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yan [13]
3 years ago
12

Problem 3.2.14a Show that 2^2x+1 +1 is divisible by 3.

Mathematics
1 answer:
elena-s [515]3 years ago
4 0

Answer:

The given expression is divisible by 3 for all natural values of x.

Step-by-step explanation:

The given expression is

2^{2x+1}+1

For x=1,

2^{2(1)+1}+1=2^{3}+18+1=9

9 is divisible by 3. So, the given statement is true for x=1.

Assumed that the given statement is true for n=k.

2^{2k+1}+1

This expression is divisible by 3. So,

2^{2k+1}+1=3n              .... (1)

For x=k+1

2^{2(k+1)+1}+1

2^{2k+2+1}+1

2^{(2k+1)+2}+1

2^{2k+1}2^2+1

Using equation (1), we get

(3n-1)2^2+1

(3n)2^2-2^2+1

(3n)2^2-4+1

(3n)4-3

3(4n-1)

This expression is also divisible by 3.

Therefore the given expression is divisible by 3 for all natural values of x.

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Prove this trigonometric equation;<br><br> - tan^2x + sec^2x = 1,
alekssr [168]
Hey there :)

- tan²x + sec²x = 1    or    1 + tan²x = sec²x

sin²x + cos²x = 1 
Divide the whole by cos²x

\frac{sin^2x}{cos^2x} + \frac{cos^2x}{cos^2x} = \frac{1}{cos^2x}

\frac{sinx}{cosx} = tanx so \frac{sin^2x}{cos^2x} = tan^2x
and
\frac{1}{cosx} = secx so \frac{1}{cos^2x} = sec^2x

Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}

1 = - tan²x = sec²x or sec²x - tanx = 1

3 0
3 years ago
Factor f(x) = 4x3 + 15x2 – 24x + 5 into linear factors given that - 5 is a zero of f(x).15f(x) = 4x3 + 15x2 - 24x + 5 =(Factor c
Basile [38]

If x=-5 is a zero, then the first factor of the polynomial would be (x + 5 )

To find the other two factors we can divide the polynomial by the expression (x+5).

Using synthetic division, we have:

-5 I 4 15 -24 5 (Coefficients of the dividend)

I -20 25 -5 (Multiplying each coefficient by the results of the substraction and adding)

-----------------------------------------------------------------------------------

4 -5 1 0 (Coefficients of the quotient)

The result of the division is 4x^2 - 5x + 1. Factoring it, we have:

4x^2 - 4x -x + 1 (Separating -5x into -x and -4x)

4x (x - 1) - (x -1) (Factoring each pair of terms)

(x-1)(4x-1) (Factoring using the common factor)

So the answer would be:

(x + 5 )(x-1)(4x-1)

3 0
1 year ago
If M9=119,what is the sum of the measures 0f 11 and 16?
mote1985 [20]
The answer is:  " 132° " .
____________________________________
Note:  m∠9 = m∠11 = m ∠16 ;

So;   m∠11 + m∠16  = 132 .
____________________________________
7 0
3 years ago
1258 rounded to the nearest thousands
GarryVolchara [31]
The answer to your problem is 1300.
5 0
3 years ago
Read 2 more answers
Sharma is building a shed and wants to determine the measurements for the roof. The span of the roof will be 10 feet and she pla
Stolb23 [73]

Answer:

In the figure below :

d = 2.08, e = 5, c = 5.42 , a = 22.78°, b = 67.22°

Step-by-step explanation:

Side lengths :

2\cdot e=10\\ \Rightarrow e=5 feet\\\frac{d}{e}=\frac{5}{12}\\\Rightarrow d=\frac{25}{12}\approx 2.08 feet

By pythagoras theorem,

c^2=d^2+e^2\\c^2=29.33\\c\approx 5.42 feet

Now to find angles,

a+b+90^{\circ}=180^{\circ}\\\Rightarrow a+b=90^{\circ}\\\tan a=\frac{d}{e}\\\Rightarrow \tan a =0.42\\\Rightarrow a=22.78^{\circ}\\\Rightarrow b=67.22^{\circ}



5 0
3 years ago
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