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UNO [17]
2 years ago
9

It takes Daphne 25 minutes to assemble a model plane. During her work day Daphne takes 30 minutes for lunch and one 15 minute br

eak. Which inequality could Daphne use to determine the number of model planes
she can assemble in her 8 hour work day?
25p - 458
Mathematics
1 answer:
natka813 [3]2 years ago
7 0

Answer:

<h2>y=25p-45</h2>

Step-by-step explanation:

We first of all start by cumulating all the time she spent for break

lunch= 30min

break= 15min

total break= 45min

also the time taken to assemble one model plane 25min

let the number of hours be p

and the total number of model plane be y

The model is

y=25p-45

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The awnser would be 43.768
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2 years ago
Jack was so frustrated with his slow laptop that he threw it out of his second story window. The height, h, of the laptop at tim
jeyben [28]

Answer:

The domain of the function is the interval [0,2.23]

see the explanation

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> the height of the laptop in units

we have

h(t)=-16t^{2}+28t+17

we know that

When the laptop hits the ground, the value of h(t) is equal to zero

so

For h(t)=0

-16t^{2}+28t+17=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-16t^{2}+28t+17=0

so

a=-16\\b=28\\c=17

substitute in the formula

x=\frac{-28(+/-)\sqrt{28^{2}-4(-16)(17)}} {2(-16)}

x=\frac{-28(+/-)\sqrt{1,872}} {-32}

x=\frac{-28(+/-)12\sqrt{13}} {-32}

x_1=\frac{-28(+)12\sqrt{13}} {-32}=-0.477

x_1=\frac{28(-)12\sqrt{13}} {32}=-0.477  ---> is not a solution

x_2=\frac{-28(-)12\sqrt{13}} {-32}

x_2=\frac{28(+)12\sqrt{13}} {32}=2.23\ sec

therefore

The domain of the function is the interval [0,2.23]

All real numbers greater than or equal to 0 seconds and less than or equal to 2.23 seconds

0\ sec \leq x \leq 2.23\ sec

5 0
2 years ago
The sum of the squares of two consecutive even integers is 884. find the integers
andriy [413]
2x + 2x +2 are the integers
4x^2 + 4x^2 +8x +4 =884 (The sum of the integers squared)
8 x^2 +8x -880 = 0

x = 10
Therefore, the integers are:
20 and 22




3 0
2 years ago
If the farmer has 234 feet of fencing, what are the dimensions of the region which enclose the maximal area?
marissa [1.9K]

Answer: 58 ft × 58 ft  

Step-by-step explanation:

Let the length of the region = x feet

And, the width of the region = y feet

Since, the perimeter of the region = 234 feet ( Given )

⇒ 2(x+y) = 234

⇒ x+y = 117

⇒ y = 117 - x

Again the area of the region, A = xy

⇒ A(x) = x(117-x)

⇒ A(x) = 117x - x^2

By differentiating the above equation with respect to x,

⇒ A'(x) = 117 - 2x  

For maxima or minima,

A'(x) = 0

\implies 117 - 2x = 0

\implies -2x = -117

\implies x = 58.5

Again differentiating equation A'(x) with respect to x,

We get, A''(x) = -2

Hence, For x = 58.5 A''(x) = negative

⇒ For x = 58.5 feet the area A(x) is maximum,

⇒ The length of the region having maximum area = x = 58.5 feet

And, the width of the region having maximum area = y = 117-x= 117 - 58.5=58.5 feet,

⇒ The dimension of the region having the maximum area = 58.5 ft × 58.5 ft

8 0
2 years ago
Read 2 more answers
Use Gauss's Law to find the charge contained in the solid hemisphere x2 + y2 + z2 ≤ a2, z ≥ 0, if the electric field is E(x, y,
Anit [1.1K]

Answer:<em><u> \frac{16}{3}πa^{3} . </u></em>

Given:

x^{2}+y^{2}+z^{2} \leq a^{2}, z \geq 0

Using Gauss's Law = ∫∫s E ·dS  

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⇒ Divergence (Gauss') Theorem  

= ∫∫∫ (1+1+6) dV  

= 8×(volume of the hemisphere, radius "a")  

= 8× (\frac{1}{2})(4/3)πa^{3}  

<em><u>= \frac{16}{3}πa^{3} . </u></em>

6 0
2 years ago
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