a 100 point test has x questions worth 2 points each and y questions worth 4 points each what is the total that is given

n a certain county, the number of Charter Schools is eleven less than twice the number of Alternative Schools. There are 35 Char

dedylja [7]

11+35/2 i think im not sure what your options are

4 0

3 years ago

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For f(x)=4sin(x2) between x=0 and x=3, find the coordinates of all intercepts, critical points, and inflection points to two dec

telo118 [61]

Answer:

Intercepts:

x = 0, y = 0

x = 1.77, y = 0

x = 2.51, y = 0

Critical points:

x = 1.25, y = 4

x = 2.17 , y = -4

x = 2.8, y = 4

Inflection points:

x = 0.81, y = 2.44

x = 1.81, y = -0.54

x = 2.52, y = 0.27

Step-by-step explanation:

We can find the intercept by setting f(x) = 0

$4sin(x^2) = 0$

$sin(x^2) = 0$

$x^2 = n\pi$ where n = 0, 1, 2,3, 4, 5,...

$x = \sqrt(n\pi)$

Since we are restricting x between 0 and 3 we can stop at n = 2

So the function f(x) intercepts at y = 0 and x:

x = 0

x = 1.77

x = 2.51

The critical points occur at the first derivative = 0

$f^{'}(x) = 4cos(x^2)2x = 8xcos(x^2) = 0$

$xcos(x^2) = 0$

$x = 0$ or

$cos(x^2) = 0$

$x^2 = \frac{\pi}{2} + n\pi$ where n = 0, 1, 2, 3

$x = \sqrt{\pi(n+1/2)}$

Since we are restricting x between 0 and 3 we can stop at n = 2

So our critical points are at

x = 1.25, $y = f(1.25) = 4sin(1.25^2) = 4$

x = 2.17 , $y = f(2.17) = 4sin(2.17^2) = -4$

x = 2.8, $y = f(2.8) = 4sin(2.8^2) = 4$

For the inflection point, we can take the 2nd derivative and set it to 0

$f^[''}(x) = 8(cos(x^2) - xsin(x^2)2x) = 8cos(x^2) - 16x^2sin(x^2) = 0$

$cos(x^2) = 2x^2sin(x^2)$

$tan(x^2) = \frac{1}{2x^2}$

We can solve this numerically to get the inflection points are at

x = 0.81, $y = f(0.81) = 4sin(0.81^2) = 2.44$

x = 1.81, $y = f(1.81) = 4sin(1.81^2) = -0.54$

x = 2.52, $y = f(2.52) = 4sin(2.52^2) = 0.27$

3 0

3 years ago

Arturo, Pedro y Jorge son hermanos y duermen en la misma habitación. Su padre compró pintura para que entre los tres pinten su c

mr Goodwill [35]

Answer:

Tanto Pedro como Jorge deberán pintar 1/4 de la habitación cada uno.

Step-by-step explanation:

Dado que el cuarto entero es igual a 1, y que Arturo por ser el mayor de los hermanos tiene que pintar 1/2 de él, la parte que falta pintar es igual a 1/2 restante.

De ese 1/2, los hermanos menores, Pedro y Jorge, deben pintar dicha fracción en partes iguales. Por lo tanto, dado que (1/2) / 2 es igual a 1/4, la fracción que tanto Pedro como Jorge deberán pintar es de 1/4 de la habitación.

4 0

3 years ago

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A total of 300 pine and maple trees will be planted in a park. There will be 2 pine trees planted for every 3 maple trees plante

mars1129 [50]

Answer:

120

Step-by-step explanation:

2 of every 5 trees are pine trees.

2/5 · 300 = 120

120 pine trees are going to be planted in the park.

5 0

3 years ago

2. What is the length of the third side of the right triangle, when both sides are 20?

Helen [10]

Well the only right triangle with two similar sides is a special triangle called a 45 45 90. After the degrees of its shape
_
two sides are x and the other is x/2 _
so in this case the other angle would be 20/2 [20 root (2), its hard to draw roots on this site so I thought I would clarify that was what I was drawing]

Hope this helps, good luck.

5 0

3 years ago

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