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3 years ago

if the population of a country increases by 35% every decade by what percentage does it increase by every year

Mathematics

1 answer:

VikaD [51]3 years ago

7 0

Answer:

have a good day for you

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The radius of a sphere decreases at a rate of 6 m/sec. find the rate at which the surface area decreases when the radius is 20 m

DanielleElmas [232]

The radius of the sphere decreases at the rate of 6 m/ sec

That is, $\frac{dr}{dt}=-6$

Surface Area of the sphere of radius r is given by $S=4\pi r^2$

Differentiating with respect to t,

$\frac{dS}{dt}=4\pi (2r)\frac{dr}{dt}=8\pi r\frac{dr}{dt}$

$\frac{dS}{dt}=8\pi (20)^2(-6)=-960\pi \: m^2/sec$

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3 years ago

Pls help due asap! Pls SHOW WORKINGS

sladkih [1.3K]

Answer:

$m\angle 1=95^{\circ}$

Step-by-step explanation:

If we drew an auxiliary line parallel to line $p$ and line $q$ that intersects the vertex of $\angle 1$ , we would form three angles, one of them being

The largest of these angles corresponds with the angle marked as $148^{\circ}$ .

The angle on the bottom right corresponds with the angle next to the one marked as $63^{\circ}$ . Therefore, its measure is $180-63=117^{\circ}$ .

Since there are $360^{\circ}$ in a circle, we can now write the following equation:

$m\angle 1+117+148=360,\\m\angle 1=\fbox{$95^{\circ}\checkmark$}$ .

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3 years ago

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Marina CMI [18]

Answer:

D. 3x - 3

Step-by-step explanation:

To find (f-g)(x) you have to subtract each fuction

(f-g)(x) = f(x) - g(x)

(f-g)(x) = 5x -2 - (2x+1)

(f-g)(x) = 5x -2 -2x -1

(f-g)(x) = 3x -3

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3 years ago

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Part 4: Identify the vertex, focus and directrix of each. Then sketch the graph.

Nezavi [6.7K]

Answer: 1) Vertex: (6, -2) Focus: (6, -7/4) Directrix: y = -9/4

2) Vertex: (-2, -1) Focus: (-7/4, -1) Directrix: x = -9/4

Step-by-step explanation:

Rewrite the equation in vertex format y = a(x - h)² + k or x = a(y - k)² + h by completing the square. Divide the b-value by 2 and square it - add that value to both sides of the equation.

(h, k) is the vertex
p is the distance from the vertex to the focus
-p is the distance from the vertex to the directrix

$\bullet\quad a=\dfrac{1}{4p}$

1) y = x² - 12x + 34

$y-34=x^2-12x\\\\y-34+\bigg(\dfrac{-12}{2}\bigg)^2=x^2-12x+\bigg(\dfrac{-12}{2}\bigg)^2\\\\\\y-34+36=(x-6)^2\\\\y+2=(x-6)^2\\\\y=(x-6)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(6,-2)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(6,-\dfrac{7}{4}\bigg)\\\\\\\text{Directrix: y= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad y=-\dfrac{9}{4}$

*******************************************************************************************

2) x = y² + 2y - 1

$x+1=y^2+2y\\\\x+1+\bigg(\dfrac{2}{2}\bigg)^2=y^2+2y+\bigg(\dfrac{2}{2}\bigg)^2\\\\\\x+1+1=(y+1)^2\\\\x+2=(y+1)^2\\\\x=(y+1)^2-2\qquad \rightarrow \qquad a=1\quad (h,k)=(-2,-1)\\$

$a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=\dfrac{1}{4}\\\\\\\text{Focus = Vertex + p}\\.\qquad \quad =\dfrac{-8}{4}+\dfrac{1}{4}\\\\.\qquad \quad =-\dfrac{7}{4}\quad \rightarrow \quad\text{Focus}=\bigg(-\dfrac{7}{4},-1\bigg)\\\\\\\text{Directrix: x= Vertex - p}\\.\qquad \qquad y=\dfrac{-8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=-\dfrac{9}{4}$