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3 years ago

A rocking chair with an orginal price of $375 is on sale for $318.75.What is the percent of discount

Mathematics

1 answer:

Rudik [331]3 years ago

5 0

The percent of the discount would be 15%.
Micah would earn $280 in 42 months.

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Limit (sin4x-4sinx)/x^3 when x close to zero

BartSMP [9]

$\Large \boxed{\sf \bf \ \ \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}=-10 \ \ }$

Step-by-step explanation:

Hello, please consider the following.

Using Maclaurin series expansion, we can find an equivalent of sin(x) in the neighbourhood of 0.

$sin(x) \sim \left(x-\dfrac{x^3}{3!}\right)\\\\\text{So, in the neighbourhood of 0}\\\\\begin{aligned}(sin(4x)-4sin(x)) &\sim \left( 4x-\dfrac{(4x)^3}{3!}-4x+\dfrac{4x^3}{3!}\right)\\\\&\sim \left(\dfrac{x^3*4*(1-4^2)}{3*2}\right)\\\\&\sim \left(\dfrac{x^3*2*(-15)}{3}\right)\\\\&\sim \left(x^3*2*(-5)\right)\\\\&\sim \left(x^3*(-10)\right)\\\end{aligned}$

Then,

$\displaystyle \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}\\\\= \lim_{x\rightarrow0} \ {\dfrac{-10*x^3}{x^3}}\\\\=-10$

Thank you

4 0

4 years ago

Read 2 more answers

Let f(x) = 4x2 + 6 and let g(x) = 8x – 6. Find f(g(x)) and g(f(x)).

Artyom0805 [142]

Answer:

f(g (x))= 32x-18

g (f (x))=32x2+42

Step-by-step explanation:

f (g (x))= 4 (8x-6)+6

32x-24-6

32x-18

g (f (x))= 8(4x2+6)-6

32x2+48-6

32x2+42

4 0

3 years ago

Solve -17 = x/-3 for x.

MA_775_DIABLO [31]

Answer:

x = 51

Step-by-step explanation:

-17 = x/-3

Multiply each side by -3

-3 * -17 = x / -3 * -3

51 = x

4 0

3 years ago

Read 2 more answers

Eli and Samantha work at a dry cleaners ironing shirts. Eli can iron 20 shirts per hour, and Samantha can iron 35 shirts per hou

MrRa [10]

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> the number of hours Eli worked

y ----> the number of hours Samantha worked

we know that

Eli and they ironed 400 shirts between them

----> equation A

Samantha worked 2 more hours than Eli

----> equation B

solve the system by substitution

substitute equation B in equation A

solve for x

Find the value of y

substitute the value of x in equation B

therefore

The number of hours Eli worked was 6 and the number of hours Samantha worked was 8

5 0

3 years ago

Factor polynomial -3x^2-16x-5

forsale [732]

Answer:

-(3x^2 + 16x + 5)

-(3x+1)(x+5)

Step-by-step explanation:

-1(3x^2+15x+x+5)

-1(3x^2+16x+5)

-3x^2-16x-5

8 0

4 years ago