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3 years ago

What is the integral of ∫4x^2 dx

Mathematics

2 answers:

dedylja [7]3 years ago

7 0

the aswers is 4/3 x³ + c

okey fine

Nataly_w [17]3 years ago

5 0

Answer:

$\boxed{\frac{4}{3} x^3 + c}$

Step-by-step explanation:

$\int\limits {4x^2} \ dx$

$= \frac{4}{3} x^3 + c$

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A salesperson earns $8 per hour plus 6% commission on her sales. In a week when she worked 40 hours, her total earnings were $69

mash [69]

Answer:

372

Step-by-step explanation:

8x40=320

692-320=372

5 0

3 years ago

. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$

So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

8 0

3 years ago

The Coolmathz family is ordering pizza. They order two pizzas. One is $15, and the other is $12. They use a coupon for 5% off th

DaniilM [7]

Answer:

30.51$

Step-by-step explanation:

15+12=27$

5% of 27$=1.35$

18% of 27=4.86

Do the math: 27+4.86-1.35=30.51

6 0

2 years ago

A. imagine that you are one of the people who left the luncheon with a contagious disease and interacted with an average of 9 di

shusha [124]

1. In line with the test each person who came into interaction with the infected person will become infected also. With this information, the calculation would be: 9 people each day for 7days would be equivalent to 9 x 7 which equals 63 people.

2. Here were 7 other people in the experiment if patient zero is left out. If each person intermingled with 6 different people every day in 7 days then the calculation would be: 7 people infected x 6 new people = 42 infected people each day

42 new people every day x 7 days = 294 infected persons.

8 0

3 years ago

Is the graph a linear function , nonlinear , function , or relation

Irina-Kira [14]

It is a linear function , Option A is the right answer.

The missing graph is attached with the image

<h3>What is a Linear Function ?</h3>

A linear function is a function that can be represented by the equation

y = mx +c

where m is the slope and the c is the intercept on y axis.

From the graph it can be seen that it is following a straight line pattern and therefore it can be represented by y = mx +c and

Therefore it is a linear function , Option A is the right answer.

To know more about Linear Function

brainly.com/question/21107621

#SPJ1

6 0

2 years ago