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Zielflug [23.3K]
3 years ago
9

What digits makes 3,71? Divisible by 3 (connections academy unit test)

Mathematics
1 answer:
wlad13 [49]3 years ago
6 0

Since we know that a number is divisible by 3 if the sum of all digits is divisible by 3.

Let us check which digits will make 371? divisible by 3.

3+7+1+0=11

11 is not divisible by 3.

Now let us check other digits as well.

3+7+1+1=12

12 is divisible by 3.

3+7+1+4=15

15 is also divisible by 3.

3+7+1+7=18

18 is divisible by 3 as well.

Therefore, 1, 4 and 7 in tenth place will make our number divisible by 3 and our numbers will be 3711, 3714 and 3717.

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If f(x) is a third degree polynomial function and g(x) = f(–2x), which of the following is NOT true?
valina [46]

Answer:

f(x) and g(x) have the same x-intercepts (is <em>not true</em>)

Step-by-step explanation:

g(x) is a reflection across the y-axis and a horizontal compression of f(x). In general those transformations will move the x-intercepts. (The y-intercept and the number of x-intercepts will remain unchanged.)

_____

<em>Comment on the question/answer</em>

f(x) = x^3 is a 3rd degree polynomial. When transformed to g(x) = -8x^2, its only x-intercept (x=0) remains the same. The answer above will not apply in any instance where the only x-intercept is on the line of reflection. (The question is flawed in that it does not make any exception for such functions.)

8 0
3 years ago
Find an equivalent system of equations for the following system: 3x + 3y = 0 −4x + 4y = −8
Rama09 [41]

Answer:

Answer:

3x + 3y = 0

7x - y = 8

Step-by-step explanation:

3 0
3 years ago
Find the exact length of the curve. 36y2 = (x2 − 4)3, 5 ≤ x ≤ 9, y ≥ 0
IrinaK [193]
We are looking for the length of a curve, also known as the arc length. Before we get to the formula for arc length, it would help if we re-wrote the equation in y = form.

We are given: 36 y^{2} =( x^{2} -4)^3
We divide by 36 and take the root of both sides to obtain: y = \sqrt{ \frac{( x^{2} -4)^3}{36} }

Note that the square root can be written as an exponent of 1/2 and so we can further simplify the above to obtain: y =  \frac{( x^{2} -4)^{3/2}}{6} }=( \frac{1}{6} )(x^{2} -4)^{3/2}}

Let's leave that for the moment and look at the formula for arc length. The formula is L= \int\limits^c_d {ds} where ds is defined differently for equations in rectangular form (which is what we have), polar form or parametric form.

Rectangular form is an equation using x and y where one variable is defined in terms of the other. We have y in terms of x. For this, we define ds as follows: ds= \sqrt{1+( \frac{dy}{dx})^2 } dx

As a note for a function x in terms of y simply switch each dx in the above to dy and vice versa.

As you can see from the formula we need to find dy/dx and square it. Let's do that now.

We can use the chain rule: bring down the 3/2, keep the parenthesis, raise it to the 3/2 - 1 and then take the derivative of what's inside (here x^2-4). More formally, we can let u=x^{2} -4 and then consider the derivative of u^{3/2}du. Either way, we obtain,

\frac{dy}{dx}=( \frac{1}{6})( x^{2} -4)^{1/2}(2x)=( \frac{x}{2})( x^{2} -4)^{1/2}

Looking at the formula for ds you see that dy/dx is squared so let's square the dy/dx we just found.
( \frac{dy}{dx}^2)=( \frac{x^2}{4})( x^{2} -4)= \frac{x^4-4 x^{2} }{4}

This means that in our case:
ds= \sqrt{1+\frac{x^4-4 x^{2} }{4}} dx
ds= \sqrt{\frac{4}{4}+\frac{x^4-4 x^{2} }{4}} dx
ds= \sqrt{\frac{x^4-4 x^{2}+4 }{4}} dx
ds= \sqrt{\frac{( x^{2} -2)^2 }{4}} dx
ds=  \frac{x^2-2}{2}dx =( \frac{1}{2} x^{2} -1)dx

Recall, the formula for arc length: L= \int\limits^c_d {ds}
Here, the limits of integration are given by 5 and 9 from the initial problem (the values of x over which we are computing the length of the curve). Putting it all together we have:

L= \int\limits^9_5 { \frac{1}{2} x^{2} -1 } \, dx = (\frac{1}{2}) ( \frac{x^3}{3}) -x evaluated from 9 to 5 (I cannot seem to get the notation here but usually it is a straight line with the 9 up top and the 5 on the bottom -- just like the integral with the 9 and 5 but a straight line instead). This means we plug 9 into the expression and from that subtract what we get when we plug 5 into the expression.

That is, [(\frac{1}{2}) ( \frac{9^3}{3}) -9]-([(\frac{1}{2}) ( \frac{5^3}{3}) -5]=( \frac{9^3}{6}-9)-( \frac{5^3}{6}-5})=\frac{290}{3}


8 0
3 years ago
There are 36 carpenters in a crew. On a certain day, 29 were present. What percent were at work? (Round your answer to the neare
Allushta [10]

Answer:

80.56%

Step-by-step explanation:

divide 36 by 29 and you get 0.8055555555. Change that into a percent to get 80.56%

8 0
3 years ago
Nori had 2 bags of apples. He used 1. bags of apples to make pies. How
Inessa05 [86]

Answer:

8/12 left

Step-by-step explanation:

8/12 of a bag left

2 1/12 = 25/12

1 5/12 = 17/12

25-17 = 8

The answer is 8/12

5 0
2 years ago
Read 2 more answers
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