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3 years ago

9

a triangular bandanna has an area of 70 inches.The height of the triangle is 8/3/4.Write and solve an equation to find the lengt

h of the base of the triangle

1 answer:

ycow [4]3 years ago

3 0

Answer:

Base = 16 inches

Step-by-step explanation:

A triangular Bandana has an area of 70 square inches

The height of the triangle is 8 $\frac{3}{4}$

Area of a triangle is given by;

$\frac{1}{2}$ × base × height

∴

$\frac{1}{2}$ × base × $\frac{35}{4}$ = 70

base = $\frac{70 * 2 * 4}{35} = 16$ inches

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Nookie1986 [14]

Answer:

$\large\boxed{y=\dfrac{1}{4}x^2-x-4}$

Step-by-step explanation:

The equation of a parabola in vertex form:

$y=a(x-h)^2+k$

<em>(h, k)</em><em> - vertex</em>

The focus is

$\left(h,\ k+\dfrac{1}{4a}\right)$

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of <em>a</em> using $k+\dfrac{1}{4a}$

<em>k = -5</em>

$-5+\dfrac{1}{4a}=-4$ <em>add 5 to both sides</em>

$\dfrac{1}{4a}=1$ <em>multiply both sides by 4</em>

$4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4$

$\dfrac{1}{a}=4\to a=\dfrac{1}{4}$

Substitute

$a=\dfrac{1}{4},\ h=2,\ k=-5$

to the vertex form of an equation of a parabola:

$y=\dfrac{1}{4}(x-2)^2-5$

The standard form:

$y=ax^2+bx+c$

Convert using

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

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3 years ago

A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in t

Zinaida [17]

Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

c) Price of per room per day = $ 157.5

when Number of rooms occupied , x = 47.5

Step-by-step explanation:

Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.

To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.

b) Find the profit function P(x).

c) Find the price of per room per day the motel should charge in order to maximize its profit.

Proof -

a)

Let

(x, y) be the point

where x represents number of rooms occupied

and y represents price of room per day.

Now,

Given that,

a room is priced at $60 per day, all 80 rooms of the motel are occupied.

So, point becomes (80, 60)

And given that For every $3 rise in the charge per room per day, one more room is vacant.

So, point becomes (79, 63)

Now, we have two points (80, 60), (79, 63)

Let us assume that,

p(x) be the price charged for each room per day

Now,

By using point - slope formula , we get

p -60 = $\frac{(63 - 60}{(79 - 80)} (x - 80)$

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

b)

Given that,

Each occupied room costs an additional $15 per day to maintain.

Let C(x) be the cost function,

Then C(x) =15 x

now,

Revenue function,

R(x) =x*p

= x*(300 -3 x )

= 300 x - 3 x²

⇒R(x) = 300 x - 3 x²

Now,

We know

Profit function = Revenue function - Cost function

⇒P(x) = R(x)-C(x)

⇒P(x) = (300 x -3 x²) -15 x

⇒P(x) = -3 x² + 285 x

c)

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = $\frac{285}{6}$

⇒x= 47.5

∴ we get

Maximize profit is when price, p = 300 - 3x

= 300 -3(47.5)

= $157.5

⇒Price of per room per day = $ 157.5

when Number of rooms occupied , x = 47.5

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3 years ago

Alex invests his money in an account paying 2% interest compounded semiannually. What is the effective annual yield on this acco

Travka [436]

Answer: 2.01%.

Step-by-step explanation:

Suppose Alex invests $1 into the account for one year. The formula is A=P0⋅(1+rk)N⋅k with P0=$1. We know that r=0.02 and k=2 compounding periods per year. Now, N=1 year. Substituting the values we have A=$1⋅(1+0.022)2=$1.0201. Now, to calculate the effective annual yield, we will use the formula rEFF=A−P0P0. rEFF=1.0201−11=0.0201 or 2.01%. When rounded to two decimals, rEFF=2.01%. However, do not include the % in your answer.

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3 years ago