Suppose that fanf g are continuous functions,

Mathematics

1 answer:

shtirl [24]1 year ago

7 0

The required result based on given continuous functions is: 207. See the explanation for same below.

<h3>What are continuous functions?</h3>

A continuous function in mathematics is one in which a continuous variation (that is, a change without a jump) of the argument causes a continuous variation of the function's value.

<h3>What is the calculation for the above solution?</h3>

Since G and F are continuous functions,

$\int_{12}^{28}) \, f(x) dx$ = 19

$\int_{12}^{28}) \, f(x) dx$ = 35

Therefore,

$\int_{12}^{28}) \, [K g(x) - 2 f(x)] dx$

= K $\int_{12}^{28}) \, g(x) dx -2 \int_{12}^{28}) \, f(x) dx$

So, given that K = 7, we have

7 x 35 - 2 x 19
= 245 - 38
= 207

Learn more about continuous functions at;
brainly.com/question/18102431
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Find all real solutions of the equation by completing the square. (Enter your answers as a comma-separated list.) x2 − 4x − 8 =

Nat2105 [25]

Answer:

After completing the square the expression is (x-2)^2 -12 =0 and real solution are x = 5.46 and x = -1.46

Step-by-step explanation:

We need to complete the square:

x^2 − 4x − 8 = 0

x^2 -2(x)(2)+(2)^2 -8 -4 =0

(x^2 -4x +4) - 12 = 0

(x-2)^2 -12 =0

Now, finding the value of x

(x-2)^2 -12 =0

(x-2)^2 = 12

taking square root on both sides

$\sqrt{(x-2)^2}= \sqrt{12} \\(x-2) = \pm\sqrt{12} \\x = \pm\sqrt{12} +2\\x = \sqrt{12}+2 \,\,and\,\,x=-\sqrt{12}+2\\x= 3.46+2 \,\,and\,\,x=-3.46+2\\x =5.46\,\,and\,\,x=-1.46$