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3 years ago

Can someone help me with part b?

Mathematics

1 answer:

Tema [17]3 years ago

3 0

Step-by-step explanation:

the average rate of change of a function f in an interval [x-low, x-high] is

(f(x-high) - f(x-low)) / (x-high - x-low)

the year 2000 means t = 2000-1980 = 20

the year 2015 means t = 2015-1980 = 35

so, we have

(A(35) - A(20)) / (35 - 20)

((-0.6(35)² + 37.2×35 + 243) - (-0.6(20)² + 37.2×20 + 243)) / 15

((-735 + 1302 + 243) - (-240 + 744 + 243)) / 15

(810 - 747) / 15 = 63/15 = 4.2

the average change rate between 2000 and 2015 is 4.2.

that means that the use of nuclear energy in the USA increased by 4.2 billions of kilowatt hours per year during that period.

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The Glazed Donut Shop made 120 donuts, and 48 of them are filled with jelly. What percent of the donuts are filled with jelly?

fomenos

Answer:

just divide 48 by 120

Step-by-step explanation:

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2 years ago

Read 2 more answers

Jamie is riding a Ferris wheel that takes fifteen seconds for each complete revolution. The diameter of the wheel is 10 meters a

Agata [3.3K]

Answer:

The answers to the question is

(a) Jamie is gaining altitude at 1.676 m/s

(b) Jamie rising most rapidly at t = 15 s

At a rate of 2.094 m/s.

Step-by-step explanation:

(a) The time to make one complete revolution = period T = 15 seconds

Here will be required to develop the periodic motion equation thus

One complete revolution = 2π,

therefore the we have T = 2π/k = 15

Therefore k = 2π/15

The diameter = radius of the wheel = (diameter of wheel)/2 = 5

also we note that the center of the wheel is 6 m above ground

We write our equation in the form

y = $5*sin(\frac{2*\pi*t}{15} )+6$

When Jamie is 9 meters above the ground and rising we have

9 = $5*sin(\frac{2*\pi*t}{15} )+6$ or 3/5 = $sin(\frac{2*\pi*t}{15} )$ = 0.6

which gives sin⁻¹(0.6) = 0.643 = $\frac{2*\pi*t}{15}$

from where t = 1.536 s

Therefore Jamie is gaining altitude at

$\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) =$ 1.676 m/s.

(b) Jamie is rising most rapidly when the velocity curve is at the highest point, that is where the slope is zero

Therefore we differentiate the equation for the velocity again to get

$\frac{d^2y}{dx^2} = -5*(\frac{\pi *2}{15} )^2*sin(\frac{2\pi t}{15})$ =0, π, 2π

Therefore $-sin(\frac{2\pi t}{15} )$ = 0 whereby t = 0 or

$\frac{2\pi t}{15}$ = π and t = 7.5 s, at 2·π t = 15 s

Plugging the value of t into the velocity equation we have

$\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) =$ - 2/3π m/s which is decreasing

so we try at t = 15 s and we have $\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi *15}{15}) = \frac{2}{3} \pi$ m/s

Hence Jamie is rising most rapidly at t = 15 s

The maximum rate of Jamie's rise is 2/3π m/s or 2.094 m/s.

7 0

3 years ago

4.4: Measuring a Picture Frame

BlackZzzverrR [31]

It’s simple, do: 8+8+10+10, just add them you will get 36. The explanation is: Perimeter is add up all the sides, since it is a rectangle it has congruent sides, so they have the same length

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3 years ago

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Harold has been hired as a salesman. He is paid a flat rate of $375 each week and earns an additional $14.25 commission for each

Andru [333]

The answer is
$c. \: y = 14.25h + 375$

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3 years ago

Find the 4th term (x-y)^12

maria [59]

Answer:

The fourth term of the expansion is -220 * x^9 * y^3

Step-by-step explanation:

Question:

Find the fourth term in (x-y)^12

Solution:

Notation: "n choose k", or combination of k objects from n objects,

C(n,k) = n! / ( k! (n-k)! )

For example, C(12,4) = 12! / (4! 8!) = 495

Using the binomial expansion formula

(a+b)^n

= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n

For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is

C(n,3)a^(n-3)b^3

=C(12,3) * x^(12-3) * (-y)^(3)

= 220*x^9*(-y)^3

= -220 * x^9 * y^3

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3 years ago