All categories

2 years ago

Need help with this....

Mathematics

1 answer:

Yakvenalex [24]2 years ago

6 0

Answer:

$\boxed{\dfrac{f(a+h)-f(a)}{h}=-3a^2-3ah-h^2}$

Step-by-step explanation:

$f(x)=-x^3+2\\\\\dfrac{f(a+h)-f(a)}{h}\\\\f(a+h)\to\text{substitute x = a + h}\\f(a)\to\text{substitute x = a}\\\\\dfrac{f(a+h)-f(a)}{h}=\dfrac{-(a+h)^3+2-(-a^3+2)}{h}\\\\\text{use}\ (x+y)^3=x^3+3x^2y+3xy^2+y^3\\\\=\dfrac{-(a^3+3a^2h+3ah^2+h^3)+2-(-a^3)-2}{h}\\\\=\dfrac{-a^3-3a^2h-3ah^2-h^3+2+a^3-2}{h}\\\\\text{combine like terms}$

$=\dfrac{(-a^3+a^3)-3a^2h-3ah^2-h^3+(2-2)}{h}\\\\=\dfrac{-3a^2h-3ah^2-h^3}{h}\\\\=\dfrac{h(-3a^2-3ah-h^2)}{h}\\\\=-3a^2-3ah-h^2$

You might be interested in

Write the equation of line in slope-intercept form

Arturiano [62]

The line crosses points (0, -1) and (2, 0)
y - (-1) = (0 - (-1))/(2 - 0) (x - 0)
y + 1 = 1/2 x
y = 1/2x - 1

4 0

2 years ago

If f is a scalar field and F, G are vector fields, then f F, F · G, and F × G are defined by the following. (f F)(x, y, z) = f(x

valentina_108 [34]

Answer:

Step-by-step explanation:

Consider curl $(fF)$ where $f$ is a scalar function and F is a vector function

$F=F_{1}i +F_{2}j +F_{3}k$

i j k

$curl(fF) = \frac{\partial}{\partial x}$ $\frac{\partial}{\partial y}$ $\frac{\partial}{\partial z}$

$fF_{1}$ $fF_{2}$ $fF_{3}$

$curl(fF)=i(\frac{\partial}{\partial y}(fF_{3})-\frac{\partial}{\partial z}(fF_{2}))-j(\frac{\partial}{\partial x}(fF_{3})-\frac{\partial}{\partial z}(fF_{1}))+k(\frac{\partial}{\partial x}(fF_{2})-\frac{\partial}{\partial y}(fF_{1}))$

$=i(\frac{\partial}{\partial y}(F_{3})+\frac{\partial}{\partial y}(f)-\frac{\partial}{\partial z}(F_{2})-\frac{\partial}{\partial z}(f))-j(\frac{\partial}{\partial x}(F_{3})+\frac{\partial}{\partial x}(f)-\frac{\partial}{\partial z}(F_{1})-\frac{\partial}{\partial z}(f))+k(\frac{\partial}{\partial x}(F_{2})+\frac{\partial}{\partial x}(f)-\frac{\partial}{\partial y}(F_{1})-\frac{\partial}{\partial y}(f))$

$curl(fF)=f(\Delta\times F)+(\Delta f)\times F$

3 0

2 years ago

Tyrone invested money for 3 years at 5% interest. If the interest paid was $60, how much money was invested? What was the total

yan [13]

Answer:

He invested $1200 and had a balance of $1260 after 3 years.

3 0

3 years ago

Lola measures three buttons for a shirt she’s making. One button is 1/8, 3/8 and 1/4 inch. The button hole is 2/6 of an inch. Wh

mel-nik [20]

Answer:

3/8

Step-by-step explanation:

That's the only one bigger than 2/6, any smaller will fall out as it's a button. You'd twist it sort of in half to get it in the hole, therefore, 3/8 is the only button that will fit.

I'm not sure if this is correct but this is how I'd go about it :)

7 0

3 years ago

A study investigated about 3000 meals ordered from Chipotle restaurants using the online site Grubhub. Researchers calculated th

Allisa [31]

Answer:

21.186%

Step-by-step explanation:

z = (x-μ)/σ,

where

x is the raw score = 2400mg

μ is the population mean = 2000mg

σ is the population standard deviation = 500mg

z = 2400 - 2000/500

z = 0.8

Probability value from Z-Table:

P(x<2400) = 0.78814

P(x>2400) = 1 - P(x<2400) = 0.21186

Converting to percentage:

0.21186 × 100

= 21.186%

Therefore, the percent of the meals

ordered that exceeded the recommended daily allowance of 2400 mg of sodium is 21.186%

7 0

3 years ago