Need help with calculus question

Answers

Answer 1

Answer:

The value of the derivative at $x=5$ is the slope of the tangent line at the point $(x,g(x))=(5,-4)$ .

So the tangent line has equation

$y-g(5)=g'(5)(x-5)\implies y+4=6(x-5)\implies\boxed{y=6x-34}$

Related Questions

A submarine descends 1/120 mile every minute. Write a product of three or more rational numbers to represent the change in the submarines elevation after 3 hours. Then find the value of the product and explain what it represents.
Need help...,.......
On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines with a standard deviation of 1. What is the test statistic in a test of the null hypothesis that the population average is 10? Can you reject the null at the 5% significance level?
2. Briana goes to the store and buys 12 items. Ifeach item is $3.25, what is her total bill withouttax?
If two systems of linear equations have the same solution set (in other words, the two systems are equivalent), then they must have the same number of equations. a. Trueb. False

If the probability that an individual with a Bachelor Degree in Underwater Basket-weaving will be hired in their first 6 months out of college is 59%, what is the probability that an individual with a Bachelor Degree in Underwater Basket-weaving will not get hired in the first 6 months out of college?

Answers

Answer: The required probability is 41%.

Step-by-step explanation:

Since we have given that

Probability that he will be hired in their first 6 month out of college = 59% = 0.59

So, we know that

total probability = 100% = 1

Probability that he will not get hired in the first 6 months out of college would be

$P(H')=1-P(H)=1-0.59=0.41=41\%$

Hence, the required probability is 41%.

Tanya has 44 quarters and dimes worth$8.30. how many of each type of coin does she have

Answers

Tanya has 26 quarters and 18 dimes.

Given that Tanya has 44 quarters and dimes which worth $8.30, we need to find the number of each coin type,

To find the same we will use the concept of system of Linear equations,

Let's solve this problem step by step.

Let's assume Tanya has x quarters and y dimes.

The value of x quarters is 25x cents.

The value of y dimes is 10y cents.

According to the given information, the total value of the quarters and dimes is $8.30, which is equivalent to 830 cents. So we have the equation:

25x + 10y = 830 ...........(Equation 1)

Tanya has 44 coins in total:

x + y = 44 ...........(Equation 2)

Now, we can solve this system of equations (Equation 1 and Equation 2) to find the values of x and y.

Multiplying Equation 2 by 25, we get:

25x + 25y = 1100 ...........(Equation 3)

Subtracting Equation 3 from Equation 1, we eliminate the x term:

25x + 10y - (25x + 25y) = 830 - 1100

-15y = -270

Dividing both sides by -15, we get:

y = (-270)/(-15) = 18

Substituting the value of y back into Equation 2, we can find x:

x + 18 = 44

x = 44 - 18 = 26

Therefore, Tanya has 26 quarters and 18 dimes.

Learn more about system of equations click;

brainly.com/question/21620502

#SPJ2

Suppose Tanya has d dimes worth 10d cents and (44-d) quarters worth 25(44-d)
cents. Now total value = 830 cents, ie., 10d + 25(44-d) = 830, ie., 1100 -830 = 15d, ie., d = 54/3 = 18. Therefore A has 18 dimes and 26 quarters.

Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 64x2 + 81y2 = 1. $ L=\iint_{R} {\color{red}9} \sin ({\color{red}384} x^{2} + {\color{red}486} y^{2})\,dA $.

Answers

$\displaystyle\iint_R\sin(384x^2+486y^2)\,\mathrm dA$

Notice that Given that $R$ is an ellipse, consider a conversion to polar coordinates:

$\begin{cases}x(r,\theta)=\frac r8\cos\theta\ny(r,\theta)=\frac r9\sin\theta\end{cases}$

The Jacobian for this transformation is

$J=\begin{bmatrix}\frac18\cos\theta&-\frac r8\sin\theta\n\frac19\sin\theta&\frac r9\cos t\end{bmatrix}$

with determinant $\det J=\frac r{72}$

Then the integral in polar coordinates is

$\displaystyle\frac1{72}\int_0^(\pi/2)\int_0^1\sin(6r^2\cos^2t+6r^2\sin^2t)r\,\mathrm dr\,\mathrm d\theta=\int_0^(\pi/2)\int_0^1r\sin(6r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{(\pi\sin^23)/(864)}$

where you can evaluate the remaining integral by substituting $s=6r^2$ and $\mathrm ds=12r\,\mathrm dr$ .

Final answer:

To evaluate the integral, we make a change of variables using the transformation x=u/8 and y=v/9 to transform the region into a unit circle. Then we convert the integral to polar coordinates and evaluate it.

Explanation:

To evaluate the given integral, we can make the appropriate change of variables by using the transformation x = u/8 and y = v/9. This will transform the region R into a unit circle. The determinant of the Jacobian of the transformation is 1/72, which we will use to change the differential area element from dA to du dv. Substituting the new variables and limits of integration, the integral becomes:

L = \iint_{R} 9 \sin (612 u^{2} + 768 v^{2}) \cdot (1/72) \,du \,dv

Next, we can convert the integral from Cartesian coordinates(u, v) to polar coordinates (r, \theta). The integral can be rewritten as:

L = \int_{0}^{2\pi} \int_{0}^{1} 9 \sin (612 r^{2} \cos^{2}(\theta) + 768 r^{2} \sin^{2}(\theta)) \cdot (1/72) \cdot r \,dr \,d\theta

We can then evaluate this integral to find the value of L.

