Does this graph show a function? Explain how you know.

Location Elevation (feet) Bottom of Death Valley -282.2 1,250.0 Top of Empire State Building Top of Washington Monument 555.5 Bo

kow [346]

Answer:

c

Step-by-step explanation:

4 0

4 years ago

will mark brainliest. PROMISE!! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. Wha

Dmitry [639]

Answer:

0.16

Step-by-step explanation:

Length = 5 units
Number of broken sticks= 3
Equal lengths = 5 units/3

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of this is:

2/5*2/5 = 4/ 25 = 0.16

Answer is 0.16

6 0

4 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. Y = (4/9) x

frez [133]

Answer:

V = 8.06 cubed units

Step-by-step explanation:

You have the following curves:

$y_1=\frac{4}{9}x^2=f(x)\\\\y_2=\frac{13}{9}-x^2=g(x)$

In order to calculate the solid of revolution bounded by the previous curves and the x axis, you use the following formula:

$V=\pi \int_a^b [(g(x))^2-(f(x))^2]dx$ (1)

To determine the limits of the integral you equal both curves f=g and solve for x:

$f(x)=g(x)\\\\\frac{4}{9}x^2=\frac{13}{9}-x^2\\\\\frac{4}{9}x^2+x^2=\frac{13}{9}\\\\\frac{13}{9}x^2=\frac{13}{9}\\\\x=\pm 1$

Then, the limits are a = -1 and b = 1

You replace f(x), g(x), a and b in the equation (1):

$V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units$

The volume of the solid of revolution is approximately 8.06 cubed units

8 0

4 years ago

Is the following true or false? d/dx[x^3e^x]=x^2e^x (3x+2)

wolverine [178]

It's false. It's a product so...
Derivative of the first TIMES the second PLUS derivative of second TIMES the first.

Derivative of the first (x^3) = 3x^2
Times the second = 3x^2 * e^x

Derivative of the second = e^x (remains unchanged)
Times the first = e^x * x^3
So the answer would be (3x^2)(e^x) + (e^x)(x^3)
which can be factorised to form x^2·e^x(3 + x)

3 0

4 years ago

David y Angie tienen dos cartulinas iguales. David corta la suya en 3 trozos iguales y Angie la corta en 7 trozos. Los dos usan

Bess [88]

Answer:

(i) David ha empleado $\frac{2}{3}$ de la cartulina.

(ii) Angie ha empleado $\frac{2}{7}$ de la cartulina.

(iii) David ha usado más cartulina.

Step-by-step explanation:

El problema indica que David y Angie emplean una cartulina del mismo tamaño cada uno. David corta la suya en 3 pedazos iguales, mientras que Angie obtiene 7 pedazos iguales. Finalmente, cada uno emplea dos de sus pedazos. A continuación, respondemos a las preguntas del enunciado:

(i) ¿Qué fracción de cartulina ha usado David?

La fracción de cartulina empleada por David es igual a los pedazos utilizados divididos por el total de pedazos. Esto es:

$x = \frac{2}{3}$

David ha empleado $\frac{2}{3}$ de la cartulina.

(ii) ¿Qué fracción de cartulina ha usado Angie?

Aplicando el mismo procedimiento del punto anterior, tenemos que:

$x = \frac{2}{7}$

Angie ha empleado $\frac{2}{7}$ de la cartulina.

(iii) ¿Quién ha usado más cartulina?

La persona que ha usado la mayor cantidad de cartulina es aquella que tiene el menor denominador. Por tanto, David ha usado más cartulina.

7 0

3 years ago