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andrew11 [14]
3 years ago
10

Consider these functions:

Mathematics
2 answers:
IgorLugansk [536]3 years ago
8 0

Answer:

The value of f(g(-2)) is 12.

Step-by-step explanation:

We'll start by solving g(-2):

g(-2)\\= (-2)^2 + 2\\= 4 + 2\\= 6

Now we can take that value and plug it into function f:

f(6)\\= \frac{-1}{2}6^2 + 5 * 6\\= -36/2 + 30\\= -18 + 30\\= 12

Alternatively, you can work out a new single function that in itself describes f(g())

f(g(x)) = -\frac{1}{2}g(x)^2 + 5g(x)\\= -\frac{1}{2}(x^2 + 2)^2 + 5(x^2 + 2)\\= -\frac{1}{2}(x^4 + 4x^2 + 4) + 5x^2 + 10\\= -\frac{1}{2}x^4 - 2x^2 - 2 + 5x^2 + 10\\= -\frac{x^4}{2} + 3x^2 + 8

and try plugging -2 into the new function

= - \frac{-2^4}{2} + 3(-2)^2 + 8\\= -16 / 2 + 3 * 4 + 8\\= -8 + 12 + 8\\= 12

rusak2 [61]3 years ago
8 0

Answer:

The answer is 12

Step-by-step explanation:

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Question in picture
Norma-Jean [14]

Answer:

63 yd²

Step-by-step explanation:

The area (A) of a trapezoid is calculated as

A = \frac{1}{2} h (a + b)

where a and b are the parallel bases and h the perpendicular height.

Here a = 8, b = 10 and h = 7, thus

A = 0.5 × 7 × (8 + 10) = 0.5 × 7 × 18 = 63 yd²

6 0
3 years ago
Cos(a) 63/65 to find sin(a) and tan(a)
Semenov [28]

Answer:

\huge\boxed{\sin\alpha=-\dfrac{16}{65},\ \tan\alpha=-\dfrac{16}{63}}\\\\or\\\\\huge\boxed{\sin\alpha=\dfrac{16}{65},\ \tan\alpha=\dfrac{16}{63}}

Step-by-step explanation:

\cos\alpha=\dfrac{63}{65}\\\\\text{use}\ \sin^2\alpha+\cos^2\alpha=1\\\\\sin^2\alpha+\left(\dfrac{63}{65}\right)^2=1\\\\\sin^2\alpha+\dfrac{3969}{4225}=1\qquad\text{subtract}\ \dfrac{3969}{4225}\ \text{from both sides}\\\\\sin^2\alpha=\dfrac{4225}{4225}-\dfrac{3969}{4225}\\\\\sin^2\alpha=\dfrac{256}{4225}\to\sin\alpha=\pm\sqrt{\dfrac{256}{4225}}\\\\\sin\alpha=\pm\dfrac{\sqrt{256}}{\sqrt{4225}}\\\\\sin\alpha=\pm\dfrac{16}{65}

\text{use}\ \tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}\\\\\text{substitute:}\\\\\tan\alpha=\dfrac{\pm\frac{16}{65}}{\frac{63}{65}}=\pm\dfrac{16}{65}\cdot\dfrac{65}{63}=\pm\dfrac{16}{63}

3 0
4 years ago
Read 2 more answers
Function f(z)=2z-(3+i)
Archy [21]
F(z) = 2z - (3+i)

1) second interate for z0 = i

first iterate = f(z0) = f(i) = 2i - 3 - i = i - 3 = z1
second iterate = f(z1) = f(i-3) = 2(i-3) - 3 - i = 2i - 6 - 3 - i = i - 9

2) third iterate for z0= 3 - i

first iterate = f(z0) = f(3 - i) = 2(3-i) - (3+i) = 6 -2i -3 - i =3 - 3i = z1
second iterate = f(z1) = f(3 -3i) = 2(3-3i) - (3+i) = 6 - 6i -3 -i = 3 - 7i = z2
third iterate = f(z2) = f(3 - 7i) = 2 (3-7i) - (3+i) = 6 - 14i - 3 - i = 3 -15i = z3.

3) first iterate for z0=0.5+i

first iterate = f(z0) = f(0.5 +i) = 2(0.5+i) - (3+i) = 1 +2i - 3 - i = - 2 + i = z1

4) third iterate for z0=-2-5i

first iterate = f(z0) = 2(- 2 - 5i) - (3 + i) = - 4 - 10i - 3 - i = -7 - 11i = z1
second iterate = f(z1) = 2( - 7 - 11i) - (3+i) = -14 - 22i - 3 - i = -17 -23i = z2
third iterate = f(z2) = 2(-17-23i) -(3+i) = -34 - 46i -3 - i = -37 - 47i = z3
8 0
3 years ago
1/2x-3/10=5/2x+7/10
Alexus [3.1K]

Answer:

-Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x= -1/2

Decimal Form:

x=0.5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

3 0
3 years ago
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AfilCa [17]

Answer:

$93000

Step-by-step explanation:

5 0
3 years ago
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