1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nataly [62]
3 years ago
15

Evaluating more integrals

Mathematics
1 answer:
Greeley [361]3 years ago
4 0

(a) The integral is equal to the area of the triangle; it has height 20 and base 10, so the area is 20*10/2 = 100.

(b) The integral is equal to the area of the semicircle with radius 10. It's also under the horizontal axis, so the area is negative. The semicircle has area \frac{\pi10^2}2=50\pi, so the integral is -50π.

(c) First compute

\displaystyle\int_{30}^{35}g(x)\,\mathrm dx

which is the area of the triangle on the right. It has height and base 5, so its area is 25/2.

Then split up the desired integral as

\displaystyle\int_0^{35}g(x)\,\mathrm dx=\int_0^{10}g(x)\,\mathrm dx+\int_{10}^{30}g(x)\,\mathrm dx+\int_{30}^{35}g(x)\,\mathrm dx

and plug in the integral values you know:

\displaystyle\int_0^{35}g(x)\,\mathrm dx=100-50\pi+\frac{25}2=\frac{225}2-50\pi

You might be interested in
Matt is saving to buy a new motorcycle. If he deposits $70 at the end of each month in an account that pays an annual interest r
satela [25.4K]
You will have $1118.25 in 15 mouth
6 0
3 years ago
The post office will accept packages whose combined length and girth is at most 42 inches. (the girth is the perimeter/distance
Vilka [71]
If x represents the length of the box, then 42-x will be the girth. Since the largest area for a given girth is that of a square, the side length of the square cross section is (42 -x)/4.

The volume as a function of package length is then
.. v(x) = x((42-x)/4)^2
This has a maximum at x=14. The corresponding volume is 686 in^3.

8 0
4 years ago
Help with Math PLZ (Questions in screenshot)
-Dominant- [34]

1.) Let's say that the circle on the graph below represents x. The arrow is pointing to all the numbers greater than x, which happens to be on -2. If it points right, this means that x can equal to any number greater than -2. So your answer is x > -2.

2.) For inequalities such as these, you can simplify just like what you do for normal equations. Let's isolate x.

x - 7 > 10

--> x > 10 + 7

---> x > 17

3.) 3x \leq 21

--> \frac{3x}{3} \leq  \frac{21}{3}

---> x \leq 7

4.) 5a - 2 < 18

--> 5a < 18 + 2

---> 5a < 20

----> \frac{5a}{5} < \frac{20}{5}

-----> a < 4

5.) 2t + 8 \geq -4(t + 1)

--> 2t + 8 \geq -4t - 4

---> 2t + 4t \geq -8 - 4

----> 6t \geq -12

-----> t \geq -2

7 0
3 years ago
Kyle is buying turkey from the deli. If turkey cost 8.50 per kilogram and he wants 3 kilograms how much will he spend on the tur
Artemon [7]

Answer:

The answer is 25.50

Hope this helps!

6 0
3 years ago
How do you solve and simplify
DedPeter [7]
F(x) = 1/(x+2)   & g(x) = x/(x-3)


(f(x) + g(x) = 1/(x+2) + x/(x-3). Reduce to same denominator:

1/(x+2) + x/(x-3) =(x-3) + x(x-3)/(x+2).(x-3) ==> (x²+3x-3)/(x+2).(x-3)

7 0
3 years ago
Other questions:
  • What is the minimum number of 7 passenger vans needed to transport 19 people? 12 6 4 3
    13·2 answers
  • This one from maths pls help
    9·1 answer
  • Sana is playing basketball.After she took 20 shots,she got in 55% of those shots.After she took 5 shots,the overall percentage o
    7·2 answers
  • How do you solve this problem?
    5·2 answers
  • What type of transformations occurred to Triangle ABC?
    8·2 answers
  • Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other s
    14·1 answer
  • Suppose the quantity demanded weekly of the Super Titan radial tires is related to its unit price by the equation p + x2 = 225 w
    9·1 answer
  • How do you solve for range because i’m so confused lol
    11·1 answer
  • Find the area of a polygon and show step by step explanation pls
    9·1 answer
  • I = [(x + cos2x = )<br>dx​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!