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LuckyWell [14K]
3 years ago
13

Can you answer the second question please

Mathematics
1 answer:
Marianna [84]3 years ago
4 0
The answer to this question will be B
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Evaluate the definite integral using the graph of f(x)<br> (Image included)
Tanya [424]

a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is

\displaystyle \int_0^3 f(x) \, dx = \frac12 \times 3 \times 5 = \boxed{\frac{15}2}

b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so

\displaystyle \int_3^5 f(x) \, dx = \int_3^4 f(x) \, dx + \int_4^5 f(x) \, dx = \int_3^4 f(x) \, dx - \int_3^4 f(x) \, dx = \boxed{0}

c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so

\displaystyle \int_5^9 f(x) \, dx = -4\times5 = -20

Then by linearity, we have

\displaystyle \int_0^9 f(x) \, dx = \left\{\int_0^3 + \int_3^5 + \int_5^9\right\} f(x) \, dx = \frac{15}2 + 0 - 20 = \boxed{-\frac{25}2}

8 0
2 years ago
1)-5.5 - 11.2 =<br> on<br> a.) 5.7<br> b.)-5.7<br> c.) 16.7<br> d.) -16.7
Bingel [31]

Answer:

C

Step-by-step explanation:

-5.5-11.2

change the subtraction to addition

5.5+11.2= 16.7

6 0
2 years ago
Read 2 more answers
Sophia wants to take out a loan of $6,000 with interest that compounds monthly. Use the formula A = P(1 + rn)n∗t to find which o
Naddika [18.5K]

Answer:

d

Step-by-step explanation:

FV = P (1 + r/m)^mn

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

m = number of compounding

a. 6000x (1 + 0.04/12)^24 = 6498.86

b. . 6000x (1 + 0.03/12)^36 =6564.31

c. . 6000x (1 + 0.01/12)^48 = 6244.76

d. . 6000x (1 + 0.05/12)^60 =6630.47

4 0
2 years ago
Math Help
-Dominant- [34]
X=1, because they both have the same height (y), so they'll cross each other!
4 0
3 years ago
Easy 20 points please tell me if I got it right and if not please tell me the right answer
mash [69]

Answer:

No, you are not correct.

It should look like this:

                              Prefer colorful decorations      Prefer neutral decorations

Pay attention                           20                                                  25

to fashion

Do not pay

attention to                              72                                                      33

fashion

Step-by-step explanation:

33 is 22% of 150. In the question it states that 70% of people do not pay attention to fashion. We need to find the other 48% here. In order to do that we multiply .48 by 150. That gets us 72. To check that answer you can add both 72 and 33 and then divide by 150, which gets 70%.

To get the amount of people that prefer neutral decorations and pay attention to fashion we need to add up 20 + 72 + 33 and that equals 125. Next, we take 150 and minus 125 of it to get 25.

<em>Hope this helps!!</em>

<em>- Kay :)</em>

3 0
2 years ago
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