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larisa86 [58]
3 years ago
12

Frank jogs in a circular garden every day. The ground measures 5 feet from the center to the inner circle and an extra 3 feet fr

om the inner circle to the outer circle. If Frank jogs around the outer circle twice, how much distance does he cover?
A. 2p(5 + 8)
B. 2p(10 + 16)
C. p(8 – 5)
D. 2p(8 + 8) ...?
Mathematics
1 answer:
dedylja [7]3 years ago
8 0
Radius of the inner circle = 5 feet
Radius of the outer circle = 8 feet
Then
Circumference of the outer circle = 2 * pi * Radius of outer circle
                                                     = 2pi(8)
Since Frank jogs twice around the outer circle,So
Total distance covered by Frank = 2pi(8 + 8)

From the above deduction, it can be easily concluded that the correct option among all the options that are given in the question is the fourth option or option "D".

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Which of the following exponential functions goes thru points (1,6) and (2,12)
Alexandra [31]

Answer:

Noting that e^b = 6/a

Step-by-step explanation:

Use the general expo function y = ae^(bx).

Subbing 6 for y and 1 for x, we get  6 = ae^(b), or   e^b = 6/a.

Subbing 12 for y and 2 for x, we get   12 = ae^(2b), or 12/a = (e^b)²

Now let's find the value of the coefficient a.  Noting that e^b = 6/a, rewrite

12/a = (e^b)² as 12/a = (6/a)².

Dividing both sides by 6/a, we get 2 = 6/a, or a = 3.

Again Noting that e^b = 6/a, e^b = 6/3, or e^b = 2.

Taking the natural log of both sides, we get b = ln 2.

Then our y = ae^(bx) becomes:

                y = 3e^(ln 2·x), or   y = 3·2^x

Note:  next time, please share the answer choices.  Thank you.

7 0
3 years ago
A candy box company places an average of 20 truffles in a one pound box. The number of truffles per box never varies from the av
storchak [24]
(x-20) 2
that is the answer

7 0
3 years ago
Find the slope of the line that goes through the given points (8,5) (6,7)
vazorg [7]
To find the slope of a line that goes through given points with known coordinates, you divide the subtraction of the y of the second point minus the y of the first point, by the subtraction of the x of the second point minus the x of the first point:
m = (yB-yA) / (xB-xA)

Let A(8,5) and B(6,7).
With yB = 7; yA = 5; xB = 6; xA = 8
m = (7-5) / (6-8)
m = 2/-2
m = -1

So the slope of the line that goes through the given points (8,5) and (6,7) is m = -1.

I've added a pic of the line with both points under the answer.

Hope this Helps! :)

4 0
3 years ago
We are interested in the dimensions of a certain rectangle. this rectangle has length twice the side of the square and width thr
Mila [183]
Area of square = s^2
Area of Rectangle = lw
l = 2s

w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
8 0
3 years ago
Given the triangle below, what is the length of the third side, rounded to the nearest whole number?
Leno4ka [110]

Answer:

Step-by-step explanation:

You need the Law of Cosines for this, namely:

x^2=21^2+14^2-2(21)(14)cos58 where x is the missing side.

x^2=441+196-311.5925 and

x^2=325.4075 so

x = 18.0 or just 18

7 0
3 years ago
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