Graph: y < 1/3x+1/2 graph the point

Mathematics

1 answer:

Galina-37 [17]3 years ago

5 0

Answer:

1/11

Step-by-step explanation:

First you have to times 1/3 and 1/2 and then you get 1/6. Then you add 1/3 and 1/2 and that's 1/5. then you add them both.

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I am 21 years old my father is 3 times my age how old eill i be when my father is 40

gtnhenbr [62]

Answer:

21+3 24×40 and you will get your answer

4 0

3 years ago

Find the most general antiderivative of the function. (Check yo f(x) = 3^x + 7 sinh(x) F(x) = Need Help? Watch It Talk to a Tuto

egoroff_w [7]

Answer:

F(x)= $\frac{3^x}{ln(3)}$ +7cosh(x)+C

Step-by-step explanation:

The function is f(x)=3ˣ+7sinh(x), so we can define it as f(x)=g(x)+h(x) where g(x)=3ˣ and h(x)=7sinh(x).

Now we have to find the most general antiderivative of the function this means that we have to calculate $\int\ {f(x)} \, dx$ wich is the same as $\int\ {(g+h)(x)} \, dx$

The sum rule in integration states that the integral of a sum of two functions is equal to the sum of their integrals. Then,

$\int\ {(g+h)(x)} \, dx$ = $\int\ {g(x)} \, dx + \int\ {h(x)} \, dx$

1- $\int\ {g(x)} \, dx =$ $\int\ {3^x} \, dx = \frac{3^x}{ln(3)}+C$ this is because of the rule for integration of exponencial functions, this rule is:

$\int\ {a^x} \, dx =\frac{a^x}{ln(x)}$ , in this case a=3

2- $\int\ {h(x)} \, dx =$ $\int\ {7sinh(x)} \, dx =7\int\ {sinh(x)} \, dx =7cosh(x)+C$ , number seven is a constant (it doesn´t depend of "x") so it "gets out" of the integral.