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3 years ago

10

Find the area contained between

le=" {y }^{2} = x" alt=" {y }^{2} = x" align="absmiddle" class="latex-formula">
and
$y = {x}^{2}$

1 answer:

marissa [1.9K]3 years ago

6 0

The area is given by

$\displaystyle\int_0^1\sqrt x-x^2\,\mathrm dx=\dfrac23x^{3/2}-\dfrac13x^3\bigg|_{x=0}^{x=1}$

so the area is

$\dfrac23-\dfrac13=\dfrac13$

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Part A: Clancey and Ethan are starting new books. So far, Clancey has read 1/4 of his book, which has 240 total pages and Ethan

Nonamiya [84]

In order to find who has read more pages, let's find the number of pages read by each one.

The number of pages read by Clancey is:

$\frac{1}{4}\cdot240=\frac{240}{4}=60$

The number of pages read by Ethan is:

$\frac{2}{5}\cdot170=\frac{340}{5}=68$

So Ethan read more pages.

The combined number of pages in both books is 240 + 170 = 410.

The combined number of pages read is 60 + 68 = 128

So the fraction is:

$\frac{128}{410}=\frac{64}{205}$

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1 year ago

Graph the equation y=-2(x-1)^2-4

sp2606 [1]

Answer:

Step-by-step explanation:

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6 0

3 years ago

A point $(x, y)$ with integer coordinates is randomly selected such that $0 \le x \le 8$ and $0 \le y \le 4$. what is the probab

ahrayia [7]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

A point (x, y) with integer coordinates is randomly selected such that $0 \le x \le 8 \:and\: $0 \le y \le 4$.$

The possible pairs of (x,y) are:

(0,0),(0,1),(0,2),(0,3),(0,4)

(1,0),(1,1),(1,2),(1,3),(1,4)

(2,0),(2,1),(2,2),(2,3),(2,4)

(3,0),(3,1),(3,2),(3,3),(3,4)

(4,0),(4,1),(4,2),(4,3),(4,4)

(5,0),(5,1),(5,2),(5,3),(5,4)

(6,0),(6,1),(6,2),(6,3),(6,4)

(7,0),(7,1),(7,2),(7,3),(7,4)

(8,0),(8,1),(8,2),(8,3),(8,4)

The Total Possible Outcomes n(S)= 45

The pair (x, y) that satisfies the given condition (say event A: $x + y \le 4$ ) are:

$(0,0),(0,1),(0,2),(0,3),(0,4)\\(1,0),(1,1),(1,2),(1,3)\\(2,0),(2,1),(2,2)\\(3,0),(3,1)\\(4,0)$

n(A)=15

Therefore:

$P(A)=\frac{n(A)}{n(S)} =\frac{15}{45} =\frac{1}{3}$

5 0

3 years ago

A triangle has sides with length of 11 feet 12 feet and 13 feet. Is it a right triangle

krek1111 [17]

Answer:

No

Step-by-step explanation:

It will be a right triangle if it follows Pyhthagoras Theorem . Where the sum of squares of two smaller sides is equal to the square of the 3rd side. Let's check ,

→ 11²+ 12² = 13²

→ 121 + 144 = 169

→ 265 ≠ 169

<h3>Hence the ∆ is not a right angled triangle </h3>

7 0

2 years ago

If you had a bank that offered 6.1% interest and compounded money 4 times a year, how many years would go by until you could tur

Verdich [7]

Answer:

t = 11.45 years

Step-by-step explanation:

A = p(1+r/n)^nt

A = future value = $12000

P = present value = $6000

n = number of periods = 4

r = interest rate = 6.1% = 0.061

t = number of years = ?

t = log(A/P) / n[log(1 + r/n)]

= log(12000/6000) / 4[log(1+0.061/4)]

= log(2) / 4[log(1 + 0.01525)]

= 0.3010 / 4[log(1.01525)]

= 0.3010 / 4(0.00657)

= 0.3010 / 0.02628

= 11.45 years

3 0

2 years ago