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maria [59]
3 years ago
12

Determina la pendiente y el ángulo de la recta tangente a la función f(x)=x2-8x+16 en el punto a(6,4)

Mathematics
1 answer:
love history [14]3 years ago
7 0

Answer:

4

75.96^{\circ}

Step-by-step explanation:

La función es

f(x)=x^2-8x+16

La derivada de la ecuación nos da la tangente

f'(x)=2x-8

El punto es (6,4)

Entonces en x=6

f'(6)=2\times 6-8=4

La pendiente de la tangente es 4.

El ángulo de la pendiente está dado por

\tan\theta=m\\\Rightarrow \theta=\tan{-1}m\\\Rightarrow \theta=\tan^{-1}4\\\Rightarrow \theta=75.96^{\circ}

El ángulo que forma la tangente con el eje x positivo es 75.96^{\circ}

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What is the slope of the line
Mrrafil [7]

The slope of the line is undefined because the line doesnt pass through the origin. In order to calculate the slope the line must both be straight and pass through the origin.

4 0
3 years ago
Sara makes a cuboid having sides 15cm and 30cm .how many such cuboids will be needed to form a cube
zhuklara [117]

cuboid=3*3*5 [i.e l*b*h]

LCM of 3,5=15

i.e 15cm is the dimension of the final cube.

therefore cuboid required across length=15/3=5

similarly, across breadth=15/3=5

similarly, across height=15/5=3

Therefore total no of cuboid=5*5*3=75

4 0
4 years ago
Multiply (7x – 6)(8x +3). A. 56x2 – 27x – 18 B. 12x2 – 50x + 8 C. 56x2 – 18 D. 56x2 – 69x + 18
Paha777 [63]
You can use the FOIL method to solve: multiply FIRST, multiply OUTSIDE, multiply INSIDE, multiply LAST to help remember to multiply all terms.

=(7x – 6)(8x + 3)
multiply first term by first term, multiply outside by outside, inside by inside, last by last
=(7x*8x) + (7x*3) + (-6*8x) + (-6*3)
multiply terms
=56x^2 + 21x - 48x - 18
combine like terms
=56x^2 - 27x - 18

ANSWER: A) 56x^2 - 27x - 18

Hope this helps! :)
7 0
3 years ago
Does the point (-4, 3) fall on the graph of this line? How do you know? Show your work. ( 2 points) PLEASE HELP ILL MARK BRAINLI
Elanso [62]

Answer:

Step-by-step explanation:

Since we know the line goes through points (8,9) and (2,4), we can construct a line in slope-intercept form

y = mx + b

where m is the slope and b is the Y-intercept.

The slope can be found using the two points provided:

\frac{y_{2} - y_{1}}{x_{2} - x_{1}}

\frac{9 - 4}{8 - 2}

\frac{5}{6}

The line is now represented as

y = \frac{5}{6}x + b

To solve for b, we can plug in one of the two points:

y = \frac{5}{6}x + b

(9) = \frac{5}{6}(8) + b

4 = \frac{20}{3} + b

b = \frac{-8}{3}

We know have our line:

y = \frac{5}{6}x - \frac{8}{3}

To determine if the point (-4, 3) falls on this line, we just plug the numbers into the equation and see if it holds true:

y = \frac{5}{6}x - \frac{8}{3}

(3) = \frac{5}{6}(-4) - \frac{8}{3}

3 = \frac{-10}{3} - \frac{8}{3}

3 = \frac{-18}{3}

3 = -6

This does not hold true, so the point is not on the line.

3 0
3 years ago
What is the y-coordinate of the solution to the system of equations?<br> y = 3x -1<br> x- y= - 9
lawyer [7]
 y=3x-1 \\&#10;x-y=-9 \\ \\&#10;\hbox{substitute 3x-1 for y in the 2nd equation:} \\&#10;x-(3x-1)=-9 \\&#10;x-3x+1=-9 \\&#10;x-3x=-9-1 \\&#10;-2x=-10 \\&#10;x=\frac{-10}{-2} \\&#10;x=5 \\ \\&#10;y=3x-1=3 \times 5-1=15-1=14 \\ \\&#10;(x,y)=(5,14)

The y-coordinate is 14.
4 0
4 years ago
Read 2 more answers
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