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1 answer:
Using derivatives, it is found that the x-values in which the slope belong to the interval (-1,1) are in the following interval:
(-15,-10).
<h3>What is the slope of the tangent line to a function f(x) at point x = x0?</h3>It is given by the derivative at x = x0, that is:
.
In this problem, the function is:
Hence the derivative is:
For a slope of -1, we have that:
0.4x + 5 = -1
0.4x = -6
x = -15.
For a slope of 1, we have that:
0.4x + 5 = 1.
0.4x = -4
x = -10
Hence the interval is:
(-15,-10).
More can be learned about derivatives and tangent lines at brainly.com/question/8174665
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As X' is the reflected point of X(0,3) , so the x co ordinate of X' = 0+8 =8 and here y co ordinate remains same.
So, X'= (8,3)
Like that way, Y' is the reflected point of Y(2,0) and Z' is the reflected point of Z(4,2)
As the point Z is lying on the line x=4 and the reflection is also across that line, so both Z and Z' represent same point.
Y'= (2+4, 0) = (6, 0)
Z' = (4, 2)
Answer:
La cantidad de horas que trabajó Hugo son 8, mientras que Eduardo trabajó 32 horas y Francisco 64 horas.
Step-by-step explanation:
En primer lugar, para determinar la ecuación que debes resolver, es conveniente establecer la variable a la que debes encontrar una solución en la ecuación. Entonces, llamas x a la cantidad de horas que trabajó Hugo.
Luego, sabes que Eduardo trabajó el cuádruple de horas de las que trabajó Hugo, esto es, cuatro veces más de las horas trabajadas por Hugo. Esto se expresa matemáticamente como 4*x.
Finalmente, Francisco trabajó el doble de horas que Eduardo, que se calcula multiplicando a las horas trabajadas por Eduardo por 2: 2*4*x= 8*x
Entre los tres hermanos trabajaron 104 horas. Esto indica que la suma de las horas trabajadas por Francisco, Eduardo y Hugo debe ser 104 horas. Esto se expresa matemáticamente como:
x + 4*x+ 8*x= 104 (Planteamiento algebraico)
Resolviendo (Procedimiento):
13*x=104
x=8
Esto significa que <u><em>la cantidad de horas que trabajó Hugo son 8</em></u>.
Eduardo trabajó 4*x, esto es 4*8, que da como resultado 32 horas. Entonces <u><em>Eduardo trabajó 32 horas.</em></u>
Por último, Francisco trabajó 8*x. Siendo x=8, entonces 8*8=64. Entonces <u><em>Francisco trabajó 64 horas.</em></u>
Answer:
The vector that describes their hike from their starting position to their final destination is .
Step-by-step explanation:
In this problem we assume that orthogonal axes coincide with the north and east. We proceed to translate each sentence from statement into vectorial equations:
(i) <em>A group of hikers walks 3 miles east and then 1 mile north:</em>
(ii) <em>After taking a break, they then hike 4 miles east to their final destination:</em>
The vector that describes their hike from their starting position to their final destination is the sum of the vectors deducted above. That is:
(1)
The vector that describes their hike from their starting position to their final destination is .