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2 years ago

Please help

Mathematics

1 answer:

igor_vitrenko [27]2 years ago

4 0

Answer:

C. Robert can read of a page every minute.

Step-by-step explanation:

Unit rate is usually based off of a unit of time and what type of time, however, it is 1.

For example, the unit rate MPH. This means "Miles per 1 hour".

Or take another example, KPH, or "Kilometers per 1 hour".

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1. What is the least common multiple of both 9 and 12?

Kisachek [45]

1. the least common multiple of 9 and 12.
9 18 27 36
12 24 36
36
2. GCF of 9 and 12
1 3 9
1 2 3 4 6 12
3

7 0

2 years ago

given y>0 and dy/dx=(3x^2+4x)/yif the point (1,√10) is on the graph relating x and y, then what is y when x=0

jonny [76]

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3x^2+4x}y\iff y\,\mathrm dy=(3x^2+4x)\,\mathrm dx$
$\implies\displaystyle\int y\,\mathrm dy=\int(3x^2+4x)\,\mathrm dx$
$\implies \dfrac12y^2=x^3+2x^2+C$

When $x=1$ you have $y=\sqrt{10}$ , so

$\dfrac12(\sqrt{10})^2=1^3+2(1)^2+C\implies 5=1+2+C\implies C=2$

and so the particular solution to the ODE is

$\dfrac12y^2=x^3+2x^2+2$

Then when $x=0$ , you get

$\dfrac12y^2=0^3+2(0)^2+2=2$
$\implies y^2=4$
$\implies y=2$

where we omitted the negative root because it's given that $y>0$ .

4 0

2 years ago

How do the values of the 1s in 14.937 and 6.1225 compare?

Darina [25.2K]

Answer:

I would say the answer is b

Step-by-step explanation:

8 0

2 years ago

Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Alik [6]

Answer:

$\alpha=3$

Step-by-step explanation:

Equation of a Circle

A circle of radius r and centered on the point (h,k) can be expressed by the equation

$(x-h)^2+(y-k)^2=r^2$

We are given the equation of a circle as

$3x^2+3y^2-6\alpha x+12y-3\alpha=0$

Note we have corrected it by adding the square to the y. Simplify by 3

$x^2+y^2-2\alpha x+4y-\alpha=0$

Complete squares and rearrange:

$x^2-2\alpha x+y^2+4y=\alpha$

$x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4$

$(x-\alpha)^2+(y+2)^2=r^2$

We can see that, if r=4, then

$\alpha+\alpha^2+4=16$

Or, equivalently

$\alpha^2+\alpha-12=0$

There are two solutions for $\alpha$ :

$\alpha=-4,\ \alpha=3$

Keeping the positive solution, as required:

$\boxed{\alpha=3}$

8 0

2 years ago

6. Find an exact value. (1 point)

vladimir2022 [97]

6 Find an exact value.
sin 75°
sin(A+B)=sin(A)cos(B)+cos(A)sin(B)
sin(45)=cos(45)=(2^0.5)/2 sin(30)=0.5 cos(30)=(3^0.5)/2
sin(45+30)=sin(45)cos(30)+cos(45)sin(30)=(6^0.5+2^0.5)/4
the answer is the letter d) quantity square root of six plus square root of two divided by four.

7. Find an exact value.
sine of negative eleven pi divided by twelve.

sin(-11pi/12) = -sin(11pi/12) = -sin(pi - pi/12) = -sin(pi/12) = -sin( (pi/6) / 2)

= - sqrt( (1-cos(pi/6) ) / 2) = -sqrt( (1-√3/2) / 2 ) = -(√3-1) / 2√2=(√2-√6)/4
the answer is the letter c) quantity square root of two minus square root of six divided by four.

8. Write the expression as the sine, cosine, or tangent of an angle.
sin 9x cos x - cos 9x sin x

sin(A−B)=sinAcosB−cosAsinB

sin(9x−x)= sin9xcosx−cos9xsinx= sin(8x)

the answer is the letter c) sin 8x

9. Write the expression as the sine, cosine, or tangent of an angle.
cos 112° cos 45° + sin 112° sin 45°

cos(A−B)=cosAcosB+sinAsinB

cos(112−45)=cos112cos45+sin112sin45=cos(67)

the answer is the letter d) cos 67°

10. Rewrite with only sin x and cos x.

sin 2x - cos 2x

sin2x = 2sinxcosx
cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 -1 = 1- 2(sinx)^2

sin2x- cos2x=2sinxcosx-(1- 2(sinx)^2=2sinxcosx-1+2(sinx)^2

sin2x- cos2x=2sinxcosx-1+2(sinx)^2

the answer is the letter b) 2 sin x cos2x - 1 + 2 sin2x

4 0

2 years ago

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