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3 years ago

What is the rate of change of the water level , in feet per hour

Mathematics

1 answer:

miskamm [114]3 years ago

4 0

A; rate of change is the same as slope, so, using the slope formula, $m= \frac{y_{2} - y\1_{1} }{ x_{2} - x_{1} }$ , where $m$ is the slope and $x_{1}$ , $x_{2}$ , $y_{1}$ , and $y_{2}$ are the $x$ and $y$ values.

Plug in $2$ points for $x$ and $y$ , water level being the $y$ and time being the $x$ since we're looking for the answer in ft/hr-- you can choose any two, but from the same row.

$m= \frac{ 30-50}{4-0}$
$m= \frac{-20}{4}$
$m= \frac{-5}{1}$
$m= -5$ ft/hr

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Which expression has the greater value? Justify your answer. −8 + 3 −8 × 3

barxatty [35]

Did u mean -8+3= and -8x3= cuz if so then it’s -8+3=-5 and -8x3=-24 so it would be -8+3

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4 years ago

Given the expression 12 over 12 to the third power.

4vir4ik [10]

Part 1:
Before we begin, you need to remember the following rule:
$\frac{x^a}{x^b} = x^{a-b}$

The given expression is:
$\frac{12}{12^3}$

Since the base is the same in both numerator and denominator, we can apply the above rule. This means that:
$\frac{12}{12^3}$ = 12¹⁻³ = 12⁻²

Part 2:
Before we begin, you need to remember the following rule:
x⁻ᵃ = $\frac{1}{x^a}$

Now, from part 1, we simplified the expression into 12⁻²
Since the power is negative, we can apply the above rule.
This means that:
12⁻² = $\frac{1}{(12)^2} = \frac{1}{12*12} = \frac{1}{144}$

Hope this helps :)

5 0

4 years ago

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On monday caroline spent 2/3hour riding her bike and 1 3/4 doing homework how many more hours did caroline spend doing homework

Andrej [43]

2/3 hour is 40 minutes. 1 3/4 hour is 1 hour and 45 minutes. So she spent 1 hour and 5 minutes or 1 1/12 hour longer doing homework.

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3 years ago

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Find the lateral area for the pyramid with the equilateral base.

Dafna11 [192]

Answer:

Option A is the correct answer.

Explanation:

The given pyramid has 3 lateral triangular side as shown below.

Base of triangle = 12 unit

We need to find perpendicular.

By Pythagoras theorem we have

Perpendicular² = 10²-6²

Perpendicular = 8 unit

So area of 1 lateral triangle = 1/2 x Base x Perpendicular.

= 1/2 x 12 x 8 = 48 unit²

Area of lateral side = 3 x 48 = 144 unit²

Option A is the correct answer.

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3 years ago

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Evaluate the following limit:

Makovka662 [10]

If we evaluate the function at infinity, we can immediately see that:

$\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle L = \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}} = \frac{\infty}{\infty}} \end{gathered}$}$

Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.

We can solve this limit in two ways.

By comparison of infinities:

We first expand the binomial squared, so we get

$\large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{x^4 - x^2 + 4}{x^3 - 5}} = \infty \end{gathered}$}$

Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.

Dividing numerator and denominator by the term of highest degree:

$\large\displaystyle\text{$\begin{gathered}\sf L = \lim_{x \to \infty}\frac{x^{4}-x^{2} +4 }{x^{3}-5 } \end{gathered}$}\\$

$\ \ = \lim_{x \to \infty\frac{\frac{x^{4} }{x^{4} }-\frac{x^{2} }{x^{4}}+\frac{4}{x^{4} } }{\frac{x^{3} }{x^{4}}-\frac{5}{x^{4}} } }$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{=\lim_{x \to \infty}\frac{1-\frac{1}{x^{2} } +\frac{4}{x^{4} } }{\frac{1}{x}-\frac{5}{x^{4} } } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{0}=\infty } \end{gathered}$}$

Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.

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2 years ago