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Leviafan [203]
3 years ago
15

Find an equation for the tangent to the curve at the given point. y=x^2+2 ; (2, 6)

Mathematics
2 answers:
Zinaida [17]3 years ago
5 0
1) Find the derivative y'=2x and y'(2)=2\cdot2=4.
2) The equation of the tangent line is y=y'(x_0)(x-x_0)+y_0, so at point (2,6): x_0=2 \\ y_0=6 and
y=4(x-2)+6
y=4x-2 -the equation of the tangent line at point (2,6).

spin [16.1K]3 years ago
5 0
Bearing in mind that in (2, 6),  x₁ = 2,    y₁ = 6.

\bf y=x^2+2\implies \left. \cfrac{dy}{dx}=2x \right|_{x=2}\implies 2(2)\implies \stackrel{m}{\underline{4}}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-6=\underline{4}(x-2)
\\\\\\
y-6=4x-8\implies y=4x-2
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Answer:

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Step-by-step explanation:

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4 0
3 years ago
The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute. a 2-row table with 10
olga nikolaevna [1]

According to the line of best fit, the value of time when the temperature reach 100°c, the boiling point of water is 5.

<h3>What is linear regression?</h3>

Linear regression is a type of regression which is used to model the statement in which the growth or decay initially with constant rate, and then slow down with respect to time.

The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute. a 2-row table with 10 columns.

  • Time (minutes X)                 0, 0.5,1.0, 1.5, 2.0,2.5,3.0, 3.5, 4,  4.5.
  • Temperature (° Celsius Y)  75, 79, 83, 86, 89, 91, 93,  94, 95, 95.5.

The sum of time is 22.5 and the sum of temperature value is 880.5. In this table,

  • The mean of time value, 2.25.
  • The mean of temperature value 88.05
  • Sum of squares 20.625
  • Sum of products 93.625

The regression equation for this data can be given as,

\hat y=4.53939 X+77.83636

Put the value of temperature (y) 100 in this equation.

100=4.53939 X+77.83636\\X=\dfrac{100-77.83636}{4.53939}\\X\approx 5

Hence, according to the line of best fit, the value of time when the temperature reach 100°c, the boiling point of water is 5.

Learn more about the regression here;

brainly.com/question/25226042

4 0
2 years ago
The value of the variable which makes an equation a true sentence is called the ___ of the equation​
kirill [66]

Answer:

Solution

Step-by-step explanation:

the value of the variable which makes an equation a true sentence is called the <u>solution</u> of the equation

4 0
3 years ago
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TEA [102]
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6 0
3 years ago
Use the expression below to complete the following tasks. (3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab) What is the additive inverse of
Basile [38]
Remember that the additive inverse are two equal numbers (or expressions) but with different signs.
 We have then, that according with the coment below:
 (3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab)
 the additive inverse is:
 (3a2 - 2b2 - 8ab) Note that is the same expression that
 (-3a2 + 2b2 + 8ab)
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 Answer:
 the additive inverse of the polynomial being subtracted is 
 (3a2 - 2b2 - 8ab)
6 0
3 years ago
Read 2 more answers
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