George is required to produce 500 frames for an art gallery. He spent $100 on the wood required for all these frames. He also spent $50 in polishing all the final frames. He rented two floors of an art gallery for about $700. What selling price should George charge the art gallery if he wants to break even?

The derivative of [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex] is [tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex].

In this question we shall use the following derivative rules:

Derivative of a sum of functions

[tex]\frac{d}{dt}(f(t) + g(t)) = \frac{df(t)}{dt} + \frac{dg(t)}{dt}[/tex] (1)

Derivative of a product of functions

[tex]\frac{d}{dt}(f(t)\cdot g(t)) = \frac{df(t)}{dt}\cdot g(t) + f(t)\cdot \frac{dg(t)}{dt}[/tex] (2)

Derivative of a constant

[tex]\frac{d}{dt}(k) = 0[/tex], [tex]\forall k \in \mathbb{R}[/tex] (3)

Derivative of a function multiplied by a constant

[tex]\frac{d}{dt}(c\cdot f(t)) = c\cdot \frac{df(t)}{dt}[/tex], [tex]\forall\, c\in \mathbb{R}[/tex] (4)

Derivative of the cosine function

[tex]\frac{d}{dt} \cos t = -\sin t[/tex] (5)

Derivative of the tangent function

[tex]\frac{d}{dt}\tan t = \sec^{2} t[/tex] (6)

Chain rule

[tex]\frac{d}{dt}f[u(t)] = \frac{df(u)}{du}\cdot \frac{du(t)}{dt}[/tex] (7)

Let be [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex], then the derivative of [tex]f(x)[/tex] is:

[tex]f'(x) = \sec^{2}x\cdot (4 + 3\cdot \cos x) + (3+\tan x)\cdot (-3\cdot \sin x)[/tex]

[tex]f'(x) = 4\cdot \sec^{2}x+3\cdot \sec x -9\cdot \sin x -3\cdot \sin x\cdot \tan x[/tex]

[tex]f'(x) = \frac{4+3\cdot \cos x}{\cos^{2}x} -\frac{9\cdot \sin x \cdot \cos x+3\cdot \sin^{2}x}{\cos x}[/tex]

[tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex]

The derivative of [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex] is [tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex].

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Answer:

Find the slope this way Hanna,

Step-by-step explanation:

slope = m

m = (y2-y1) / (x2-x1)

you are given the two points

P1 = (-2,-6)  in the form (x1,y1)

P2 = (2,2) in the form (x2,y2)

plug those into the slope formula above

m = (2-(-6) ) / (2 - (-2) )

m = (2 +6) / (2+2)

m = 8 / 4

m = 2  

if you need more explanation just leave a comment, it will show up and I'll come look at your question

Answer: Its B

Step-by-step explanation: Hope this was helpful I am not to sure this is the right answer but let me know if it is

Answer:

40°

Step-by-step explanation:

Base length, b = adjacent = 3020 feets

Height of building, h = opposite = 2534 feets

The angle of elevation formed :

Using the trigonometry relation:

Tan θ = opposite / Adjacent

Tan θ = 2534 / 3020

Tan θ = 0.8390728

θ = tan^-1(0.8390728)

θ = 39.999

= 40°

Answer:

Step-by-step explanation:

Remark

Since the chords of the circle are equal and non intersecting, The 2 bisecting perpendiculars are going to be equal.

Equation

5x = 7x - 8           Subtract 7x from both sides

5x - 7x = - 8

-2x = - 8              Divide by - 2

x = - 8/-2

x = 5

Answer:

48

Step-by-step explanation:

Add 84+48 to get 132. subtract 180 the total to the 132 to get 48.

Answer:

its not 10 points its says 8

Step-by-step explanation:

Answer:

80% is greater

Step-by-step explanation:

Answer:

The number 80% is greater than 7/9

Step-by-step explanation:

Answer:

44:99 = 4:9

108:36 = 3:1

33:9 = 11:3

49:14 = 7;2

hope it helps

Answer:

h

Step-by-step explanation

12 inches in 1 foot.

2.54 cm in 1 inch.

5x 12=60 inches

60 +4=64inches.

64 x 2.54=162.56 cm

Answer:

H. 162.56 cm

Step-by-step explanation:

12 inches in 1 foot.

2.54 cm in 1 inch.

5x 12=60 inches

60 +4=64inches.

64 x 2.54=162.56 cm

Answer:

its a

Step-by-step explanation:

i did it

Answer:

A

Step-by-step explanation:

Answer:

f(x)=320(1.16)^x

Step-by-step explanation:

This is an exponential equation with an initial population at x=0 of 320 (because 1.16^0=1, and 320*1=320) After the first year, there are 371 bunnies. After two years, there are 431, etc etc.

Answer:

f(x)=320(1.16)^x

This is an exponential equation with an initial population at x=0 of 320 (because 1.16^0=1, and 320*1=320) After the first year, there are 371 bunnies. After two years, there are 431, etc etc.

Step-by-step explanation:

7/10 - 1/2 = 7/10 - 5/10 = 2/10

Answer:

4/4

Step-by-step explanation:

Answer:

2935 Mexican pesos

Step-by-step explanation:

First, it's worth noting that at current exchange rates, your $100 will equal upwards of 2,395 pesos in Mexico.

Answer:

Tan ∠E = 63/16 = 3.9375

Step-by-step explanation:

Tan ∠E = 63/16 = 3.9375

Answer:

Try 63/16 which is 4.0625

Step-by-step explanation:

Again im sorry if its incorrect. XD hope it helps tho. doing the rest o ur question noe .. tehe

Answer:

140.00

Step-by-step explanation:

20 x 4 = 80 hours worked

80 x 8.00 = $640.00

640.00 - 500.00 = 140.00

Answer:

424 ft

Step-by-step explanation:

Answer:

424 feet is the answer rrrr

Answer:

2.5 and -0.75

Answer:

The centroid of ABC is (3 , 2).

