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2 years ago

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What is 17/20 - 4/15

1 answer:

Zinaida [17]2 years ago

4 0

Hello there, today you gave us the problem $\frac{17}{20}-\frac{4}{15}$ ,

Our first step is to give them common denominators, which is $\frac{51}{60}-\frac{16}{60}$ , solve it and we get $\frac{35}{60}$ as our answer, which can be simplified down to $\frac{7}{12}$

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Which pair of monomials has the least common multiple (LCM) of 54x2y3?

Lera25 [3.4K]

ANSWER

The correct answer is D.

EXPLANATION

If we express the monomial,

$18 {x}^{2} y$

as product of primes, we obtain:

$2 \times {3}^{2} \times {x}^{2}y$

If we express the monomial

$27x {y}^{3}$

as product of primes we obtain:

$= {3}^{3} \times x {y}^{3}$

The least common multiple of these two binomials is the product of the highest powers of the common factors.

The LCM is

$= 2 \times {3}^{3} \times {x}^{2} {y}^{3}$

$=54 {x}^{2} {y}^{3}$

Therefore the correct answer is D.

6 0

3 years ago

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I need help on a equation −4a5⋅6a5

Pavel [41]

I don’t understand the equation but you can use Photomath to solve any equation you need to solve. It’s and app for free.

7 0

3 years ago

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

3 0

3 years ago

How does the length of the diameter of a circle relate to the length of the radius of that same circle

djyliett [7]

The diameter is twice as big as the radius

7 0

3 years ago

What is the pattern and the 2 next numbers of 7, 14, 8, 16, 10, 20, 14,

Norma-Jean [14]

Answer:

Next 2 numbers are 28,22

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers