All categories

3 years ago

Answer quickly please

Mathematics

2 answers:

bulgar [2K]3 years ago

6 0

Answer: C just took the test :)

KIM [24]3 years ago

4 0

The correct answer is C.

You can tell this by factoring the equation to get the zeros. To start, pull out the greatest common factor.

f(x) = x^4 + x^3 - 2x^2

Since each term has at least x^2, we can factor it out.

f(x) = x^2(x^2 + x - 2)

Now we can factor the inside by looking for factors of the constant, which is 2, that add up to the coefficient of x. 2 and -1 both add up to 1 and multiply to -2. So, we place these two numbers in parenthesis with an x.

f(x) = x^2(x + 2)(x - 1)

Now we can also separate the x^2 into 2 x's.

f(x) = (x)(x)(x + 2)(x - 1)

To find the zeros, we need to set them all equal to 0

x = 0

x + 2 = 0

x = -2

x - 1 = 0

x = 1

Since there are two 0's, we know the graph just touches there. Since there are 1 of the other two numbers, we know that it crosses there.

You might be interested in

If h(x) is the inverse of f(x), what is the value of h(f(x))?

Mekhanik [1.2K]

Hello,

f(x) has as inverse f^(-1)(x)
and (fof^(-1))(x)=(f^(-1)of)(x)= x (the neutral function)
so h(f(x))=x

8 0

3 years ago

Read 2 more answers

Find the length of the following two-dimensional curve. r (t ) = (1/2 t^2, 1/3(2t+1)^3/2) for 0 < t < 16

andrezito [222]

Answer:

r = 144 units

Step-by-step explanation:

The given curve corresponds to a parametric function in which the Cartesian coordinates are written in terms of a parameter "t". In that sense, any change in x can also change in y owing to this direct relationship with "t". To find the length of the curve is useful the following expression;

$r(t)=\int\limits^a_b ({r`)^2 \, dt =\int\limits^b_a \sqrt{((\frac{dx}{dt} )^2 +\frac{dy}{dt} )^2)} dt$

In agreement with the given data from the exercise, the length of the curve is found in between two points, namely 0 < t < 16. In that case a=0 and b=16. The concept of the integral involves the sum of different areas at between the interval points, although this technique is powerful, it would be more convenient to use the integral notation written above.

Substituting the terms of the equation and the derivative of r´, as follows,

$r(t)= \int\limits^b_a \sqrt{((\frac{d((1/2)t^2)}{dt} )^2 +\frac{d((1/3)(2t+1)^{3/2})}{dt} )^2)} dt$

Doing the operations inside of the brackets the derivatives are:

1 ) $(\frac{d((1/2)t^2)}{dt} )^2= t^2$

2) $\frac{(d(1/3)(2t+1)^{3/2})}{dt} )^2=2t+1$

Entering these values of the integral is

$r(t)= \int\limits^{16}_{0} \sqrt{t^2 +2t+1} dt$

It is possible to factorize the quadratic function and the integral can reduced as,

$r(t)= \int\limits^{16}_{0} (t+1) dt= \frac{t^2}{2} + t$

Thus, evaluate from 0 to 16

$\frac{16^2}{2} + 16$

The value is $r= 144 units$

5 0

3 years ago

Find 2x2 − 2z4 + y2 − x2 + z4 if x = −4, y = 3, and z = 2 can you help me

Natali [406]

Alright, so plugging it in, we get 2(-4)^2=2(2)^4+3^2-(-4)^2+2^4. Use PEMDAS with parenthesis and exponents to then get (2)(16)+9-16+16. Multiplying 1 and 16, we get 32+41-16+16=73

8 0

3 years ago

Can someone help pleas

Lena [83]

Step-by-step explanation:

According to picture 1, it is A. corresponding.

Also according to picture 2, it is E. same side interior.

And according to picture 3, it is D. vertical

6 0

3 years ago

The moon is about 240,000 miles from earth earth what is the distance written as a whole number multiplied by a power of ten

Varvara68 [4.7K]

This would be 24 X 10⁴

7 0

3 years ago