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babymother [125]
3 years ago
11

Can somebody answer this question for me?

Mathematics
1 answer:
xxMikexx [17]3 years ago
3 0
The opposite inner angles equal the outer one
(3x+5) = 2x + 30
x = 25

(3*25)+5
TSQ = 80 
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How do you determine the area under a curve in calculus using integrals or the limit definition of integrals?
RSB [31]

Answer:

Please check the explanation.

Step-by-step explanation:

Let us consider

y = f(x)

To find the area under the curve y = f(x) between x = a and x = b, all we need is to integrate y = f(x) between the limits of a and b.

For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:

A=\int _a^b|f\left(x\right)|dx

    = \int _{-2}^2\left|x^2-4\right|dx

\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx

   =\int _{-2}^2x^2dx-\int _{-2}^24dx

solving

\int _{-2}^2x^2dx

\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1

   =\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}

    =\left[\frac{x^3}{3}\right]^2_{-2}

computing the boundaries

     =\frac{16}{3}

Thus,

\int _{-2}^2x^2dx=\frac{16}{3}

similarly solving

\int _{-2}^24dx

\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax

     =\left[4x\right]^2_{-2}

computing the boundaries

      =16

Thus,

\int _{-2}^24dx=16

Therefore, the expression becomes

A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx

  =\frac{16}{3}-16

  =-\frac{32}{3}

  =-10.67 square units

Thus, the area under a curve is -10.67 square units

The area is negative because it is below the x-axis. Please check the attached figure.

   

6 0
3 years ago
Find the indicated side of the<br> triangle.<br> 7<br> 30°<br> b<br> a = [?]
nirvana33 [79]

Answer:

14

Step-by-step explanation:

you have opposite but need to find hypotenuse so you use SOH (sine=opposite/hypotenuse)

so sin(30)= 7/a

7/sin(30)=14

Hope its right

5 0
3 years ago
Teo has a combination of quarters, loonies, and toonies in his pocket.
finlep [7]

Answer:

343

Step-by-step explanation:

There are quarters(25¢), loonies ($1), and toonies ($2)

And total number of coins is 9

If loonies ($1), and toonies ($2) are one, then quarters(25¢) is 7

If quarters(25¢), and toonies ($2) are one, then loonies ($1)is 7

If loonies ($1), and quarters(25¢) are one, then toonies ($2) is 7

So possible number number of combination for an item that cost between $10 and $12 is

= 1^3 * 1^3 * 7^3

= 343

hope this helps, stay safe :)

3 0
3 years ago
The temperature was -2F. Dropped 9F. What is the temperature after it dropped 9F
xz_007 [3.2K]
-11 degrees F I hope this helps
8 0
3 years ago
Read 2 more answers
What is 3 9/10 times -8/3
Triss [41]

Answer:

-52 / 5

Step-by-step explanation:

3 9/10 * -8 / 3 = 39 / 10 * -8 / 3 = -52 / 5

8 0
3 years ago
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