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3 years ago

It is given that A is directly proportional to r2 and r> 0. When r=5, A=75.

Mathematics

1 answer:

torisob [31]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

Given A is directly proportional to r² then the equation relating them is

A = kr² ← k is the constant of proportion

To find k use the condition when r = 5, A = 75 , then

75 = k × 5² = 25k ( divide both sides by 25 )

3 = k

A = 3r² ← equation of proportion

(a)

when r = 4, then

A = 3 × 4² = 3 × 16 = 48

(b)

when A = 147 , then

147 = 3r² ( divide both sides by 3 )

49 = r² ( take the square root of both sides )

r = $\sqrt{49}$ = 7

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What is true for f(x)=bx

kozerog [31]

Answer:

f'(x) = b

Step-by-step explanation:

f(x) = bx

f' (x) = d/dx (bx)

using d/dx ( a * x ) = a

f' (x) = b <-- solution.

4 0

3 years ago

Part I: Measuring Parts of a Circle

cluponka [151]

Answer:

case a) The approximate circumference of circle is $5.9\ units$ and the ratio of circumference to Diameter is $\frac{C}{D}=2.95$

case b) The approximate circumference of circle is $6\ units$ and the ratio of circumference to Diameter is $\frac{C}{D}=3$

case c) The approximate circumference of circle is $6.24\ units$ and the ratio of circumference to Diameter is $\frac{C}{D}=3.12$

Step-by-step explanation:

we know that

The approximate circumference of each circle, is equal to the perimeter of each inscribed polygon

case A) the figure is an inscribed pentagon

step 1

Find the approximate circumference of circle

The perimeter of the pentagon is equal to

$P=5s$

where

$s=1.18\ units$

substitute

$P=5(1.18)=5.9\ units$

therefore

The approximate circumference of circle is $5.9\ units$

step 2

Find the ratio of circumference to Diameter

we know that

The radius is half the diameter so

$D=2r=2(1)=2\ units$

The ratio is equal to

$\frac{C}{D}=5.9/2=2.95$

case B) the figure is an inscribed hexagon

step 1

Find the approximate circumference of circle

The perimeter of the hexagon is equal to

$P=6s$

where

$s=1\ units$

substitute

$P=6(1)=6\ units$

therefore

The approximate circumference of circle is $6\ units$

step 2

Find the ratio of circumference to Diameter

we know that

The radius is half the diameter so

$D=2r=2(1)=2\ units$

The ratio is equal to

$\frac{C}{D}=6/2=3$

case C) the figure is an inscribed dodecahedron

step 1

Find the approximate circumference of circle

The perimeter of the dodecahedron is equal to

$P=12s$

where

$s=0.52\ units$

substitute

$P=12(0.52)=6.24\ units$

therefore

The approximate circumference of circle is $6.24\ units$

step 2

Find the ratio of circumference to Diameter

we know that

The radius is half the diameter so

$D=2r=2(1)=2\ units$

The ratio is equal to

$\frac{C}{D}=6.24/2=3.12$

<em>Conclusion</em>

We know that

The exact value of the ratio $\frac{C}{D}$ is equal to

$\frac{\pi D}{D}=\pi$

The approximate value of the circumference will be closer to the real one when the number of sides of the inscribed polygon is greater

4 0

3 years ago

Could someone pls help me and explain this if you know it!!

yanalaym [24]

Answer:

25% on question one

Step-by-step explanation:

For example, on question one, 5 students drink more than half a dozen sodas a week. If there is a total of 20 students you'd divide 5 by 20 and that should be the answer.

8 0

3 years ago

For what value(s) of x are the following undefined? a 5x^2+x+11/x^2−4

irga5000 [103]

Answer:

Undefined at x = 2 and x = -2

Step-by-step explanation:

(5x²+x+11)/(x²-4)

Function becomes undefined when the denominator goes to zero.

x² - 4 = 0

x = 2, -2

4 0

3 years ago

The orgin of the coordinate plane is the point at (0,0). Why is the orgin an important point?

stiks02 [169]

<u>Importance of origin:</u>

The point at which the two axes intersect is called the origin. The intersecting x- and y-axes divide the coordinate plane into four sections.

The origin is at 0 on the x-axis and 0 on the y-axis. Since the origin has an x-coordinate of 0 and a y-coordinate of 0, its ordered pair is written (0, 0).

The origin is used to determine the coordinates for every other point on the graph. It is generally the starting point on a grid.

In general, origin is the place where something comes from or the place where something originates.

8 0

3 years ago