Learn more about Evaluation of Integrals here:

brainly.com/question/32205191

#SPJ11

Calculate had a net income of 5 million dollars in 2010, while a small competing company, Computate, had anet income of 2 millions dollars. The management of Calculate develops a business plan for future growth
that projects an increase in net income of 0.5 million per year, while the management of Computate
develops a plan aimed at increasing its net income kshy15% each year.
a. Create standard mathematical model (table, graph, or equations) for the projected net income for the
next 10 years for both companies. Make sure that each model is accurate and labeled properly so that it
represents the situation
b. If both companies were able to meet their net income growth goals, which company would you choose
to invest in? Why?
c. When, if ever, would your projections suggest that the two companies have the same net income? How
did you find this? Will they ever have the same net income again?

Answers

9514 1404 393

Answer:

a) see the attached spreadsheet (table)

b) Calculate, for a 10-year horizon; Computate for a longer horizon.

c) Year 13; no

Step-by-step explanation:

a) The attached table shows net income projections for the two companies. Calculate's increases by 0.5 million each year; Computate's increases by 15% each year. The result is rounded to the nearest dollar.

b) After year 4, Computate's net income is increasing by more than 0.5 million per year, so its growth is faster and getting faster yet. However, in the first 10 years, Calculate's net income remains higher than that of Computate. If we presume that some percentage of net income is returned to investors, then Calculate may provide a better return on investment.

The scenario given here is only interested in the first 10 years. However, beyond that time frame (see part C), we find that Computate's income growth far exceeds that of Calculate.

c) Extending the table through year 13, we see that Computate's net income exceeds Calculate's in that year. It continues to remain higher as long as the model remains valid.

Final answer:

To create a mathematical model for the next 10 years' projected net income for Calculate and Computate, use the given growth rates. Compare the projected net incomes to decide which company to invest in. Find the year when the two companies have the same net income.

Explanation:

To create a mathematical model for the projected net income for the next 10 years for both companies, we can use equations. Let's start with Calculate:

Net Income(Calculate) = 5 + 0.5*year

For Computate, the net income growth rate is 15%, so the equation would be:

Net Income(Computate) = 2 * (1 + 0.15)^year

To compare the two companies' projected net income, we can create a table or graph using the equations. By comparing the values, we can determine which company would be a better choice for investment. To find when the two companies have the same net income, we can set the two equations equal to each other and solve for the year.

Learn more about Projected net income here:

brainly.com/question/33816331

#SPJ3

9. In City A, the temperature rises 9 from 8 A.M. to 9 A.M. Then the temperature drops 8 from 9 A.M. to 10 A.M. In City B, the temperature drops 5º from 8 A.M. to 9 A.M. Then the temperature drops 4º from 9 A.M. to 10 A.M. a. What expression represents the change in temperature for City A? b. What integer represents the change in temperature for City A? c. What expression represents the change in temperature for City B? d. What integer represents the change in temperature for City B? e. Which city has the greater change in temperature from 8 A.M. to 10 A.M.? 10.

Answers

a.The expression for temperature change in City A is 9 + (-8)

b.The amount the temperature changes for City A = 1°F

c.The expression for temperature change in City B is -1 + (-3) = -4°F

d.The amount the temperature changes for City B = -4°F

What is temperature?

The degree of hotness or coldness of an object is called as temperature.

Now it is given that,

In City A,

rise in temperature from 8 am to 9 am = 9°F

drop in temperature from 9 am to 10 am = 8°F

In City B,

drop in temperature from 8 am to 9 am = 1°F

drop in temperature from 9 am to 10 am = 3°F

a.The expression for temperature change in City A

rise in temperature = +9°F

drop in temperature = -8°F

∴the expression for change in temperature for City A = 9 + (-8)

b.The amount the temperature changes for City A = 9 + (-8)= 1°F

c.The expression for temperature change in City B

drop in temperature = -1°F

drop in temperature = -3°F

∴the expression for change in temperature for City A = -1 + (-3)

d.The amount the temperature changes for City B = -1 + (-3)= -4°F

Hence,the required answers are,

a.The expression for temperature change in City A is 9 + (-8)

b.The amount the temperature changes for City A = 1°F

c.The expression for temperature change in City B is -1 + (-3) = -4°F

d.The amount the temperature changes for City B = -4°F

More about temperature change :

brainly.com/question/18365386

#SPJ2

Point R is on line segment QS. Given RS = 2 and QS = 10, determine the length QR

Answers

Answer: QR=12

Step-by-step explanation:

10+2=12

Other Questions

if a cyclist rides at a constant rate of 24 miles per hour, how long would it take the cyclist to ride 156 miles

Graph the equation x= -7/2 by plotting points

38 = y/2. What equals y?

A 46- inch piece of steel is cut into three pieces so that the second piece is twice as long ad the first piece , and the third piece is one inch more than six times the length of the first piece. Find the lengths of the pieces.