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3 years ago

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Mathematics

1 answer:

faust18 [17]3 years ago

5 0

Answer:the diameter is 7

Step-by-step explanation: 21.98 divide by pi is 7 so diameter is 7

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According to data from a medical association, the rate of change in the number of hospital outpatient visits, in millions, in

GaryK [48]

Answer:

a) $f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000$

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient visits, in millions, is given by:

$f'(t)=0.001155t(t-1980)^{0.5}$

a) To find the function f(t) you integrate f(t):

$\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt$

To solve the integral you use:

$\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}$

Next, you replace in the integral:

$\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C$

Then, the function f(t) is:

$f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'$

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient visits.

Hence C' = 264,034,000

The function is:

$f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000$

b) For t = 2015 you have:

$f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7$

3 0

3 years ago

Farmer Bill sold potatoes at the farm market. He sold a quarter to the first person, 4/9 of what was left to the second person,

mel-nik [20]

Answer: 120 lb of potatoes.

Step-by-step explanation:

Let the pounds of potatoes sold by farmer Bill = X lb

Fractional part sold to the first person = 1/4

Therefore 1/4 of X = 1/4 x X

= X/4 lb of potatoes.

No of potatoes left for sale = X - X/4

= ( 4x - x )/4

= 3x/4 lb.

Fractional part sold to the second person out of the reminder = 4/9

Therefore 4/9 of 3x/4 = 4/9 x 3x/4

= x/3 lb of potatoes.

Amount of potatoes left for sale = 3x/4 - x/3

Resolve into fraction , we have = (9x - 4x)/12, because 12 is the LCM.

= 5x/12

Third buyer bought 4/5 of the left over = 4/5 of 5x/12

= x/3 lb of potatoes.

Amount of potatoes left = 5x/12 - x/3

Resolve in to fraction again taking 12 as the LCM = ( 5x - 4x )/12

= x/12 lb of potatoes .

Therefore, the left over was 10 lb .

To determine the value of x now which correspond to the amount of potatoes sold by Farmer Bill, we shall the equate the left to x/12 = 10

we now cross multiply to get the value of x x = 120 lb.

therefore the pound of potatoes sold by farmer Bill = 120 lb.

4 0

3 years ago

Is 1.0277 a rational number

ch4aika [34]

<h2>Answer:</h2><h2>Its rational</h2>

<h2>Hope this helps!!</h2>

8 0

3 years ago

Read 2 more answers

For the given statement Pn, write the statements P1, Pk, and Pk+1.

Leno4ka [110]

Answer:

$P_{1}$ = 2

$P_{k}$ = k(k+1)

$P_{k+1}$ = (k+1)(k+2)

Step-by-step explanation:

We are given the statement,

$P_{n}$ as 2 + 4 + 6 + . . . + 2n = n(n+1)

That is,

$P_{n}$ as 2 + 4 + 6 + . . . + 2n = $\sum_{i=1}^{n}2i$

So, we have,

$P_{1}$ = $\sum_{i=1}^{1}2i$ = 2

$P_{k}$ = $\sum_{i=1}^{k}2i$ = 2 + 4 + 6 + . . . + 2k = k(k+1)

$P_{k+1}$ = $\sum_{i=1}^{k}2i$ = 2 + 4 + 6 + . . . + 2k + 2(k+1) = (k+1)(k+2)

Thus, we get,

$P_{1}$ = 2

$P_{k}$ = k(k+1)

$P_{k+1}$ = (k+1)(k+2)

7 0

3 years ago

Read 2 more answers

The diagram shows the blueprint of a vegetable garden. All dimensions are given in yards.

Delicious77 [7]

Answer:

Step-by-step explanation:

i saw another brainly and he seemed to be correct and i got it right :)!

6 0

3 years ago