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Travka [436]
2 years ago
12

I need help with this pls use 3.14 with or the formula with area

Mathematics
1 answer:
Leni [432]2 years ago
6 0
Rectangle:
A=l(w)

A=12(6)

A=72cm^2

Semicircle:
r=6/2

r=3

A=(3.14(r)^2(1/2)

A=3.14(3)^2(1/2)

A=3.14(9)(1/2)

A=14.13cm^2

A=14.1cm^2

Total area: 72cm^2 + 14.1cm^2 = 86.1cm^2
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An object is thrown straight up from the top of a 100-foot platform at a velocity of 48 feet per second. The height h(t) of the
julsineya [31]

Answer:

  • The maximum height is 136 ft
  • The time it takes to achieve this height is 1.5 s.

Explanation:

<u>1. Function for the height (given):</u>

    h(t)=-16t^2+48t+100

<u />

<u>2. Type of function</u>

That is a quadatic function, whose graph is a parabola that opens downward.

The maximum of the function, i.e. the maximum height, is the vertex of the parabola.

The vertex of a parabola with the genral equation   y=ax^2+bx+c  is at the x-coordinate

                       x=-b/(2a)

<u>3. Time to achieve the maximum height</u>

Substitute b with 48 and a with - 16:

        t=-48/(2(-16))=48/32=3/2=1.5

Then, time when the object achieves the maximum height it 1.5s

<u />

<u>4. Maximum height:</u>

Replace t with 1.5 in the equation, to find the maximum height, h(1.5)

     h(1.5)=-16(1.5)^2+48(1.5)+100=136

Then, the maximum height is 136 ft

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3 years ago
Tim must read 2 books from a list of 7 recommended books for his summer reading program. In how many different ways can Tim choo
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There are 21 ways Tim choose 2 books from the 7 recommended book

<em><u>Solution:</u></em>

Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program

To find: different ways can Tim choose 2 books from the 7 recommended books

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

<em><u>The formula for combinations is:</u></em>

n C_{r}=\frac{n !}{r !(n-r) !}

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 books from 7 books

Therefore, n = 7 and r = 2

<em><u>Substituting values in above formula, we get</u></em>

\begin{aligned}&7 C_{2}=\frac{7 !}{2 !(7-2) !}\\\\&7 C_{2}=\frac{7 !}{2 ! \times 5 !}\end{aligned}

For a number n, the factorial of n can be written as,

n !=n \times(n-1) \times(n-2) \dots \dots \times 2 \times 1

Therefore, we get

7 C_{2}=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}\\\\7C_2 = 7 \times 3 = 21

Thus there are 21 ways Tim choose 2 books from the 7 recommended book

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Step-by-step explanation:

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