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jenyasd209 [6]
2 years ago
5

Mr. Marsh tells his class that he is thinking of two numbers and wants his students to guess the numbers. He gives them the foll

owing hints. The two numbers have a sum of zero. The two numbers have a distance of 2.5 units between them on the number line.
Mathematics
1 answer:
Kobotan [32]2 years ago
5 0

Answer:

1.25 and - 1.25

Step-by-step explanation:

additive inverses: a number and its opposite have a sum of 0

x and y are opposite number, one positive and another negative

distance = 2.5 with midpoint "0"

x = 2.5/2 = 1.25

y = -1.25

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F(x) = 3x + x3
____ [38]

Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

\frac{d}{dx}\left(3x+x^3\right)

\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'

=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)

solving

\frac{d}{dx}\left(3x\right)

\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'

=3\frac{d}{dx}\left(x\right)

\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1

=3\cdot \:1

=3

now solving

\frac{d}{dx}\left(x^3\right)

\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}

=3x^{3-1}

=3x^2

Thus, the expression becomes

\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)

                    =3+3x^2

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value  f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 =  3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

x=\sqrt{4},\:x=-\sqrt{4}

x=2,\:x=-2

Thus, the value of x​ will be:

x=2,\:x=-2

5 0
3 years ago
I don't get this question lol
Papessa [141]
Multiply the x values by -1/2, and then add three, that will give you the y values
7 0
3 years ago
How do you work out 9/10 divided by 6/7??
Helga [31]
\frac{9}{10} \div \frac{6}{7}
You just flip 6/7 so it would be 7/6 and then you times it.
\frac{9}{10} \div \frac{6}{7}
\frac{9}{10} \times \frac{7}{6} = \frac{63}{60} = \frac{21}{20} 

6 0
3 years ago
Geometry: please only comment if you know the answer I need help with this please
stich3 [128]

Answer:

Step-by-step explanation:

8 0
2 years ago
(4x3y3)3<br>me pueden ayudar​
Dominik [7]

Answer:

12x9y9

Step-by-step explanation:

( 4x3y3 ) 3

= 4x ⋅ 3 ⋅ 3y ⋅ 3 ⋅ 3 ⋅ 3

= 12x9y9

7 0
2 years ago
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