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Rzqust [24]
3 years ago
10

Water is added or drained from a tank each day. The first day, 910 of a gallon is added to the empty tank. The second day, 710 o

f a gallon is drained from the tank. The third day, 810 of a gallon is added to the tank. The fourth day, 610 of a gallon is drained from the tank. The amount of water in the tank after 15 days is given by 910+(−710)+810+(−610)+⋯+310+(−110)+210 9 10 + ( − 7 10 ) + 8 10 + ( − 6 10 ) + ⋯ + 3 10 + ( − 1 10 ) + 2 10 . How much water is in the tank after 15 days? Write your answer as a decimal. gallon(s)
Mathematics
1 answer:
dimulka [17.4K]3 years ago
8 0

Answer:

The quantity of water in the tank after 15 days is 1610.0 gallons OR 1.61 × 10³ gallons.

Step-by-step explanation:

The amount of water in the tank after 15 days is given by the series

910+(−710)+810+(−610)+⋯+310+(−110)+210

From the series, we can observe that, if water is added for a particular day then water will be drained the following day.

Also, for a day when water is to be added, the quantity to be added will be 100 gallon lesser than the quantity that was last added. Likewise, for a day when water is to be drained, the quantity to be drained will be 100 gallons lesser than the quantity that was last drained.

Hence, we can complete the series thus:

910+(−710)+810+(−610)+710(-510)+610(-410)+510(-310)+410(-210)+310+(−110)+210

To evaluate this, we  get

910-710+810-610+710-510+610-410+510-310+410-210+310-110+210

= 1610.0 gallons

Hence, the quantity of water in the tank after 15 days is 1610 gallons OR 1.61 × 10³ gallons.

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Sindrei [870]

The intercepts and the graph on your worksheet are not correct. Please see below for details:

x^2-2x-3=0 has solutions at x=-1 and x=3 (use the quadratic formula to solve). That means these are the x-intercepts, namely points:

(-1,0) and (3,0).

The y-intercept comes from setting x=0 and calculating the y value:

y=0^2-2\cdot0-3=-3

so the y-intercept is (0,-3).

Now to the graph: Based on the form of the function we can see this is a quadratic function and its graph will be a parabola. You can reformat the expression in the following form

y = x^2-2x-3=(x-1)^2-4

and that will indicate that the apex of the parabola (open up) will be at the point (1,-4).

Knowing the apex, the x intercepts, and the y intercept, we can graph it now.

Graph is in the image attached.

6 0
3 years ago
Not sure how to do #69, it's a calc 1 question
Gnoma [55]
Let A( t , f( t ) ) be the point(s) at which the graph of the function has a horizontal tangent => f ' ( t ) = 0.

But, f ' ( x ) = [ ( x^2 ) ' * ( x - 1 ) - ( x^2 ) * ( x - 1 )' ] / ( x - 1 )^2 =>
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f ' ( t ) = 0 <=> t^2 - 2t = 0 <=> t * ( t - 2 ) = 0 <=> t = 0 or t = 2 => f ( 0 ) = 0; f ( 2 ) = 4 => A 1 ( 0 , 0 ) and A 2 ( 2 , 4 ).
3 0
2 years ago
Quadrilateral DUCKDUCKD, U, C, K is inscribed in circle OOO. What is the measure of \angle K∠Kangle, K?
N76 [4]

Answer:

Measure of ∠K=180-∠U

Or

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Step-by-step explanation:

Given:

DUCK quadrilateral inscribed in circle with center O

To Find:

Measure angle K

Solution:

Here the Quadrilateral in inscribed in a circle with center O named as DUCK

So angle K and  U are opposite to each other

We know that the angle of Quadrilateral inscribed in a circle are supplemenatry angles

Hence

∠U+∠K=180

Or The ∠K=1/2*m∠arc(DUC).

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5 0
3 years ago
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What is 2/5 times 15/16
Flauer [41]
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6 0
3 years ago
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sweet [91]

The answer is A) x=0.3

Step-by-step explanation:

Move all terms containing xx to the left side of the equation.

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Move all terms not containing x to the right side of the equation.

14x=4.214x=4.2

Divide each term by 14 and simplify

x=0.3

3 0
3 years ago
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