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Nina [5.8K]
3 years ago
12

Help.... .................​

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
5 0
You would set them equal to each other and solve for x, because alternate exterior angles are always congruent. hope this helps!
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A father is 32 years older than his son. In four years,
sergiy2304 [10]

Answer:

  • father: 36
  • son: 4

Step-by-step explanation:

Let s represent the son's age now. Then s+32 is the father's age. In 4 years, we have ...

  5(s+4) = (s+32)+4

  5s +20 = s +36 . . . . . eliminate parentheses

  4s = 16 . . . . . . . . . . . . subtract s+20

  s = 4

The son is now 4 years old; the father, 36.

_____

<em>Alternate solution</em>

In 4 years, the ratio of ages is ...

  father : son = 5 : 1

The difference of their ages at that time is 5-1 = 4 "ratio units". Since the difference in ages is 32 years, each ratio unit must stand for 32/4 = 8 years. That is, the future age ratio is ...

  father : son = 40 : 8

So, now (4 years earlier), the ages must be ...

  father: 36; son: 4.

5 0
3 years ago
Find a power series representation of e^x sin(x)
liberstina [14]
The Taylor series is defined by:
f(x) = \sum \frac{f^n (a)}{n!} (x-a)^n

Let a = 0.
Then its just a matter of finding derivatives and determining how many terms is needed for the series.

Derivatives can be found using product rule:
f^n (x) = e^x g^{n-1} (x) + e^x g^n (x)  \\ g^0 (x) = sin x

Do this successively to n = 6.
f^1 (x) = e^x (sinx +cos x) \\ f^2 (x) = e^x (2cos x)  \\ f^3 (x) = e^x(2cos x - 2sin x)  \\ f^4 (x) = e^x (-4 sin x)  \\ f^5 (x) = e^x(-4sinx -4cos x) \\ f^6(x) = e^x(-8cos x)

Plug in x=0 and sub into taylor series:
e^x  sin x = x+x^2 +\frac{x^3}{3} -\frac{x^5}{30}-\frac{x^6}{90}...

If more terms are needed simply continue the recursive derivative formula and add to taylor series.
6 0
3 years ago
Which value completes the table?
larisa [96]
-17 -35
-3 -3
-2 0
-31 -87
17 57
7 0
4 years ago
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Solve for x<br><br> 2(x+5)-7=3(x-2)
andriy [413]

x=9

I'm sorry if I'm wrong

5 0
3 years ago
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The cooking club made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed tw
Neko [114]

Answer:

10

Step-by-step explanation:

Each pie was cut into 6 pieces. 6 x 10= 60.

3 0
3 years ago
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