What is the minimum value of the function y=|x+3|-2 ?

Arisa [49]

(t + 12) ^ 2
(t + 12) (t + 12)
t ^ 2 + 12t + 12t + 144 144 24
t ^ 2 + 24t + 144 -------|--------
(t + 12) (t + 12) = 0 12,12 | 24

t = -12

5 0

3 years ago

c) A firm is considering an investment that will earn a 6% rate of return. If it were to borrow the money, it would have to pay

statuscvo [17]

no the firm will not do the investment. because if the firm borrows the money & invest it in the project then the return will be 6% but the cost is 8%. so it will lose 2%.

it also should not invest his own money on the project to get get the 6% return. because he could have loan the money to someone else & get 8% return. therefore his opportunity cost of investing the money is greater than the return.

therefore he should not make the investment .

8 0

3 years ago

The sum of the digits of a two digit number is 6z the number with its digits reversed is 18 less than the original number. Find

Debora [2.8K]

Answer:

42

Step-by-step explanation:

Given:-

The Sum of the Digit of a Two Digit number is 6.

On reversing, the number is 18 less than the original number.

To Find:-

The original Number.

Let the Ones digit be "x"

ten's digit be = (6 - x)

Original Number = x + 10(6 - x) = 60 - 9x

Now, Atq.

One's Digit = (6 - x)

Ten's digit = x

New Number = 10 × x + (6 - x) = 9x + 6.

So,

(New Number) - (Original Number) = 18

(9x + 6 ) - (60- 9x) = 18

9x + 6 - 60 + 9x = 18

18x - 54 = 18

18x = 18 + 54.

18x = 72

x = 72/18

x = 4.

Therefore,

One's Digit = x = 4

Ten's digit = 6 - x = 2

Original Number = 42

6 0

3 years ago

A ball is thrown vertically upward from the top of a building 160 feet tall with an initial velocity of 48 feet per second. The

alina1380 [7]

Answer:

# after 5 seconds, the ball strikes the ground

# The ball reaches maximum height at t = 1.5 seconds

# The max height is 196 feet

Step-by-step explanation:

The equation is:

$d(t)=-16t^2+48t+160$

t is the time

d(t) is the distance traveled

Initial height is 160 feet and initial velocity is 48 ft/sec

If we want to find the time it takes the ball to hit the ground, we let d(t) equal to 0 and find t. Shown below:

$-16t^2+48t+160=0\\t^2-3t-10=0\\(t-5)(t+2)=0\\t=5,-2$

We disregard t = -2 since time can't be negative. We take t = 5

Thus, after 5 seconds, the ball strikes the ground.

The equation is a quadratic of the form: $ax^2+bx+c$

Matching equations, we can say:

a = -16

b = 48

c = 160

The time when ball reaches max height is given as:

$t=-\frac{b}{2a}$

Substituting, we find:

$t=-\frac{b}{2a}\\t=-\frac{48}{2(-16)}\\t=1.5$

The ball reaches maximum height at t = 1.5 seconds

The max height can be found by putting t = 1.5 into the original equation. Shown below:

$d(t)=-16t^2+48t+160\\d(1.5)=-16(1.5)^2+48(1.5)+160\\=196$

The max height is 196 feet

8 0

3 years ago

Evaluate 6+ a for a = 11. The value of the expression is (Simplify your answer.)

grigory [225]

Answer:

17

Step-by-step explanation:

Note that it is given that:

The variable, a, is given the value of 11. Therefore, plug in 11 for a in the given expression. Simplify:

6 + a

a = 11

6 + (11) = 17

17 is your answer.

~

3 0

2 years ago

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