Step-by-step explanation:

The steps are :

[tex]centre = ( \frac{x1 + x2 + x3}{3} \: , \: \frac{y1 + y2 + y3}{3} )[/tex]

[tex]centre = ( \frac{2 + ( - 1) + 8}{3} \: , \: \frac{2 + 0 + 4}{3} )[/tex]

[tex]centre = ( \frac{9}{3} \: , \: \frac{6}{3} )[/tex]

[tex]centre = (3 \: , \: 2)[/tex]

Answer:

The centroid of ∆ABC is (3 , 2).

Step-by-step explanation:

Solution :

Here's the required formula to find the centroid of ∆ABC :

[tex]{\star{\footnotesize{\purple{\underline{ \boxed{\sf{\pink{Centroid = \bigg( \dfrac{x_1 + x_2 + x_3}{3} \: , \: \dfrac{y_1 + y_2 + y_3}{3} \bigg)}}}}}}}}[/tex]

Where :

Substituting all the given values in the formula to find the centroid of ∆ABC

[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{x_1 + x_2 + x_3}{3} \: , \: \dfrac{y_1 + y_2 + y_3}{3} \bigg)}}}}[/tex]

[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{2 + ( - 1) + 8}{3} \: , \: \dfrac{2 +0 + 4}{3} \bigg)}}}}[/tex]

[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{2 - 1 + 8}{3} \: , \: \dfrac{2 +0 + 4}{3} \bigg)}}}}[/tex]

[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{10 - 1}{3} \: , \: \dfrac{2 + 4}{3} \bigg)}}}}[/tex]

[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{9}{3} \: , \: \dfrac{6}{3} \bigg)}}}}[/tex]

[tex]{\implies{\small{\sf{Centroid = \bigg( \cancel\dfrac{9}{3} \: , \: \cancel\dfrac{6}{3} \bigg)}}}}[/tex]

[tex]{\implies{\small{\sf{Centroid = \Big( 3\: , \: 2 \Big)}}}}[/tex]

[tex]\star{\underline{\boxed{\rm{\red{Centroid = \Big( 3\: , \: 2 \Big)}}}}}[/tex]

Hence, the centroid of ∆ABC is (3 , 2).

[tex]\rule{300}{1.5}[/tex]

Answer:

Answer to question 7: -2x+5y+9

Answer to question 8: 2x-6y+1

Answer:

7.) -2x + 5y + 9 ; 8.) 2x - 6y + 1

Step-by-step explanation:

7.)

7 + 2x + 5y - 4x + 2 ⇒ -2x + 5y + 9

2x - 4x ⇒ -2x

5y ⇒ 5y

7 + 2 ⇒ 9

8.)

-4y + 2x - 2y + 1 ⇒ 2x - 6y + 1

2x ⇒ 2x

-4y - 2y ⇒ -6y

1 ⇒ 1

Answer:

noninvasive I will not pay any fee in full and the other fees for my undergraduate degree

Answer:

B

Step-by-step explanation:

Y is the total cost, 22x is how many tickets bought, and 10 is the parking cost

Answer:

A

Step-by-step explanation:

30% of 30000 is 9000, 30000-9000=21000 (1 year)

30% of 21000 is 6300, 21000-6300=14700 (2 years)

30% of 14700 is 4410, 14700-4410= 10290 (3 years)

30% of 10290 is 3087, 10290-3097= 7203 (4 years)

30% of 7203 is 2160.9, 7203-2160.9= 5042.1 (5 years)

Answer:

-64

Step-by-step explanation:

Answer:

4, -3

Step-by-step explanation:

I believe it'd be 4, -3 due to the shape moving seven units downwards, though I've only messed with triangles so I may be wrong. Sorry if I am.

Answer:

angle 3 and angle 2 are complementary angle.

Answer:

242

Step-by-step explanation:

Answer:

242

Step-by-step explanation:

Given

9a² + 2b² ← substitute a = 4 and b = 7

= 9(4)² + 2(7)²

= 9(16) + 2(49)

= 144 + 98

= 242

Answer:

15

Step-by-step explanation:

Given

Hypotenuse (h) = 17 cm

perpendicular (p) = 8 cm

base (b) = ?

we know by using Pythagoras theorem

b = √h² - p²

= √ 17² - 8²

= √ 225

= 15 cm

or

YZ = 15 cm

Hope it will help :)❤

Answer:

150

Step-by-step explanation:

1/2 multiply base times hieght

Answer:

150

Step-by-step explanation:

given in the pic above

in the pic its 15×10

i have written mistakely 15×12

Answer:

$86

Step-by-step explanation:

first you gotta find the interest

4,600 * 1% = 46

so the interest is $46

then you add the interest and late fees together to get the payment for the month

46 + 40 = $86

your total cost is $86

The fess plus interest of the month will be $86 after missing a payment.

Given:

Balance  = $4600

Interest rate = 0.01

Step 1: Calculate the interest for the month.

Interest for the month = Balance × Monthly Interest Rate

Substituting the value back to the formula

Interest for the month= $4,600 × 0.01

                                      = $46

Step 2: Add the late payment fee.

Late payment fee = $40

Step 3: Total fees plus interest for the month.

Total = Interest for the month + Late payment fee

Total = $46 + $40

Total = $86

So, fees plus interest for the month when you miss a payment amount to $86.

Learn more about interest here:

https://brainly.com/question/28272078

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