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Margarita [4]
3 years ago
6

The rate at which sand is poured into a bag is modeled by the function r given by r(t)=15t−2t2, where r(t) is measured in millil

iters per second and t is measured in seconds after the sand begins pouring. How many milliliters of sand accumulate in the bag from time t=0 to time t=2 ?
Mathematics
1 answer:
balu736 [363]3 years ago
6 0

Answer:

35 mililiters

Step-by-step explanation:

Given

r(t) = 15t - 2t^2

Required

Accumulated amount from t = 0 to 2

This implies that, we substitute the values of t from 0 to 2 in the function

r(0) = 15*0 - 2*0^2= 0

r(1) = 15*1 - 2*1^2= 13

r(2) = 15*2 - 2*2^2= 22

The accumulated sand (r) is:

t = r(0) + r(1) + r(2)

r = 0 + 13 + 22

r = 35

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Pie

Logarithmic are inverse of exponential functions. The point where graph of f and g intersect is (0, ∞)

<h3>Logarithmic function</h3>

Logarithmic are inverse of exponential functions. Given the following functions;

g(x)=log2x and g(x)=log10x

The point where the graphs intersect is the point where g(x) = g(x)

Equate

log2x = log10x

2x = 10x

The value of x that made them equal is 0

Determine the value of g(x)

g(0) = log2(0)

g(0) = ∞

Hence the point where graph of f and g intersect is (0, ∞)

learn more on log function here: brainly.com/question/13473114

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7 0
2 years ago
The area of the triangle is eqaula to the sqare show that x²-3x-2=0​
agasfer [191]

Answer:

Step-by-step explanation:

Area of square = area of triangle

side*side = \dfrac{1}{2}b*h\\\\\\x*x=\dfrac{1}{2}*(x+1)(x+2)\\x^{2}=\dfrac{1}{2}[x*x +x*2+1*x+1*2]\\\\\\x^{2}=\dfrac{1}{2}[x^{2}+2x+x+2]\\\\\\x^{2}=\dfrac{1}{2}[x^{2}+3x+2]\\\\\\Multiply \ both \ sides \ by \ 2\\\\2x^{2}=x^{2}+3x+2\\\\2x^{2}-x^{2}-3x-2 = 0

x² - 3x - 2 = 0

8 0
2 years ago
to angie's ladder was 22 feet tall above the ground lying against the wall of her house.the base of the ladder was 5 feet tall.w
Talja [164]

Answer:


Step-by-step explanation:

Okay, so attached is a diagram of the triangle we are solving. Because buildings are almost always perpendicular (90 degrees) to the ground, it is a right triangle.

You can now use the pythagorean theorem with the sides to fill in the other side:


a^2+ b^2= c^2

5^2 + b^2= 22^2

25+b^2=484

b^2= 459

b=21.42


Okay, so for slope you need 2 points- think of the wall as your y axis, and the ground as your x axis. The ladder is the line.

Your first point is (-5,0) because the bottom of the ladder is touching the ground (no y movement) and the bottom of the ladder is 5 feet from the base of the wall and ground (origin).

The second point is going to be (0, 21.42) because that is the height of the wall where the ladder is touching (x is at origin). The 21.42 is positive, because you can't have negative height.

Okay so far? :)

(-5,0) and (0, 21.42)

(x1, y1) and (x2, y2)

slope= (y2-y1)/(x2-x1)

slope= (21.42-0)/ (0-(-5)) ---- becomes positive

slope= 4.284

(Note: slope could also be negative if you put the ladder on the other side of the wall- 5 would become positive... google "positive vs negative slopes" for more info)


Hopefully that answers your question!

3 0
3 years ago
Can somebody help pls
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5 0
3 years ago
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Explain why all squares must be rectangles but not all rectangles are squares
Neko [114]
A square is a quadrilateral with all four angles right angles and all four sides of the same length. ... Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.
5 0
2 years ago
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