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My name is Ann [436]
3 years ago
14

On a business trip, Jon must drive from his office to a clients's office, a distance of 216 miles. He sets off a 8 a.m. Suppose

that he drives at a constant speed of 66 mph. Find the rule of the function f(t) that gives his distance from the client's office at time t hours (with t = 0 corresponding to 8 a.m.) A. f(t) = 216 + 66t B. f(t) = 216 - 66t C. f(t) = 66 D. f(t) = 216-66 66
Mathematics
1 answer:
chubhunter [2.5K]3 years ago
3 0

Answer:

b.) f(t) = 216 - 66t

Step-by-step explanation:

Since we consider t and time travelled in hours and we are given that the average speed of Jon is 66mph, then we can calculate the distance travelled at any point in time by Jon.

Distance = Speed * time.

Distance = 66 * t = 66t.

Since total distance from clients house 216 miles and distance travelled by Jon at any point in time is 66t, then remaining distance to be covered from the clients house, that is distance between Jon and the clients house becomes:

Distance from client house = 216 - 66t.

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A baseball player hit 57 home runs in a season. Of the 57 home​ runs, 15 went to right​ field, 20 went to right center​ field, 1
Sidana [21]

Place the part (amount going to the left field), over the total amount of homerun:

(a) 2/57 is your probability

(b) Divide 2/57

2/57 = 0.035, or 3.5%

YES, it is unusual for this player to hit a home run to left field, for he only has a 3.5% chance.

hope this helps

8 0
3 years ago
Find the dimensions of an open rectangular box with a square base that holds 2000 cubic cm and is constructed with the least bui
Vesnalui [34]
<h3>The dimensions of the given rectangular box are:</h3><h3>L  =   15.874 cm  , B  =  15.874 cm   , H = 7.8937 cm</h3>

Step-by-step explanation:

Let us assume that the dimension of the square base = S x S

Let us assume the height of the rectangular base = H

So, the total area of the open rectangular box  

= Area of the base +  4 x ( Area of the adjacent faces)

=  S x S  +  4 ( S x H)   = S² +  4 SH   ..... (1)

Also, Area of the box  = S x S x H  =  S²H

⇒ S²H = 2000

\implies H = \frac{2000}{S^2}

Substituting the value of H in (1), we get:

A = S^2 + 4 SH =  S^2 + 4 S(\frac{2000}{S^2}) =  S^2 + (\frac{8000}{S})\\\implies A  =  S^2 + (\frac{8000}{S})

Now, to minimize the area put :

(\frac{dA}{dS} ) = 0 \implies 2S  - \frac{8000}{S^2}  = 0\\\implies S^3 = 4000\\\implies S  = 15.874 \approx 16 cm

Putting the value of S  = 15.874 cm in the value of H , we get:

\implies H = \frac{2000}{S^2}  =  \frac{2000}{(15.874)^2} = 7.8937 cm

Hence, the dimensions of the given rectangular box are:

L  =   15.874 cm

B  = 15.874 cm

H = 7.8937 cm

3 0
3 years ago
1) Let f(x)=ax2+bx+c for some value of a, b and c. f intersects the x-axis when x=−2 or x=3, and f( 1 3 )=−25. Find the values o
antiseptic1488 [7]

Answer:

1) a = -⅙, b = ⅙, c = 1

2) 6 units

Step-by-step explanation:

1) f(x) = ax² + bx + c

Given the roots, we can write this as:

f(x) = a (x + 2) (x − 3)

We know that f(13) = -25, so we can plug this in to find a:

-25 = a (13 + 2) (13 − 3)

-25 = 150a

a = -⅙

Therefore, the factored form is:

f(x) = -⅙ (x + 2) (x − 3)

Distributing:

f(x) = -⅙ (x² − x − 6)

f(x) = -⅙ x² + ⅙ x + 1

Graph: desmos.com/calculator/6m6tjoodvb

2) Volume of a right prism is area of the base times the height.

V = Ah

The base is an equilateral triangle.  Area of a triangle is one half the base times height.

V = ½ ab h

The height of the triangle is the same as the height of the prism.

V = ½ bh²

In an equilateral triangle, the height is equal to half the base times the square root of 3.

V = ½ b (½√3 b)²

V = ⅜ b³

Given that V = 81, solve for b.

81 = ⅜ b³

216 = b³

b = 6

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