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3 years ago

Consider the circles shown. Circle A has a radius of 6 inches. Circle B has a radius 20% greater than

Mathematics

1 answer:

butalik [34]3 years ago

5 0

Answer:

Answer should be D and E

Step-by-step explanation:

First, you need to figure out the radius of B.

As radius of A is 6 in, 20% of 6in would be 1.2in. So total radius of B = 6+1.2 = 7.2

Now you get the radius of B, calculate th area of B using the formula πr^2.

= π(7.2)^2 = 162.86 = area of B

Now, all answers except D and E is smaller than B. So, the answer would be D and E.

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2. The number of atoms of a particular chemical element is modelled by

____ [38]

9514 1404 393

Answer:

a) 600

b) see below

c) 1.26 hours

Step-by-step explanation:

a) The value of y when x=0 is the coefficient of the exponential term:

y = 600·3^(-0) = 600·1 = 600

There were 600 atoms to start.

b) see attached for a graph

c) The graph shows 150 atoms at t = 1.26, about 1.26 hours after the start of time counting.

If you want to find that value algebraically, substitute for y and solve for x. Logarithms are involved.

150 = 600·3^(-x)

150/600 = 3^(-x)

log(1/4) = -x·log(3)

x = -log(1/4)/log(3) = log(4)/log(3) ≈ 1.2618595

After about 1.26 hours, there were 150 atoms.

6 0

3 years ago

The power of ten representation of four thousandths

m_a_m_a [10]

Answer:

if its thousandths, its 4 x 10^-1. If you mean 4000, its 4 x 10^3

Step-by-step explanation:

5 0

2 years ago

A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 20 inches long

Pie

Answer:

Surface area of pyramid with base equilateral triangle is $390+100\sqrt{3}$ square inches

Step-by-step explanation:

Recall the following result:

The total surface area(S) of a regular pyramid is given by,

$S = \frac{1}{2}pl+B$ ...... (1)

Here, p represents the perimeter of the base , $l$ the slant height and B the base area of the pyramid.

From the given information:

Side of equilateral triangle = 20 inches

Slant height of the pyramid( $l$ ) = 13 inches.

First find the perimeter and Area of the base pyramid.

Perimeter of equilateral triangle(p) = $3 \times (side)$

= $3 \times 20 = 60 inches$

Area of equilateral triangle(B) = $\frac{\sqrt{3} }{4} \times (side)^{2}$

= $\frac{\sqrt{3} }{4} \times (20)^2 = 100\sqrt{3}$ square inches.

Substitute the above values in equation (1) as shown below:

$S=\frac{1}{2} \times 60 \times 13+100\sqrt{3}$

$S= 390+100\sqrt{3}$ square inches

Hence, the surface area of pyramid with base equilateral triangle is $390+100\sqrt{3}$ square inches.

6 0

3 years ago

Will give brain thingy if you get this right.

PolarNik [594]

1 less than or greater than -2

7 0

2 years ago

Read 2 more answers

A plane is traveling 600 miles. It takes the plane 5 hours against the wind and 4 hours with the wind. What is the speed of the

madam [21]

Answer: the speed of the plane in still air is 135 miles per hour

the speed of the wind is 15 miles per hour

Step-by-step explanation:

Let x represent the speed of the plane in still air

Let y represent the speed of the wind.

The distance travelled by the plane is 600 miles.

Distance travelled = speed × time

It takes the plane 5 hours against the wind. This means that the total speed is (x-y) miles per hour. Therefore,

600 = 5(x- y) = 5x - 5y - - - - - - - 1

It takes the plane 4 hours with the wind. This means that the total speed is (x+y) miles per hour. Therefore,

600 = 4(x+ y) = 4x + 4y - - - - - - - - 2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

2400 = 20x - 20y

3000 = 20x + 20y

Adding both equations

5400 = 40x

x = 5400/40 = 135

Substituting x = 135 into equation 1, it becomes

4 × 135 + 4y = 600

540 + 4y = 600

4y = 600 - 540 = 60

y = 60/4 = 15

6 0

3 years ago