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3 years ago

Find the simplified form of (t^4/10y^4)^-4

1 answer:

5 0

The answer is [(10,000*y^16)/t^16]. At first, you have to distribute the exponent -4 to the numerator and denominator by virtue of the law of exponent, (a/b)^n = [(a^n)/(b^n)]. After distribution, you get (t^-16)/[(10^-4)*(y^-16)]. To simplify the negative exponent, follow the law of exponent: a^-m = 1/a^m. Thus, you now have [(10^4)*(y^16)]/(t^16). Hence, the answer is [(10,000*y^16)/t^16].

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Show why the limit as x approaches 0 (csc(x)-cot(x)) involves an indeterminate form, and then prove that the limit equals 0.

Nadusha1986 [10]

Answer with Step-by-step explanation:

We are given that $\lim_{x\rightarrow 0 }(csc(x)-cot(x))$

We have to prove that why the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form and prove that the limit equals to 0.

$\lim_{x\rightarrow 0 }(\frac{1}{sinx}-\frac{cosx}{sinx})$

Because $csc(x)=\frac{1}{sinx}$ and $cot(x)=\frac{cosx}{sinx}$

$\lim_{x\rightarrow 0 }(\frac{1-cosx}{sinx})$

$\frac{1-cos0}{sin0}$

We know that cos 0=1 and sin 0=0

Substitute the values then we get

$\frac{1-1}{0}=\frac{0}{0}$

We know that $\frac{0}{0}$ is indeterminate form

Hence, the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form.

L'hospital rule:Apply this rule and differentiate numerator and denominator separately when after applying $\lim_{x\rightarrow a }$ we get indeterminate form $\frac{0}{0}$

Now,using L' hospital rule

$\lim_{x\rightarrow 0 }\frac{0+sinx}{cosx}$

because $\frac{dsinx}{dx}=cosx,\frac{dcosx}{dx}=-sinx}$

Now, we get

$\lim_{x\rightarrow 0 }\frac{sinx}{cos x}$

$\frac{sin0}{cos0}$

$\frac{0}{1}=0$

Hence, $\lim_{x\rightarrow 0 }(csc(x)-cot(x))=0$

5 0

2 years ago

Determine whether the ordered pair (6, 1) satisfies the equation y = 10 - 4x

Viktor [21]

Plug in the point
1 = 10 - 4(6)
1 = 10 - 24
1 = -14, false
Solution: B

4 0

3 years ago

PLS ANSWER ASAP THANKS TO YOU!

grandymaker [24]

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

in a round robin tennis tournament involving 7 players, each player will play every other player twice. How many total matches w

baherus [9]

Total number of ways to make a pair:

The first player can be any one of 7 . For each of those . . .
The opponent can be any one of the remaining 6 .

Total ways to make a pair = 7 x 6 = 42 ways .

BUT ... every pair can be made in two ways ... A vs B or B vs A .
So 42 'ways' make only (42/2) = 21 different pairs.

If every pair plays 2 matches, then (21 x 2) = 42 total matches will be played.

Now, is that an elegant solution or what !

8 0

3 years ago

Matt buys 9 cookies, and of them are chocolate chip. How many chocolate chip cookies did he buy? A .3 cookies B. 6 cookies C.8 c

inessss [21]

Answer:

B. 6 cookies

Step-by-step explanation:

Given :

9 cookies
2/3 of them are chocolate chip

Number of chocolate chip

Total x fraction of chocolate chip
9 x 2/3
3 x 2
6 cookies

8 0

1 year ago

Read 2 more answers