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1 year ago

Does anyone know this?

Mathematics

1 answer:

Ilia_Sergeevich [38]1 year ago

3 0

Answer:

a is 7

Step-by-step explanation:

counting all of the 90° angles and then g and h are in the middle so you add the middle also

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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.

The result then is:

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

$\int\ {3^x} \, dx +\int\ {7sinh(x)} \, dx = \frac{3^x}{ln(3)} +7cosh(x) + C$

The letter C is added because the integrations is undefined.

7 0

2 years ago

What is the solution to this equation? X/4 =-12

Natasha2012 [34]

Answer:

C. x=-48

Step-by-step explanation:

x/4=-12

multiply both sides by 4

4x/4=4 (-12)

simplify

x=-48

7 0

2 years ago

Write the equation of the line with x-intercept -2 and y-intercept -1 in slope-intercept form

eduard

The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.

Now that we have two points, we can solve for slope m

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Given two points} \\ (-2,0)\rightarrow(x_1,y_1) \\ (0,-1)\rightarrow(x_2,y_2) \\ \\ \text{Substitute} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-0}{0-(-2)} \\ m=-\frac{1}{2} \end{gathered}$

Now that we have both m and b. Substitute these values to the slope intercept form

$\begin{gathered} \text{Slope intercept form is} \\ y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Substitute the values from before and we get} \\ y=-\frac{1}{2}x-1 \end{gathered}$

5 0

6 months ago

Please help!!!? Find m

Maru [420]

Answer:

Step-by-step explanation:

$m\angle F =tan^{-1}\frac{4}{6}\\m\angle F =33.690067526\degree\\m\angle F =33.7\degree$