of the equation to isolate the unknown. This would leave -1.5x = -16.5. Next, we can remove the negative signs so both sides of the equation are positive and easier to work with. This leaves 1.5x = 16.5. Finally, dividing both sides by 1.5 gives us "x = 11", which means that after 11 years, the canyon floor will be at -31 feet.

4 0

2 years ago

Arc AB is One-sixth of the circumference of a circle. What is the radian measure of the central angle? StartFraction pi over 6 E

oksian1 [2.3K]

Answer:

StartFraction pi Over 3 EndFraction

Step-by-step explanation:

we know that

The circumference of a circle subtends a central angle of 360 degrees or 2π radians

by proportion

Find out the central angle for an arc equal to One-sixth of the circumference of a circle

Let

x -----> the measure of the central angle in radians for an arc equal to One-sixth of the circumference

$\frac{C}{2\pi}=\frac{(C/6)}{x}\\\\x=2\pi(C/6)/C\\\\x=\frac{2\pi}{6}$

Simplify

$x=\frac{\pi}{3}$

therefore

StartFraction pi Over 3 EndFraction

5 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

Peyton plans to deposit her next paycheck into her savings account.she makes $12.50 per hour and her next paycheck will be h hou

Snowcat [4.5K]

Answer: Current savings account balance

Step-by-step explanation:

since the equation is y = mx + b

mx would be the starting point so she earns 12.50 per hour so it's the current amount she has is 12.50.

Sorry if it dosen't make sense.

5 0

2 years ago

a basketball player made 27 free throws in her last 45 tries. what is the experimental probability that she will make her next f

Strike441 [17]

Hey mark me brainlest but ur answer is 27/45

Bess ur day.

8 0

2 years ago