Ask question

Ask question

All categories

3 years ago

11

Find the number b such that the line y = b divides the region bounded by the curves x = y^2 − 1 and the y-axis into 2 regions wi

th equal area. Give your answer correct to 3 decimal places.

1 answer:

max2010maxim [7]3 years ago

7 0

Hello,

We may exchange x and y.
$-A_1= \int\limits^b_0 {x^2-1} \, dx = \dfrac{b^3}{3} -b\\
-A_2= \int\limits^1_b {x^2-1} \, dx =- \dfrac{2}{3} - \dfrac{b^3}{3}+b\\
-A_1=-A_2==\textgreater\ b^3-3b+1=0\\
sol={1.532088886238 , -1.879385241572 , 0.347296355334 }\\
The\ solution\ is\ 0.347296355334 .$ ≈0.347

<span class="sg-text sg-text--link sg-text--bold sg-text--link-disabled sg-text--blue-dark"> pdf </span>

You might be interested in

Which symbol, >, <, or = will complete the statement

trapecia [35]

Answer:

<

Step-by-step explanation:

-4.2 + 1.5 = -2.7 and -5.4 + 2.1 = -3.3

-2.7 is less than -3.3

7 0

2 years ago

Read 2 more answers

Can someone answer this question please?

Slav-nsk [51]

Answer:

Therefore,

(x , y) YES / NO

(-4, -5) Yes, It is a Solution.

(1 , - 3) No, not a Solution.

(9 , 6) No, not a Solution.

(-6 , 2) No, not a Solution.

Step-by-step explanation:

Given:

$4x-7y=19$

To Determine:

Given ordered pair is a solution or not ?

Solution:

For (-4,-5)

Substitute x = -4 and y = -5 in above equation

Left Hand Side = 4 × (-4) - 7 × (-5)

= -16+35

= 19

Right Hand Side = 19

Left Hand Side = Right Hand Side

Satisfied

Hence (-4, -5) is the SOLUTION to 4x - 7y =19 (YES)

For (1, -3)

Substitute x = 1 and y = -3 in above equation

Left Hand Side = 4 × (1) - 7 × (-3)

= 25

Right Hand Side = 19

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (1, -3) is NOT the Solution to 4x - 7y =19 (NO)

For (9, 6)

Substitute x = 9 and y = 6 in above equation

Left Hand Side = 4 × (9) - 7 × (6)

= -6

Right Hand Side = 19

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (9, 6) is NOT the Solution to 4x - 7y =19 (NO)

For (-6, 2)

Substitute x = -6 and y = 2 in above equation

Left Hand Side = 4 × (-6) - 7 × (2)

= -38

Right Hand Side = 19

Left Hand Side ≠ Right Hand Side

Not Satisfied

Hence (-6, 2) is NOT the Solution to 4x - 7y =19 (NO)

Therefore,

(x , y) YES / NO

(-4, -5) Yes, It is a Solution.

(1 , - 3) No, not a Solution.

(9 , 6) No, not a Solution.

(-6 , 2) No, not a Solution.

6 0

3 years ago

Please help I don’t understand how to do this

lara [203]

Answer:

65 degrees

Step-by-step explanation:

All angles of a triangle have to add up to 180 degrees. After establishing that, we can see that there are two angles given. 25 degrees and a 90-degree symbol. So if two angles add up to 115 degrees, we can do 180-115=65 to find the angle of C.

6 0

1 year ago

Read 2 more answers

Evaluate the function f(x) at the given numbers (correct to six decimal places). F(x) = x2 − 5x x2 − x − 20 , x = 5.5, 5.1, 5.05

exis [7]

we are given

$f(x)=\frac{x^2-5x}{x^2-x-20}$

Firstly, we will simplify it

$f(x)=\frac{x(x-5)}{(x-5)(x+4)}$

$f(x)=\frac{x}{(x+4)}$

At x=5.5:

we can plug x=5.5

$f(5.5)=\frac{5.5}{(5.5+4)}$

$f(5.5)=0.578947$

At x=5.1:

we can plug x=5.1

$f(5.1)=\frac{5.1}{(5.1+4)}$

$f(5.1)=0.56043956$

At x=5.05:

we can plug x=5.05

$f(5.05)=\frac{5.05}{(5.05+4)}$

$f(5.05)=0.558011$

At x=5.01:

we can plug x=5.01

$f(5.01)=\frac{5.01}{(5.01+4)}$

$f(5.01)=0.5560488$

At x=5.005:

we can plug x=5.005

$f(5.005)=\frac{5.005}{(5.005+4)}$

$f(5.005)=0.5558023$

At x=5.001:

we can plug x=5.001

$f(5.001)=\frac{5.001}{(5.001+4)}$

$f(5.001)=0.5556049$

At x=4.9:

we can plug x=4.9

$f(4.9)=\frac{4.9}{(4.9+4)}$

$f(4.9)=0.5505617$

At x=4.95:

we can plug x=4.95

$f(4.95)=\frac{4.95}{(4.95+4)}$

$f(4.95)=0.5530726$

At x=4.99:

we can plug x=4.99

$f(4.99)=\frac{4.99}{(4.99+4)}$

$f(4.99)=0.55506117$

At x=4.995:

we can plug x=4.995

$f(4.995)=\frac{4.995}{(4.995+4)}$

$f(4.995)=0.55503085$

At x=4.999:

we can plug x=4.999

$f(4.999)=\frac{4.999}{(4.999+4)}$

$f(4.999)=0.55550616$

7 0

3 years ago

What can you say about the Y values are the two functions??? Help please !!!!

velikii [3]

Answer:

D. The minimum y-value of g(x) approaches -3

Step-by-step explanation:

Form a table for values of x with corresponding values for f(x) and g(x)

<u>x </u> <u>f(x)=3x²-3 g(x)=2^x -3 </u>

-3 =3(-3²)-3=24 2⁻³ -3 = -2.88

-2 =3(-2²)-3=9 2⁻² -3 = -2.75

-1 =3(-1²)-3=0 2⁻¹-3 = -2.5

0 =3(0²)-3= -3 2⁰ -3 = -2

1 =3(1²)-3=0 2¹ -3 = -1

2 =3(2²)-3=9 2²- 3 = 1

3 =3(3²)-3=24 2³ -3= 5

From the table above, you can see the minimum value of y in g(x) -2.88 approaches -3

7 0

2 years ago