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2 years ago

If f(x)=2x²-5x and h(x)=7x-13, find (h-f)(-4)

Mathematics

1 answer:

elena-s [515]2 years ago

6 0

$-14x^{2} -x+33$ Answer:

Step-by-step explanation:

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Consider the following equation. f(x, y) = y3/x, P(1, 2), u = 1 3 2i + 5 j (a) Find the gradient of f. ∇f(x, y) = Correct: Your

BaLLatris [955]

$f(x,y)=\dfrac{y^3}x$

a. The gradient is

$\nabla f(x,y)=\dfrac{\partial f}{\partial x}\,\vec\imath+\dfrac{\partial f}{\partial y}\,\vec\jmath$

$\boxed{\nabla f(x,y)=-\dfrac{y^3}{x^2}\,\vec\imath+\dfrac{3y^2}x\,\vec\jmath}$

b. The gradient at point P(1, 2) is

$\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}$

c. The derivative of $f$ at P in the direction of $\vec u$ is

$D_{\vec u}f(1,2)=\nabla f(1,2)\cdot\dfrac{\vec u}{\|\vec u\|}$

It looks like

$\vec u=\dfrac{13}2\,\vec\imath+5\,\vec\jmath$

so that

$\|\vec u\|=\sqrt{\left(\dfrac{13}2\right)^2+5^2}=\dfrac{\sqrt{269}}2$

Then

$D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}$

$\boxed{D_{\vec u}f(1,2)=\dfrac{16}{\sqrt{269}}}$

7 0

3 years ago

Solve for W 4w^2+9w= -2

7nadin3 [17]

Answer:

$w_1=-\frac{1}{4},w_2=-2}$

Step-by-step explanation:

$4w^2+9w=-2$

$4w^2+9w+2=0$

$w^2+9w+8=0$

$(w+1)(w+8)=0$

$(4w+1)(w+2)=0$

$w_1=-\frac{1}{4},w_2=-2}$

3 0

2 years ago

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter

andreev551 [17]

Answer:

Step-by-step explanation:

In each case, draw the right triangle which produces the inverse trig value. That is, label the two sides as needed, and calculate the third side.

It should be clear that

$tan(sin^{-1} x/4) = x/\sqrt{16-x^{2} }$

$sin(tan^{-1} x/4) = x/\sqrt{16+x^{2} }$

sin(2α) = 2 sinα cosα

So,

$1/2 sin(2sin^{-1} x/4) = (1/2)(x/4) * x/\sqrt{16-x^2} = x^{2} /(8\sqrt{16-x^2})$

See what you can do with the others.

6 0

3 years ago

Find 2a for a = 3- 4 = 34

Usimov [2.4K]

Answer:

Step-by-step explanation:

2x34(adding value of a)

8 0

3 years ago

The mean of a normally distributed dataset is 12, and the standard deviation is 2.

Schach [20]

So lets do it like this:
z = (X-Mean)/SD
z1 = (8-12)/2 = - 2 
z2 = (16-12)/2 = + 2 
According to the Empirical Rule 68-95-99.7 
Mean more or less 2SD covers 95% of the values 
So the percentage of data points falling between 8 and 16 = 95%
I hope this can help

5 0

3 years ago