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3 years ago

How do you solve this problem ?

Mathematics

2 answers:

SVEN [57.7K]3 years ago

7 0

9514 1404 393

Answer:

$2\cdot y^{\frac{5}{8}}$

Step-by-step explanation:

The applicable rules of exponents are ...

$(a^b)^c=a^{bc}\\\\(ab)^c=a^c\cdot b^c\\\\\sqrt[n]{x^m}=x^{\frac{m}{n}}$

So, the given expression can be rewritten to ...

$(4\sqrt[4]{y^5})^{\frac{1}{2}}=(4^{\frac{1}{2}})(y^{\frac{5}{4}})^{\frac{1}{2}}= 2\cdot y^{\frac{5}{4}\cdot\frac{1}{2}}=\boxed{2\cdot y^{\frac{5}{8}}}$

_____

k = 2; n = 5/8

svetlana [45]3 years ago

3 0

Answer: 2y124√y12

How to: <u>Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.</u>

Have a great day and stay safe !

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To the nearest degree what is the measure of each exterior angle of a regular hexagon ?

otez555 [7]

This is the concept of geometry, the total sum of angles in a hexagon is given by:
(n-2)*180
=(6-2)*180
=720
the size of each interior angle will be:
120°
N/B
the exterior and interior angles are supplementary to each other.
Therefore the size of the exterior angle will be:
180-120
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the answer is A

3 0

3 years ago

Read 2 more answers

2(x-3)=2x-6 is an example of which property

Jlenok [28]

2(x-3)=2x-6 This is distributive property.

2(x-3)= 2x - 2*3 = 2x-6

7 0

3 years ago

A street light is at the top of a 25 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 6

Burka [1]

Answer:

Tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

Step-by-step explanation:

Given : In the figure attached, Length of girl EC = 4 ft

Length of street light AB = 25 ft

Girl is moving away from the light with a speed = 6 ft per sec.

To Find : Rate ( $\frac{dw}{dt}$ ) of the tip (D) of the girl's shadow (BD) moving away from th

light.

Solution : Let the distance of the girl from the street light is = x feet

Length of the shadow CD is = y feet

Therefore, $\frac{dx}{dt}=6$ feet per sec. [Given]

In the figure attached, ΔAFE and ΔADE are similar.

By the property of similar triangles,

$\frac{x}{21}=\frac{x+y}{25}$

25x = 21(x + y)

25x = 21x + 21y

25x - 21x = 21y

4x = 21y

y = $\frac{4x}{21}$

Now we take the derivative on both the sides,

$\frac{dy}{dt}=\frac{4}{21}\times \frac{dx}{dt}$

= $\frac{4}{21}\times 6$

= $\frac{8}{7}$

≈ 1.14 ft per sec.

Since w = x + y

Therefore, $\frac{dw}{dt}= \frac{dx}{dt}+\frac{dy}{dt}$

$\frac{dw}{dt}=6+1.14$

= 7.14 ft per sec.

Therefore, tip of the shadow of the girl is moving with a rate of 7.14 feet per sec.

3 0

3 years ago

Please help me <br> Show your work <br> 10 points

Svet_ta [14]

<h2>Answer</h2>

After the dilation $\frac{5}{3}$ around the center of dilation (2, -2), our triangle will have coordinates:

$R'=(2,3)$

$S'=(2,-2)$

$T'=(-3,-2)$

<h2>Explanation</h2>

First, we are going to translate the center of dilation to the origin. Since the center of dilation is (2, -2) we need to move two units to the left (-2) and two units up (2) to get to the origin. Therefore, our first partial rule will be:

$(x,y)$ → $(x-2, y+2)$

Next, we are going to perform our dilation, so we are going to multiply our resulting point by the dilation factor $\frac{5}{3}$ . Therefore our second partial rule will be:

$(x,y)$ → $\frac{5}{3} (x-2,y+2)$

$(x,y)$ → $(\frac{5}{3} x-\frac{10}{3} ,\frac{5}{3} y+\frac{10}{3} )$

Now, the only thing left to create our actual rule is going back from the origin to the original center of dilation, so we need to move two units to the right (2) and two units down (-2)

$(x,y)$ → $(\frac{5}{3} x-\frac{10}{3}+2,\frac{5}{3} y+\frac{10}{3}-2)$