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1 year ago

Find the value of c that makes t^2 - 22t+ c a perfect square trinomial.

Mathematics

1 answer:

allochka39001 [22]1 year ago

8 0

The expression is a perfect square trinomial if and only if c = 121.

<h3>How to get the value of c?</h3>

A perfect square trinomial is written as:

(a + b)^2 = a^2 + b^2 + 2ab

In this case, we have:

t^2 - 22t + c

We can rewrite this as:

t^2 - 2*11*t + c

Then we have:

a = t

b = -11

And we will have that:

c = b^2 = (-11)^2 = 121

Then we have:

t^2 - 2*11*t + 121

Which is a perfect square trinomial:

(t - 11)^2 = t^2 - 22t + 121

Learn more about perfect squares:

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A 50 foot rope weighing a total of 32 lbs extended over a cliff that is 35 feet to the ground. A large 8 pound bucket with 19 ga

larisa86 [58]

Answer:

A function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is $W=16(50-x)+(19-\frac{x}{5})(8.3)x$ and the work to get the bucket to the top of the cliff is 3726 foot-lbs

Step-by-step explanation:

Work done to lift the rope by distance x feet:

$W_1=32(\frac{50-x}{2})$

Work done to lift the bucket by distance x feet:

$W_2=(19-\frac{x}{5})(8.3)x$

On reaching top 7 gallons of water spilled out so , on going up by x feet $\frac{7x}{35}=\frac{x}{5}$ gallons of water spilled out.

a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground:

$W=16(50-x)+(19-\frac{x}{5})(8.3)x$

Now the work to get the bucket to the top of the cliff i.e. x =35

$W=16(50-35)+(19-\frac{35}{5})(8.3)(35)$

W=3726

Hence, a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is $W=16(50-x)+(19-\frac{x}{5})(8.3)x$ and the work to get the bucket to the top of the cliff is 3726 foot-lbs

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2 years ago

A.Write an inequality that represents the fact that while making your productyou can’t exceed this spending limit.

Artist 52 [7]

Answer is A, you made a profit of 50$

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3 years ago

Read 2 more answers

The total cost, in dollars, to order x units of a certain product is modeled by C(x)=5x²+320 . According to the model, for what

lora16 [44]

Answer:

The minimum cost per unit is obtained for an order of 8 units.

Step-by-step explanation:

Since the total cost is modeled by;

C(x)=5x²+320

Then;

1 unit costs; C(x)=5(1)²+320 = 325

cost per unit 325/1 = 325

8 units costs; C(x)=5(8)²+320 = 640

cost per unit = 640/8 = 80

80 units costs; C(x)=5(80)²+320 = 32320

Cost per unit = 32320/80 = 404

The minimum cost per unit is obtained for an order of 8 units.

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3 years ago

Find 4,290 + 3,602. Explain how to use mental math to solve.

lina2011 [118]

Answer: 7892

explanation: add each number individually left to right. 4+3 , 2+6 , 9+0 , 0+2

4 0

3 years ago

A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t is measured in seconds.

pantera1 [17]

Answer:

3.189 seconds

Step-by-step explanation:

You want f(t) = 0, so ...

0 = -16t^2 +13.4t +120

0 = t^2 -0.8375t -7.5 . . . . divide by -16

0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*

0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square

√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root

t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875

It will take the rock about 3.189 seconds to hit the ground.

_____

* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...

(t^2 -2at +a^2) = (t -a)^2

Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.

_____

<em>Comment on the question</em>

We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...

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3 years ago