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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}

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A submarine traveling 200 meters below the surface of the ocean increases its depth by 45 meters. Adam says that the new locatio
melisa1 [442]

Adam made an error of 400 meters

Explanation:

Since, submarine traveling 200 meters below the surface of the ocean

and when the depth increases by 45 meters then submarine new location is

200+45=245 meters below from the surface of ocean.

But Adam says that new location is at -155 meters.

So, error is,   245-(-155)=400 meters

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https://brainly.in/question/13000874

8 0
2 years ago
!Brainliest!
harina [27]

Answer:

m = 3

n = 14

p = 2

Step-by-step explanation:

Given:

\frac{7}{x}-\frac{3}{2}=\frac{n-mx}{px}

We need to find the values of m, n, p

Solution:

We will first solve the L.H.S

L.H.S = \frac{7}{x}-\frac{3}{2}

Now we will first make the denominator common by taking L.C.M

=\frac{7\times 2}{x\times 2}-\frac{3\timesx}{2\timesx}\\\\= \frac{14}{2x}-\frac{3x}{2x}

Now the denominator is common hence we will subtract the numerators.

L.H.S = \frac{14-3x}{2x}

Now Comparing the the value of L.H.S with R.H.S we can say that;

\frac{14-3x}{2x}=\frac{n-mx}{px}

m = 3

n = 14

p = 2

4 0
3 years ago
Read 2 more answers
Simplify the expression. 68 – 18 ÷ 3 • 6 Please help
MAXImum [283]
Remember PEMDAS (Parenthesis, Exponents, Multiplication, Divison, Addition and Subtraction)

Also note that Multiplication and Division needs to be done left to right and the same goes for Addition and Subtraction.

So in your problem, the first operation we need to do is division.

68 - (18/3) x 6
68 - 6 x 6

Now we do multiplication
68 - 6 x 6
68 - 36

Finally we do subtraction because that's the only operation we have left to do
68 - 36 = 32

So your answer should be 32.
5 0
3 years ago
Someone plzzzz help on #16
Artemon [7]

Answer: x/3 = 18

Step-by-step explanation:

if x/3 is 18, then 18 - 7 = 11

7 0
3 years ago
I WILL GIVE BRAINLIEST TO WHOEVER IS CORRECT
irinina [24]

the third choice is correct


6 0
3 years ago
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