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3 years ago

10

A lock is using 3 digits from 1 to 7 as its lock combination, the numbers can be repeated. How many different possible lock comb

inations are there?

1 answer:

Oksi-84 [34.3K]3 years ago

7 0

The question is an illustration of selection (or combination)

The number of lock combination is 343

The given parameters are:

<em /> $n = 7$ <em> --- the number of digits to select from</em>

<em /> $r = 3$ <em> --- the number of digits the lock uses</em>

<em />

Because the digits can be repeated, the number of lock combinations is:

$Lock = n^r$

So, we have:

$Lock = 7^3$

$Lock = 343$

Hence, the number of lock combination is 343

Read more about combinations at:

brainly.com/question/15301090

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

4 years ago

What is the area of this parallelogram?<br> h = 2 in.<br> A<br> b= 10 in.<br> in.<br> in²

asambeis [7]

The area of a parallelogram is 20 inches square

<h3>What is the area of a parallelogram?</h3>

The area of a parallelogram is the base of the shape multiplied by the height

Area of parallelogram = b × h

Where h = height = 2 In

base = 10 in

Area = 2 × 10

Area = 20 Inches square

Thus, the area of a parallelogram is 20 inches square

Learn more about a parallelogram here:

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2 years ago

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Check all that apply.

stealth61 [152]

The correct answer would be x>5
I hope this helps.

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4 years ago

Be sure to explain your answer<br>as clear as possible.

vekshin1

Positive exponent? An index would imply that the base, x, had a fractional exponent.

My Dear Aunt Sally used to say, "If there's a negative exponent in your face, then flip your base!"

In other words, if the exponent is negative, take the reciprocal of the base, x → $\frac{1}{x}$ and change the exponent to positive.

Therefore: $x^{-3} = \frac{1}{x^3}$

I have cross the fraction bar line change the exponent sign.

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4 years ago

Combine Like Terms 4a + 7a

slamgirl [31]

4a+7a= 11a
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3 years ago

Read 2 more answers