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devlian [24]
3 years ago
7

The function f(x) = 1 + 1.5 ln (x + 1) models the average number of free-throws a basketball player can make consecutively durin

g practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After how many days of practice can the basketball player make an average of 9 consecutive free throws? (Hint: replace f(x) by 9 and solve)
Mathematics
1 answer:
ElenaW [278]3 years ago
3 0
9 = 1 + 1.5 ln (x + 1)
8 = 1.5 ln (x + 1)
16/3 = ln (x + 1)
e^(16/3) = x + 1
x = e^(16/3) - 1
x = 206.127 days of practice
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The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times l
sergij07 [2.7K]

Answer:

(a)

h=3x

(b)

A=\frac{\sqrt{3} }{4} x^2

(c)

A=\frac{3\sqrt{3} }{2} x^2

(d)

V=\frac{3\sqrt{3} }{2} x^3 units^3

Step-by-step explanation:

We are given a regular hexagon pyramid

Since, it is regular hexagon

so, value of edge of all sides must be same

The length of the base edge of a pyramid with a regular hexagon base is represented as x

so, edge of base =x

b=x

Let's assume each blank spaces as a , b , c, d

we will find value for each spaces

(a)

The height of the pyramid is 3 times longer than the base edge

so, height =3*edge of base

height=3x

h=3x

(b)

Since, it is in units^2

so, it is given to find area

we know that

area of equilateral triangle is

=\frac{\sqrt{3} }{4} b^2

h=3x

b=x

now, we can plug values

A=\frac{\sqrt{3} }{4} x^2

(c)

we know that

there are six such triangles in the base of hexagon

So,

Area of base of hexagon = 6* (area of triangle)

Area of base of hexagon is

=6\times \frac{\sqrt{3} }{4} x^2

=\frac{3\sqrt{3} }{2} x^2

(d)

Volume=(1/3)* (Area of hexagon)*(height of pyramid)

now, we can plug values

Volume is

=\frac{1}{3}\times\frac{3\sqrt{3} }{2} x^2\times (3x)

V=\frac{3\sqrt{3} }{2} x^3 units^3


3 0
3 years ago
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Anna007 [38]
It would be: 3(x + 21) ≤ -26
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In short, Your Answer would be -47/3 or 15.67

Hope this helps!

8 0
3 years ago
Solve using any method. Choose the correct ordered pair.
lesya692 [45]

Answer:

C

Step-by-step explanation:

-2 + 7 = 5

7 0
3 years ago
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Aliun [14]

<span>5 nickels , 2 quarters, and 1 pennies = 8 coins.</span>

<span> he received 2 quarters</span>

5 0
3 years ago
Charlene wants to build a fence around her rectangular garden. The garden measures 20 meters by 60 meters. 
myrzilka [38]
The perimeter because the fence goes AROUND the yard, not in it.

P = 2w + 2l

P = 2(60) + 2(20)

P = 120 + 40

P = 160

Charlene needs 160 meters of fencing material.
3 0
3 years ago
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