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TEA [102]
1 year ago
13

Consider the following equation. cos x = x3 (a) Prove that the equation has at least one real root. f(x) = cos x − x3 is continu

ous on the interval [0, 1], f(0) = 0, and f(1) = cos 1 − 1 ≈ −0.46 0. Since 0 −0.46, there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation cos x − x3 = , or cos x = x3, in the interval (0, 1). (b) Use your calculator to find an interval of length 0.01 that contains a root.

Mathematics
1 answer:
skelet666 [1.2K]1 year ago
4 0

Answer:

b. 0.86, 0.87

Step-by-step explanation:

a. Find attached solution to a

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6. Problems and Applications Q6 Consider an economy that produces only chocolate bars. In year 1, the quantity produced is 3 bar
natulia [17]

Answer:

Year 1 GDP Deflator is 100%

Year 2 GDP Deflator is 30%

Year 3 GDP Deflator is 14.29%

Inflation Rate between year 2 and year 3 is 50%

The Real GDP growth Rate for Year 2 and year 3 is 110%

Step-by-step explanation:

Year 1  

 Price of chocolate bar is $2 and 3 bars are sold that year so the real GDP is 3 x $2=$6 which we are also given that this year is the nominal base year so the nominal GDP is also $6. GDP is the sum of all market value produced products in an economy. Therefore that’s why we calculated as the price of a chocolate multiplied the number produced. To calculate the GDP Deflator will be as follows:

GDP Deflator= (nominal GDP/Real GDP) x 100

                      = ($6/$6) x 100

                       = 100%  

Year 2

Price of chocolate bars is $4 per bar and 5 bars were produced therefore Real GDP =$4 x 5 = $20, now we will calculate the GDP deflator as we have been told that year  is the nominal year therefore nominal GDP is $6.

GDP Deflator= (nominal GDP/Real GDP) x 100

                       = ($6/$20) x100

                        = 30%

Year 3

Price of chocolate bars is $6 per bar and 7 bars were produced therefore Real GDP =$6 x 7 =$42, now we calculate the GDP deflator as we have been told that year 1 is the nominal year therefore nominal GDP is $6.

GDP Deflator = (nominal GDP/ Real GDP) x 100

                      = ($6/$42)

                       =14.29%

Now we calculate the inflation rate between year 2 and year 3.we use the CPI (consumer price index to get the inflation rate for year 2 ad 3)

Consumer Price Index = (Current price of bar/previous price of bar) x 100 formula for CPI

                      = ($6/$4) x 100= 150%-100%

                         = 50% is the inflation rate as the consumer price gave us a positive value.

Now we compute the real GDP growth rate between year 2 and year 3

Real GDP growth rate = [  (current Real GDP- Previous Real GDP)/Previous Real GDP] x 100

                                      = ($42-$20)/$20

                                       = 110% so real GDP grew by 110% from year 2 to year 3.

8 0
2 years ago
Matthew ran 3/8 mile and then walked 7/10 mile. Which pair of fractions can he use to find how far he went in all? (A 15/40 and
Strike441 [17]
Before we could add these numbers, 3/8 and 7/10 need a common denominator. Both 8 and 10 go into 40.

8 goes into 40 five times
3/8= (3*5)/40 = 15/40

10 goes into 40 four times
7/10= (7*4)/40= 28/40

ANSWER: A) 15/40 and 28/40

Hope this helps! :)
7 0
2 years ago
Read 2 more answers
Need help on answer I’m not so sure what to do
ratelena [41]
You divide four dhndhdhdjdjdjdjjd
7 0
2 years ago
Read 2 more answers
1. & 2. In the diagram below, points A, B, and C are collinear. Answer each of the following questions. The figure shown bel
KiRa [710]

Answer:

a). AB = 8 in

b). AB = 9.75 in

c). AC = 6.5 in

d). BC = 1.5 in

Step-by-step explanation:

a). Since, AB = AC + CB

   Length of AC = 5 in. and CB = 3 in.

   Therefore, AB = 5 + 3 = 8 in.

b). Given : AC = 6.25 in and CB = 3.5 in

   Therefore, AB = AC + CB = 6.25 + 3.5

   AB = 9.75 in.

c). Given: AB = 10.2 in. and BC = 3.7 in.

    AB = AC + BC

    AC = AB - BC

    AC = 10.2 - 3.7

    AC = 6.5 in

d). Given: AB = 4.75 in and AC = 3.25 in.

   BC = AB - AC

   BC = 4.75 - 3.25 = 1.5 in.

4 0
1 year ago
People are arriving at a party one at a time. While waiting for more people to arrive they entertain themselves by comparing the
Marina CMI [18]

Answer:

=(k−1)*P(X>k−1) or (k−1)365k(365k−1)(k−1)!

Step-by-step explanation:

First of all, we need to find PMF

Let X = k represent the case in which there is no birthday match within (k-1) people

However, there is a birthday match when kth person arrives

Hence, there is 365^k possibilities in birthday arrangements

Supposing (k-1) dates are placed on specific days in a year

Pick one of k-1 of them & make it the date of the kth person that arrives, then:

The CDF is P(X≤k)=(1−(365k)k)/!365k, so the can obtain the PMF by  

P(X=k) =P (X≤k) − P(X≤k−1)=(1−(365k)k!/365^k)−(1−(365k−1)(k−1)!/365^(k−1))=

(k−1)/365^k * (365k−1) * (k−1)!

=(k−1)*(1−P(X≤k−1))

=(k−1)*P(X>k−1)

6 0
2 years ago
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