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3 years ago

Can someone help me with this problem? I dont really understand it.

Mathematics

1 answer:

Allushta [10]3 years ago

4 0

OH I KNOW I KNOW TEACHER. its its wait im in middle school what the heck am i doing in here.

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I need help with this

Monica [59]

Using derivatives, it is found that regarding the tangent line to the function, we have that:

The slope is of 962.

The equation of the line is y = 962x - 5119.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:

f(x) = 5x³ + 2x + 1.

The derivative is given by:

f'(x) = 15x² + 2.

Hence the slope at x = 8 is:

m = f'(8) = 15(8)² + 2 = 962.

The line goes through the point (8,f(8)), hence:

f(8) = 5(8)³ + 2(8) + 1 = 2577.

Hence:

y = 962x + b

2577 = 962(8) + b

b = -5119.

Hence the equation is:

y = 962x - 5119.

More can be learned about tangent lines at brainly.com/question/8174665

#SPJ1

7 0

2 years ago

If 1=36, 2=38, 3=39, what does 4 equal to? kindly explain

timama [110]

Answer: 4=40 ! Its a pattern

8 0

3 years ago

Read 2 more answers

Another fairly simple one, pretty much a free Brainliest and 30 points.

Alchen [17]

Answer:

Solution given:

$8\frac{7}{12}-3\frac{1}{3}=\frac{8*12+7}{12}-\frac{3*3+1}{3}$

= $\frac{103}{12}-\frac{10}{3}$

taking lcm

= $\frac{103-10*4}{12}=\frac{63}{12}=\frac{21}{4}=5\frac{1}{4}$

7 0

3 years ago

Read 2 more answers

it is claimed that proportion in favor of proportion A is greater than 60%. A sample of size 100 found 69 in favor. what is the

GenaCL600 [577]

Answer:

The alternative hypothesis is $H_1: p > 0.6$ .

The critical value is $Z_c = 1.645$

Step-by-step explanation:

It is claimed that proportion in favor of proportion A is greater than 60%.

This means that at the null hypothesis, we test if the proportion is of at most 60%, that is:

$H_0: p \leq 0.6$

At the alternative hypothesis, we test if the proportion is more than 60%, that is:

$H_1: p > 0.6$

What is (are) the critical value?

The critical value is the value of Z with a p-value 1 subtracted by the standard significance level of 0.05, since we are testing if the mean is more than a value, so, looking at the z-table, $Z_c = 1.645$

7 0

3 years ago

Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solution

Alex Ar [27]

Answer:

Step-by-step explanation:

We have to take the derivatives for both functions and replace in the differential equation. Hence

for y=e^{-5x}:

$y(x)=e^{-5x}\\y'(x)=-5e^{-5x}\\y''(x)=25e^{-5x}\\$

for y=e^{6x}:

$y(x)=e^{6x}\\y'(x)=6e^{6x}\\y''(x)=36e^{6x}\\$

Now we replace in the differential equation y'' − y' − 30y = 0

for y=e^{-5x}:

$25e^{-5x}+5e^{-5x}-30e^{-5x}=0\\25+5-30=0$

for y=e^{6x}:

$36e^{6x}-6e^{6x}-30=0\\36-6+30=0$

Now, to know if both function are linearly independent we calculate the Wronskian

$W(f,g)=fg'-f'g$

$W(e^{-5x},e^{6x})=(e^{-5x})(6e^{6x})-(-5e^{-5x})(e^{6x})\neq 0$

I hope this is useful for you

Best regard

7 0

3 years ago