Which is the value of this expression when j=-2 and k=-1? <br><br> ( jk ^-2 / j^-1 k^-3 ) ^3

KatRina [158]

Hi!

I have attached 2 images that should help you understand :)

First, look at the edits I made to the image you posted. I separated the shape into smaller shapes so that we can find the area of each individual one.

Let's start with the rectangle.

To find the area of a rectangle, multiply the width times the height.
10 · 4 = 40

Rectangle = 40cm

Next up, the red triangles.

I have included another image showing the triangles combined into rectangles. So we can find the area of the triangles just like we would rectangles!

(let me know if you don't understand how I found the width + height of the triangles)

5 · 10 = 50

Red triangles = 50cm

And finally, the green triangles.

8 · 7 = 56

Green triangles = 56cm

Add it all together and you get...

40 + 50 + 56 = 146

The answer to the question is 146cm.

Next time you are having trouble with something like this, picture the triangles as rectangles! :)

3 0

3 years ago

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 $=\$(30.91-15.01)M$

$=\$15.90M$

3 0

3 years ago

Plz Help Only 1 question 24 POINTS

SOVA2 [1]

Dog No dog Total
Cat 31 10 41
No cat 24 7 31
Total 55 17 144

4 0

3 years ago

Write an equation for the translation of x^2+y^2=25 by 7 units left and 2 units down

soldi70 [24.7K]

Your equation is a circle where the center is the origin (0, 0) and the radius is 5. With the translation, the new center is (- 7, - 2). Radius stays the same.

Your new equation is:

(x + 7)² + (y + 2)² = 25

4 0

3 years ago

What is the product ?

Aneli [31]

Answer: 25x^2 - 1^2

Explanation:

(5x+1) (5x-1)

(5x)^2 - 1^2

25x^2 - 1^2

7 0

2 years ago

Read 2 more answers

Which is the value of this expression when j=-2 and k=-1? ( jk ^-2 / j^-1 k^-3 ) ^3