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Ksivusya [100]
2 years ago
8

Please help urgently extra points and mark brainlist

Mathematics
1 answer:
Sergeeva-Olga [200]2 years ago
3 0

Answer:

B. -3.5 and +3.5

Step-by-step explanation:

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[tex]cos {}^{4} α+sin {}^{4} α= \frac{1}{4} (3+cos4α)<br>Prove:<br>​
asambeis [7]

Given:

\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)

To prove:

The given statement.

Proof:

We have,

\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)

LHS=\cos^4 \alpha+\sin^4\alpha

LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2

LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha     [\because a^2+b^2=(a+b)^2-2ab]

LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha      [\because \cos^2 \alpha+\sin^2\alpha=1]

LHS=1-2\cos^2 \alpha+2\cos^4 \alpha

Now,

RHS=\dfrac{1}{4}(3+\cos 4 \alpha)

RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)]        [\because \cos 2\theta=2\cos^2\theta -1]

RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha]

RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2]        [\because \cos 2\theta=2\cos^2\theta -1]

RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)]        [\because (a-b)^2=a^2-2ab+b^2]

RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2]

RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha]

RHS=1+2\cos^4 \alpha-2\cos \alpha

RHS=1-2\cos^2 \alpha+2\cos^4 \alpha

LHS=RHS

Hence proved.

8 0
3 years ago
Use the distributive property two different ways to find the product of 127 and 32
cricket20 [7]
127 = 100 +27
32 = 30 +2
so 127 x 32 = (100 + 27) x (30+2) = (100x30) + (100x2) + (27x30) +(27x2)
= 3000+200+810+54 = 4064

second way:

127 = 100 + 27
127 x 32 = (100+27) x 32 = (100x 32) + ( 27x32) = 3200 + 864 = 4064
5 0
3 years ago
George drives at 45mi/h. write two expressions for the number of miles George travels in h hours
GaryK [48]

45h=miles in h hours

7 0
3 years ago
Read 2 more answers
If thewronskian w of f and g is 3e4t,and if f(t) = e2t,find g(t).
ehidna [41]
W(f(x),g(x))=\begin{vmatrix}f(x)&g(x)\\f'(x)&g'(x)\end{vmatrix}=f(x)g'(x)-g(x)f'(x)

We have f(t)=e^{2t}\implies f'(t)=2e^{2t}, so

W(f(t),g(t))=e^{2t}g'(t)-2e^{2t}g(t)=3e^{4t}
\implies e^{-2t}g'(t)-2e^{-2t}g(t)=3
\implies\dfrac{\mathrm d}{\mathrm dt}[e^{-2t}g(t)]=3
\implies e^{-2t}g(t)=\displaystyle\int3\,\mathrm dt
\implies e^{-2t}g(t)=3t+C
\implies g(t)=3te^{2t}+Ce^{2t}

where C is any arbitrary constant.
8 0
3 years ago
Mike spent half of his allowance going to the movies.He washed the family car and earned 9 dollars.What is his weekly allowance
Bezzdna [24]

Answer:

18

Step-by-step explanation:

If he spends half his money then washes the family car and he ends up with 18 dollars that means he spent 9 witch is half of 18 and he adds 9 more dollars which is why his allowance is 18 dollars

7 0
3 years ago
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