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3 years ago

Which graph represents x - 1 ≤ 3

Mathematics

1 answer:

MAVERICK [17]3 years ago

3 0

The first graph.

The equation is x - 1 $\leq$ 3
In order to solve it, you need to get x by itself.
Add 1 to both sides. 3+1=4
x $\leq$ 4

Since this is your sign $\leq$ the arrow has to point towards the left, and the circle needs to be colored in.

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A 12-cm-long thin rod has the nonuniform charge density λ(x)=(2.0 nC/cm)e−|x|/(6.0 cm), where x is measured from the center of t

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the total charge is

$Q=24(1-\exp(-1))nC\approx15.171nC$

Step-by-step explanation:

Since x is measured from the center, that means that x=0 is the center so the edges of the rod correspond to x=-6 and x=6. that meas that the total charge can be calculated as

$Q=\int^{6}_{-6}2\exp\left(\frac{-|x|}{6}\right)dx$

separating the integral from -6 to 0 and from 0 to 6, taking into account that |x|=-x for x<0 and |x|=x for x >=0, we get $Q=\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx+\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx$

using the substitution x=-u in the first integral we get $\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx=-\int^{0}_{6}2\exp\left(\frac{-u}{6}\right)du=\int^{6}_{0}2\exp\left(\frac{-u}{6}\right)du$

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3 years ago

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All square numbers have an odd numberof factors. A prime number by definition has exactly 2 factors - 1 and itself.

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If f(x)=x^2+2x+3, find f(1)

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To solve this problem, we must substitute in 1 for the variable x in the equation. This is because the function as written is f(x), meaning that the function is evaluated as x currently, but we want to evaluate it at 1. To do this, all we have to do is replace each variable x with a 1 and simplify.

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

f(1) = (1)^2 + 2(1) + 3

To simplify, we first to compute the exponents. This is because of the order of operations, which says that we should solve parentheses first, exponents next, then multiplication/division, then addition/subtraction last.

f(1) = 1 + 2(1) + 3

Next, as outlined above, we should perform the multiplication.

f(1) = 1 + 2 + 3

Finally, we can finish solving by adding together the remaining terms.

f(1) = 6

Therefore, your answer is 6.

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