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3 years ago

A tile installer has selected four different size square tiles to cover a floor. The areas of the tiles are:

Mathematics

1 answer:

snow_lady [41]3 years ago

3 0

Answer:

C and D

Step-by-step explanation:

The length of the sides will be irrational if it is not a whole number. The tile installer has a square shape, so the formula for area is

area= $side^{2}$

Since we need to find if the side has the whole number, we can make the function to solve for side

side= $\sqrt{area} }$

Then the side for each tile installer will be:

A= $\sqrt{25 in^{2} }$ = 5 inch

B= $\sqrt{36 in^{2} }$ = 6 inch

C= $\sqrt{46 in^{2} }$ = 6.78 inch

D= $\sqrt{60 in^{2} }$ = 7.74 inch

Both C and D have irrational sides

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The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R′(x)=(x+1)ln(x+1)R ′ (x)=(x+1)ln(x+

jekas [21]

Answer:

Total revenue = $\frac{169}{2}\ln(13)-\frac{169}{4}$ dollars

Step-by-step explanation:

$R'(x)=(x+1)\ln(x+1)$

Integrate with respect to $x$ .

$R(x)=$ ∫ $(x+1)\ln(x+1)$ dx

Take $x+1=u$

Differentiate with respect to $x$

$dx=du$

So,

$R(x)=$ ∫ $u\ln(u)\,du$

Use integration by parts: ∫f g dx = f∫ g dx-∫(∫g dx)f' dx

Therefore,

$R(x)=$ $\frac{u^2}{2}\ln(u)$ $-$ ∫ $\frac{u^2}{2}\frac{1}{u}\,du$

= $\frac{u^2}{2}\ln(u)$ $-$ ∫ $\frac{u}{2}\,du$

Put $u=x+1$

$R(x)= \frac{(x+1)^2}{2}\ln(x+1)-\frac{(x+1)^2}{4}$

To find total revenue from the sale of the first 12 calculators, put $x=12$

$R(x)= \frac{(12+1)^2}{2}\ln(12+1)-\frac{(12+1)^2}{4}\\\\= \frac{(13)^2}{2}\ln(13)-\frac{(13)^2}{4}\\\\=\frac{169}{2}\ln(13)-\frac{169}{4}$

Total revenue = $\frac{169}{2}\ln(13)-\frac{169}{4}$ dollars

4 0

2 years ago

Write 935.97 in expanded form

Korolek [52]

<span> 935.97 = 900 + 30 + 5 + 0.9 + 0.07

hope it helps</span>

7 0

3 years ago

Which of the following measurements could be the side lengths of a right triangle?

nataly862011 [7]

For this case we have that every rectangle traingule complies with the Pythagorean theorem:

$c = \sqrt {a ^ 2 + b ^ 2}$

Where:

c: It is the hypotenuse

b: It's the base

a: It's the height

It is noted that if we replace:

$a = 66\\b = 88\\c = \sqrt {66 ^ 2 + 88 ^ 2}\\c = 110$

So, we have $c = 110 \ in ^ 2$

If we evaluate the other options we will obtain wrong results.

Thus, a rectangle triangle can have measurements of:

66 in, 88 in and 110 in respectively

Answer:

Option b

8 0

3 years ago

Which of these values for p and a will cause the function f(x)=Pa^x to be an exponential growth function?

Lera25 [3.4K]

Grouth is when a>1
if a=1, theer is no change
if a<1, it is exponetial decay

B is answer

8 0

2 years ago

Read 2 more answers

Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.

Airida [17]

X²-2x-3 = 0 let's start by grouping the "x"s

(x² - 2x + [?])² - 3 = 0

so, we have a missing fellow there, in order to make the group, a perfect square trinomial, namely to "complete the square", hmmm so the tell-tale fellow is the middle term.

from a perfect square trinomial we know that the middle term is a product of 2 and the "term on the left" and the "term on the right", like

$\bf \begin{array}{cccccllllll}
 a^2& + &2 a b&+& b^2\\
\downarrow && &&\downarrow \\
 a&& && b\\
&\to &( a + b)^2&\leftarrow 
\end{array}\qquad \qquad \quad 
\begin{array}{cccccllllll}
 a^2& - &2 a b&+& b^2\\
\downarrow && &&\downarrow \\
 a&& && b\\
&\to &( a - b)^2&\leftarrow 
\end{array}$

$\bf \textit{therefore}\qquad 2(x)(\boxed{?})=\stackrel{middle~term}{2x}\implies \boxed{?}=\cfrac{2x}{2x}\implies \boxed{?}=1$

aha!! so our missing fellow is 1.

now, let's keep in mind that all we're doing is borrowing from our very good friend Mr Zero, 0. So if we add 1², we also have to subtract 1².

(x² - 2x + 1² - 1²) - 3 = 0

(x² - 2x + 1) -1 -3 =0

(x - 1)² - 4 = 0

(x - 1)² = 4

5 0

3 years ago