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3 years ago

What is the area of a triangle length 2.5 height 8.75

Mathematics

2 answers:

gregori [183]3 years ago

3 0

Area of a triangle = 0.5 x base x height
= 0.5 x 2.5 x 8.75
= 10.94 (units squared)

bekas [8.4K]3 years ago

3 0

My Geometry teacher used to say,

"My students, ahh. Textbooks. They say, 'My pretty little students, here's a formula! I will give you numbers and you plug it in.' Then he would say, 'I don't like textbooks. I'm a rebel! So, I derive the formula.'"

He made us derive it. But the formula is this: 1/2 x b x h. Why? The real formula is because two equal triangles are both HALF of a PARALLELOGRAM.

Parallelogram area formula is b x h, or base x height. So half of that?
(b x h) / 2, or 1/2 x b x h.

Plug this in.

Assuming your triangle is equilateral, I plug in 2.5 for the base and 8.75 for the height.

So, what's 1/2 x 2.5 x 8.75?

It's 10.9375.

Rounded, it's 10.94.

You have it.

Just remember, it's about WHY this formula works.

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Answer:

D) p > -2

Step-by-step explanation:

5 + p > 3

5 + p - 5 > 3 - 5

p > -2

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2 years ago

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An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial co

Blizzard [7]

Answer:

$(a)$ $C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ $x=82 \text{planes}$

$(c)$ $p=\$30.91 M\;\; \text{per plane}$

$(d)$ maximum profit $=\$ 15.90M$

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

$m(x)=20x-5x^{\frac{3}{4}}+0.01x^2$

$(a)$ Find the cost, demand (or price), and revenue functions.

$C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ Find the production level that maximizes profit.

$f=R(x)-C(x)$

$\Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)$

$\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx$

$x=320-7.7p$

$p=\frac{320-x}{7.7}$

$\frac{dp}{dx} = \frac{-1}{7.7}$

$\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0$

$\Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0$

$\Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0$

$\Rightarrow x=82 \text{planes}$

$(c)$ Find the associated selling price of the aircraft that maximizes profit.

$p=\frac{320-82}{7.7}$

$\Rightarrow p=\$30.91 M\;\; \text{per plane}$

$(d)$ Find the maximum profit.

Manufacturing cost of one plane is:

$m(1)=20-5+0.01$

$=\$15.01 M$

maximum profit $=\$(30.91-15.01)M$

$=\$15.90M$

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2 years ago

Are the given lengths 24, 60, 66, sides of a right triangle?

GarryVolchara [31]

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Answer:

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Step-by-step explanation:

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