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adelina 88 [10]
3 years ago
10

Question # 5 What is the constant of proportionality in the following equation? b = 1.25c​

Mathematics
1 answer:
Gnesinka [82]3 years ago
8 0

Answer:

someone will be with you in a moment

Step-by-step explanation:

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A carton of large eggs way about 1.5 pounds. If a carton holds a dozen eggs, how many pounds does each egg weigh
nata0808 [166]
0.125 or 1/8 of a pound is your answer
3 0
3 years ago
my water sprinkler turns 5 degrees with every click. if it turns 60 degrees total, how many times has it clicked?
Ket [755]
12 times because you divide 60 by 5 and get 12.
4 0
3 years ago
From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh
Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

Step-by-step explanation:

Volume =  height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x  (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so,  4 (3x² - 60x +225)=0

3x² - 60x+225=0   (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

x(x-15) - 5(x-15) =0

Either (x-15)=0

x=15

Or x-5=0

x = 5

if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

7 0
3 years ago
Select the basic integration formula you can use to find the indefinite integral.
kondaur [170]

Answer:

\int \dfrac{du}{u}=\log|u|+C

\int u^n du=\dfrac{u^{n+1}}{n+1}+C

\int \dfrac{du}{u\sqrt{u^2-a^2}}=\dfrac{1}{a}\csc^{-1}(\dfrac{x}{a})+C

Step-by-step explanation:

a.

\int \dfrac{du}{u}=\log|u|+C    [\because \int \dfrac{dx}{x}=\log |x|+C]

b.

\int u^n du=\dfrac{u^{n+1}}{n+1}+C    [\because \int x^n dx=\dfrac{x^{n+1}}{n+1}+C]

c.

\int \dfrac{du}{u\sqrt{u^2-a^2}}=\dfrac{1}{a}\csc^{-1}(\dfrac{x}{a})+C        [\because \dfrac{adx}{x\sqrt{x^2-a^2}}=\csc^{-1}(\dfrac{x}{a})+C]

3 0
3 years ago
Which of these is NOT an integer
Tema [17]

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

Option A

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow  \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}

⸻⸻⸻⸻

\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}

⸻⸻⸻⸻

\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}

⸻⸻⸻⸻

\text{Option \textbf{A} does not simplify into an integer.}

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

7 0
2 years ago
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