Which expression is equivalent to 0.1 (2x + 3

What is the approximate surface area of the sphere if circumference is 37.68?

damaskus [11]

The surface area of a sphere is A = 4 π R² .

Sadly, the question doesn't give you 'R', so you have to
back it out of the circumference.

 Circumference = π (diameter)

Divide each side by π : Diameter = circumference / π

Radius = 1/2 diameter: Radius = circumference / (2 π)

 Area = 4 π R² =

 4 π (circumference/2π)² =

 4 π (circumference)² / 4 π²

Divide top and bottom by 4π : Area = (Circumference)² / π

 Circumference = 37.68 units

 Area = (37.68)² square units /π =

 451.93 square units

8 0

3 years ago

A hiker starting at point P on a straight road wants to reach a forest cabin that is 2 km from a point Q, 3 km down the road fro

pantera1 [17]

Answer:

2.19 km

Step-by-step explanation:

If x is the distance she walks down the road before turning, then the total time is:

t = x/8 + √((3 − x)² + 2²) / 3

t = x/8 + √(9 − 6x + x² + 4) / 3

24t = 3x + 8√(13 − 6x + x²)

24t = 3x + 8(13 − 6x + x²)^½

Take derivative of both sides with respect to x.

24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

When t is a minimum, dt/dx = 0.

0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)

3 / (6 − 2x) = 4(13 − 6x + x²)^-½

3 / (24 − 8x) = (13 − 6x + x²)^-½

(24 − 8x) / 3 = (13 − 6x + x²)^½

(24 − 8x)² / 9 = 13 − 6x + x²

576 − 384x + 64x² = 117 − 54x + 9x²

459 − 330x + 55x² = 0

Solve with quadratic formula.

x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)

x = (330 ± √7920) / 110

x = 2.19 or 3.81

Since 0 < x < 3, x = 2.19.

7 0

3 years ago

Which of the following options have the same value as 65% of 20

Natasha2012 [34]

Answer:

Opt A and D

Step-by-step explanation:

65% is 100 based number, this means that 65% is the same as 65/100, or 0,65.

65% of 20 is obtained performing the following operation:

0,65 * 20

or

65*20/100

Any of them

7 0

4 years ago

Read 2 more answers

At the beginning of the month Leslie's parents put $35.00 on her account. If lunch costs $2.55 per day, how much money would be

Annette [7]

Answer:

$73.25

Step-by-step explanation:

35 + 2.55(15) = 38.25 + 35 = 73.25

6 0

3 years ago

Solve for x. x = ___

const2013 [10]

Answer:

x = 2

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{little}{big}$ .

$\frac{36}{36 + 12}=\frac{24}{24 + 6x - 4}$

To solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$36(24 + 6x - 4)=(36+12)(24)\\36(6x + 20)=48(24)\\216x + 720 = 1152 \\216x = 432\\\frac{216x}{216}=\frac{432}{216} \\x = 2$

3 0

3 years ago

Which expression is equivalent to 0.1 (2x + 3​

Which expression is equivalent to 0.1 (2x + 3