What is the initial value of the function represented by this table?

Will is 34% taller than Wanda, so Will's height is ____% of Wanda's height.

insens350 [35]

The easiest way for me to do this is too set their heights to actual numbers. Say Wanda is 100 feet tall (which I know isn’t a thing, but 100 is always an easy number for percentages.) If will is 34% taller than 100 feet, 1% is 1 foot, so Will is 134 feet tall. 134 / 100 is 134%, so will’s height is 134% of Wanda/s height. Hope this helps!

4 0

3 years ago

Read 2 more answers

Find the exact length of the curve. 36y2 = (x2 − 4)3, 5 ≤ x ≤ 9, y ≥ 0

IrinaK [193]

We are looking for the length of a curve, also known as the arc length. Before we get to the formula for arc length, it would help if we re-wrote the equation in y = form.

We are given: $36 y^{2} =( x^{2} -4)^3$
We divide by 36 and take the root of both sides to obtain: $y = \sqrt{ \frac{( x^{2} -4)^3}{36} }$

Note that the square root can be written as an exponent of 1/2 and so we can further simplify the above to obtain: $y = \frac{( x^{2} -4)^{3/2}}{6} }=( \frac{1}{6} )(x^{2} -4)^{3/2}}$

Let's leave that for the moment and look at the formula for arc length. The formula is $L= \int\limits^c_d {ds}$ where ds is defined differently for equations in rectangular form (which is what we have), polar form or parametric form.

Rectangular form is an equation using x and y where one variable is defined in terms of the other. We have y in terms of x. For this, we define ds as follows: $ds= \sqrt{1+( \frac{dy}{dx})^2 } dx$

As a note for a function x in terms of y simply switch each dx in the above to dy and vice versa.

As you can see from the formula we need to find dy/dx and square it. Let's do that now.

We can use the chain rule: bring down the 3/2, keep the parenthesis, raise it to the 3/2 - 1 and then take the derivative of what's inside (here $x^2-4$ ). More formally, we can let $u=x^{2} -4$ and then consider the derivative of $u^{3/2}du$ . Either way, we obtain,

$\frac{dy}{dx}=( \frac{1}{6})( x^{2} -4)^{1/2}(2x)=( \frac{x}{2})( x^{2} -4)^{1/2}$

Looking at the formula for ds you see that dy/dx is squared so let's square the dy/dx we just found.
$( \frac{dy}{dx}^2)=( \frac{x^2}{4})( x^{2} -4)= \frac{x^4-4 x^{2} }{4}$

This means that in our case:
$ds= \sqrt{1+\frac{x^4-4 x^{2} }{4}} dx$
$ds= \sqrt{\frac{4}{4}+\frac{x^4-4 x^{2} }{4}} dx$
$ds= \sqrt{\frac{x^4-4 x^{2}+4 }{4}} dx$
$ds= \sqrt{\frac{( x^{2} -2)^2 }{4}} dx$
$ds= \frac{x^2-2}{2}dx =( \frac{1}{2} x^{2} -1)dx$

Recall, the formula for arc length: $L= \int\limits^c_d {ds}$
Here, the limits of integration are given by 5 and 9 from the initial problem (the values of x over which we are computing the length of the curve). Putting it all together we have:

$L= \int\limits^9_5 { \frac{1}{2} x^{2} -1 } \, dx = (\frac{1}{2}) ( \frac{x^3}{3}) -x$ evaluated from 9 to 5 (I cannot seem to get the notation here but usually it is a straight line with the 9 up top and the 5 on the bottom -- just like the integral with the 9 and 5 but a straight line instead). This means we plug 9 into the expression and from that subtract what we get when we plug 5 into the expression.

That is, $[(\frac{1}{2}) ( \frac{9^3}{3}) -9]-([(\frac{1}{2}) ( \frac{5^3}{3}) -5]=( \frac{9^3}{6}-9)-( \frac{5^3}{6}-5})=\frac{290}{3}$

8 0

3 years ago

One afternoon, 27 people withdraw $100 from an ATM. What was the overall change in the amount of money in the machine?

Usimov [2.4K]

Answer:

The change is a decrease of $2700.

Step-by-step explanation:

Given

Total Number of people = 27

Amount each person withdrew = $100

The total withdrawn amount by 27 people = 100 × 27

= $2700

Let M be the amount of money in the ATM at the beginning.

As $2700 was drawn from the ATM, therefore, the change the amount of money in the machine will be:

M - 2700

It means the change is a decrease of $2700.

3 0

3 years ago

How do I solve this?

maksim [4K]

Answer:

Answer A represents this

x <= -3 ; x > 9

Step-by-step explanation:

Isolate x on each of the inequalities:

4 x + 4 <= - 8

subtract 4 from both sides

4 x <= - 12

divide both sides by 4 to isolate x completely (notice 4 is positive, so there is NO flipping of the inequality symbol)

x <= -3

This inequality is represented by shading the left section of the number line starting at x = -3 (make sure you draw a SOLID dot to mae clear that the point x = -3 is also included in your drawing.

The other inequality:

11 x - 11 > 88

add 11 to both sides

11 x > 99

divide both sides by 11 to isolate x (notice again that 11 is a positive number, so the inequality doesn't change with the division)

x > 9

This inequality is represented by shadowing the right hand side of the number line starting at x = 9. Make sure you draw an EMPTY dot on the number 9 to indicate that x = 9 is NOT included.

4 0

3 years ago

CAN SOMEONE PLS HELP !! due soon and will give brainliest!

andre [41]

Answer: Domain Expansion

Step-by-step explanation:

7 0

3 years ago