1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Daniel [21]
3 years ago
13

Find the number a such that the line x = a bisects the area under the curve y = 1/x2 for 1 ≤ x ≤ 4. 8 5​ (b) find the number b s

uch that the line y = b bisects the area in part (a).
Mathematics
1 answer:
IceJOKER [234]3 years ago
3 0

a. We're looking for a such that

\displaystyle\int_1^a\frac{\mathrm dx}{x^2}=\int_a^4\frac{\mathrm dx}{x^2}

-\dfrac1x\bigg|_{x=1}^{x=a}=-\dfrac1x\bigg|_{x=a}^{x=4}

1-\dfrac1a=\dfrac1a-\dfrac14

\dfrac54=\dfrac2a\implies\boxed{a=\dfrac85}

b. Integrating with respect to y will make things easier.

y=\dfrac1{x^2}\implies x=\dfrac1{\sqrt y}

(where we take the positive square root because we know x>0)

Now we want to find b such that

\displaystyle\int_0^b\frac{\mathrm dy}{\sqrt y}=\int_b^1\frac{\mathrm dy}{\sqrt y}

2\sqrt y\bigg|_{y=0}^{y=b}=2\sqrt y\bigg|_{y=b}^{b=1}

2\sqrt b=2-2\sqrt b

4\sqrt b=2\implies\boxed{b=\dfrac14}

You might be interested in
Write a polynomial function with the real<br> zeros -3, 0, and 3.
suter [353]

f(x)=x(x-3)(x+3)

7 0
1 year ago
4. Elena va a una fiesta pero no sabe que ponerse, así que lanza un moneda y un dado al
taurus [48]

Answer:

  • <u>1/4</u>

Explanation:

Hola. Puesto que tu pregunta está en español, te responderé en el mismo lenguage.

Estas son las posibilidades dadas por la combinación moneda/dado

                                      Número de combinaciones

Moneda: prenda

    Cara: vestido                 1 de 2:          1/2

     Sello: falda                    1 de 2:          1/2

Dado: color

    Par: negro                      3 de 6:          3/6

    Impar: café                     3 de 6:         3/6

En total son 2 × 6 resultados: 12 (incluye resultados repetidos, no son todos diferentes entre sí)

¿Cuántas combinaciones tienen vestido y color negro?

  • P(Vestido∩negro) = ?

Es decir: moneda = cara y dado = par

  • Son 1 × 3 = 3.

Por tanto, la probabilidad de vestido negro es:

  • 3 de 12 = 3/12 = 1/4 ← respuesta

Hay otras formas de resolverlo. Por ejemplo;

Como los resultados de lanzar la moneda y el dado son independientes:

  • P(Vestido∩negro) = P(Vestido) × P(Negro)
  • P(Vestido) = 1/2
  • P(Negro) = 3/6 = 1/2
  • P(Vestido) × P(Negro) = 1/2 × 1/2 = 1/4 ← mismo resultado
8 0
3 years ago
Hya think of a number "m" . She square it, add "y" to the answer and then subtract 7 from it. The final answer is "A". 1) Derive
Bond [772]
<h2><u>Solution (1)</u> :</h2>

Given, to find A we have to :

  • square m
  • Add y to m²
  • Subtract 7 from m² + y

From the question, the following equation can be formed :

=\tt  A = {m}^{2}   + y - 7

Therefore, the formula for finding A = m² + y - 7

<h2><u>Solution (2)</u> :</h2>

The value of A we can derive from the formula is :

=\tt A =  {m}^{2}  + y - 7

Value of m = 3 (given)

Which means :

=\tt A =   {3}^{2}  + y  - 7

=\tt \: A = 9 + y - 7

=\tt A = 9 - 7 + y

\color{plum} =\tt A = 2 + y

Thus, the value of A = 2+y

Therefore, the value of A = <u>2+y</u>

7 0
2 years ago
g Bonus: Assume that among the general pediatric population, 7 children out of every 1000 have DIPG (Diffuse Intrinsic Pontine G
patriot [66]

Answer:

0.9586

Step-by-step explanation:

From the information given:

7 children out of every 1000 children suffer from DIPG

A screening test designed contains 98% sensitivity & 84% specificity.

Now, from above:

The probability that the children have DIPG is:

\mathbf{P(positive) = P(positive \  |  \ DIPG) \times P(DIPG) + P(positive  \ | \  not \DIPG)\times P(not  \ DIPG)}= 0.98\imes( \dfrac{7}{1000}) + (1-0.84) \times (1 - \dfrac{7}{1000})

= (0.98 × 0.007) + 0.16( 1 - 0.007)

= 0.16574

So, the probability of not having DIPG now is:

P(not \ DIPG \  |  \ positive) = \dfrac{ P(positive  \ | \  not DIPG)\timesP(not \  DIPG)} { P(positive)}

=\dfrac{ (1-0.84)\times (1 - \dfrac{7}{1000}) }{ 0.16574}

=\dfrac{ 0.16 ( 1 - 0.007) }{0.16574}

= 0.9586

8 0
2 years ago
The price of a television in a certain store was a dollars in June. On the first day of each month after June, the price was red
Shtirlitz [24]

Answer:

0.8

Step-by-step explanation:

multiply 1.00 .20 4 times

6 0
2 years ago
Other questions:
  • Each side of an equilateral triangle measures 9cm. Find the height, h, of the triangle.
    8·1 answer
  • a trip to portland oregon, from boston will take 7 3/4 hours. Assuming we are two--thirds fo the way there, how much longer, in
    11·1 answer
  • Find the surface area
    13·1 answer
  • The Atlanta news media recently published that " we found a high correlation (r = 1.25) between number of days that students wer
    11·1 answer
  • MARK AS BRIANLEST IF ANSWER RIGHT
    10·1 answer
  • What x value solves the equation?<br> 3x - 5 = 1<br> x=
    12·2 answers
  • Find the perfect square of 57600​
    10·1 answer
  • 1.5 horas para realizar un afinamiento; 0,2 horas para limpiar la bateria; 0,75 horas para cambiar el aceite y el filtro del mot
    8·1 answer
  • A pasta recipe calls for 2 tablespoons of water for every 3 eggs. Using this
    13·2 answers
  • The difference of a positive integer and an integer that is greater than it
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!