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Triss [41]
3 years ago
13

A room has a cathedral ceiling. If the walls in the room are 10 feet high and the ceiling is 18 feet high in the center of the r

oom that is 35 feet wide, find the slope of the left side of the ceiling. Express your answer as a decimal rounded to two places.

Mathematics
1 answer:
9966 [12]3 years ago
4 0
Check the picture below

notice, the run is half 35

recall slope = rise/run

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If f(x)= 3x^2- 4 and g(x) = 2x-6, what is g(f(2))?<br> -16<br> 0-2<br> O 8<br> 10
nexus9112 [7]

Answer:

10

Step-by-step explanation:

g(f(x)) = g(3x² - 4) = 2(3x² - 4) - 6

so

g(f(2) = 2(3*2² - 4) - 6 = 2*8 - 6 = 16 - 6 = 10

6 0
2 years ago
Which of the following is not a solution to the inequality graphed below?
Irina18 [472]

Answer:

C ( 1,-2)

Step-by-step explanation:

We can plot the points and see what point is not in the shaded section

8 0
3 years ago
Halp me on my math plz
liubo4ka [24]
Post a better quistion
6 0
3 years ago
Help. <br>Please its urgent show workings.<br>​
laiz [17]

Answer:

see explanation

Step-by-step explanation:

There are 2 possible approaches to differentiating these.

Expand the factors and differentiate term by term, or

Use the product rule for differentiation.

I feel they are looking for use of product rule.

Given

y = f(x). g(x) , then

\frac{dy}{dx} = f(x).g'(x) + g(x).f'(x) ← product rule

(a)

y = (2x - 1)(x + 4)²

f(x) = 2x - 1 ⇒ f'(x) = 2

g(x) = (x + 4)²

g'(x) = 2(x + 4) × \frac{d}{dx} (x + 4) ← chain rule

       = 2(x + 4) × 1

        = 2(x + 4)

Then

\frac{dy}{dx} = (2x - 1). 2(x + 4) + (x + 4)². 2

    = 2(2x - 1)(x + 4) + 2(x + 4)² ← factor out 2(x + 4) from each term

    = 2(x + 4) (2x - 1 + x + 4)

    = 2(x + 4)(3x + 3) ← factor out 3

    = 6(x + 4)(x + 1)

--------------------------------------------------------------------------

(b)

y =  x(x² - 1)³

f(x) = x ⇒ f'(x) = 1

g(x) = (x² - 1)³

g'(x) = 3(x² - 1)² × \frac{d}{dx} (x² - 1) ← chain rule

        = 3(x² - 1)² × 2x

        = 6x(x² - 1)²

Then

\frac{dy}{dx} = x. 6x(x² - 1)² + (x² - 1)³. 1

    = 6x²(x² - 1)² + (x² - 1)³ ← factor out (x² - 1)²

    = (x² - 1)² (6x² + x² - 1)

     = (x² - 1)²(7x² - 1)

----------------------------------------------------------------------

(c)

y = (x² - 1)(x³ + 1)

f(x) = x² - 1 ⇒ f'(x) = 2x

g(x) = (x³ + 1) ⇒ g'(x) = 3x²

Then

\frac{dy}{dx} = (x² - 1). 3x² + (x³ + 1), 2x

   = 3x²(x² - 1) + 2x(x³ + 1) ← factor out x

   = x[3x(x² - 1) + 2(x³ + 1) ]

   = x(3x³ - 3x + 2x³ + 2)

   = x(5x³ - 3x + 2) ← distribute

    = 5x^{4} - 3x² + 2x

--------------------------------------------------------------------

(d)

y = 3x³(x² + 4)²

f(x) = 3x³ ⇒ f'(x) = 9x²

g(x) = (x² + 4)²

g'(x) = 2(x² + 4) × \frac{d}{dx}(x² + 4) ← chain rule

       = 2(x² + 4) × 2x

       = 4x(x² + 4)

Then

\frac{dy}{dx} = 3x³. 4x(x² + 4) + (x² + 4)². 9x²

    = 12x^{4}(x² + 4) + 9x²(x² + 4)² ← factor out 3x²(x² + 4)

    = 3x²(x² + 4) [ 4x² + 3(x² + 4) ]

    = 3x²(x² + 4)(4x² + 3x² + 12)

    = 3x²(x² + 4)(7x² + 12)

5 0
2 years ago
May someone help me out with this please please
torisob [31]
I = PRT/100 I = Simple Interest P = Principal R = Interest Rate per period T = Time ( no. of periods ) Interest = (2500×9.5×3)/100 = 712.50 Answer : $2500 - $712.50 = $1787.50
8 0
3 years ago
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