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arlik [135]
3 years ago
9

Original: 379 New: 83

Mathematics
1 answer:
VladimirAG [237]3 years ago
5 0
379x=89
_______
379 =379

x=0.21
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Find an equation of a line that is tangent to the graph of f and parallel to the given line. Please see picture
ivanzaharov [21]

Answer:

y = 3x - 2 (smaller y-intercept)

y = 3x + 2 (larger y-intercept)

Step-by-step explanation:

First let's write the generic equation of a line:

y = ax + b

This line needs to be parallel to the line 3x - y + 5 = 0, so it needs to have the same slope of this line.

The line 3x - y + 5 = 0 has a slope of 3, so our line has a = 3:

y = 3x + b

Now we need to find the values of b that make this line tangent to the function f(x) = x^3

Let's first find the derivative of f(x) in relation to x:

df(x)/dx = 3x^2

This derivative is the slope of the tangent line to the function for any value of x. We need a slope of 3, so:

3x^2 = 3

x^2 = 1

x = ±1

Now, to find the y-values, we have:

f(1) = 1^3 = 1

f(-1) = (-1)^3 = -1

So, using the points (1,1) and (-1,-1) in our parallel line, we have:

first line using (1,1) : 1 = 3*1 + b

b = -2

second line using (-1,-1) : -1 = -3*1 + b

b = 2

The value of b is the y-intercept of the line, so the line with smaller y-intercept is y = 3x - 2, and the line with larger y-intercept is y = 3x + 2

8 0
3 years ago
A car travels at a rate of 45 miles per hour for 5 hours. Let y be the distance, in miles, the car travels for a given amount of
Nuetrik [128]

Answer:

0 ≤ x ≤ 5

Step-by-step explanation:

I used the Desmos calculator

6 0
3 years ago
141÷6 (a) Write a story problem that matches this expression. (b) Solve the problem. (c) Does the quotient in your problem have
avanturin [10]

There is a type of ammo in f/o/r/t/n/i/t/e that can be magically used for every single gun. You open an ammo box, and out pops 141 rounds of that ammo. You have already collected 6 guns. How many rounds go into each gun?

The answer is 23.5

THERE IS A REMAINDER??

Nothing happens! Literally! It never happened! There is no ammo that can be used for all the guns. GG and hope to see you on the game sometime, cause...i am not allowed to have it.

8 0
3 years ago
Y = x^2 + 2x - 8 Solve with zeros
Katen [24]

Answer:

x=-4  x=2

Step-by-step explanation:

y = x^2 + 2x - 8

Set equal to zero

0 = x^2 + 2x - 8

Factor

What two numbers multiply to -8 and add to 2

4 * -2 = -8

4+-2 = 2

0=(x+4) ( x-2)

Using the zero product property

x+4 =0   x-2 =0

x=-4  x=2

6 0
3 years ago
Solve for x: 24x + 12 = 16
vfiekz [6]

Answer:

x=1/6 or x=0.1666666667

Step-by-step explanation:

5 0
2 years ago
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