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3 years ago

Properties of exponents Rewrite the expression in the form b^n—— (b^2)^3/7

Mathematics

1 answer:

exis [7]3 years ago

3 0

Answer:

$b^{\frac{6}{7}}$ is the required expression.

Step-by-step explanation:

$(b^2)^{\frac{3}{7}}\\\\\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\\\\=b^{2\cdot \frac{3}{7}}\\\\=b^{\frac{6}{7}}$

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Good Stuff is giving away free pens to each of the first 200 people who come in the store today. In the first hour, they gave aw

AnnyKZ [126]

Answer:

50 pens

Step-by-step explanation:

x= 25 percent of 200

25/100 times X/200

Cross multiply them and you get

100x=5000

X=5000/100

X=50

25 percent of 200 is 50.

Which means they have away 50 pens

7 0

3 years ago

Read 2 more answers

) The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters from the center of the slick

Feliz [49]

Answer:

Therefore the mass of the of the oil is 409.59 kg.

Step-by-step explanation:

Let us consider a circular disk. The inner radius of the disk be r and the outer diameter of the disk be (r+Δr).

The area of the disk

=The area of the outer circle - The area of the inner circle

= $\pi (r+\triangle r)^2- \pi r^2$

$=\pi [r^2+2r\triangle r+(\triangle r)^2-r^2]$

$=\pi [2r\triangle r+(\triangle r)^2]$

Since (Δr)² is very small, So it is ignorable.

∴ $A=2\pi r\triangle r$

The density $\delta (r)= \frac{40}{1+r^2}$

We know,

Mass= Area× density

$=(2r \pi \triangle r)(\frac{40}{1+r^2}})$

Total mass $M=\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i$

Therefore

$\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i=\int_0^5 \frac{80r\pi }{1+r^2}dr$

$=40\pi[ln(1+r^2)]_0^5$

$=40\pi [ln(1+5^2)-ln(1+0^2)]$

$=40\pi ln(26)$

= 409.59 kg (approx)

Therefore the mass of the of the oil is 409.59 kg.

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2 years ago

Edward deposited $10,000 into a savings account 2 years ago. The simple interest rate is 4%. How much money did Edward earn in

Allisa [31]

Answer: 10400

Step-by-step explanation:

4 0

3 years ago

prakriti needs $3500 for high study in america after see.if $1=105Nrp if bank charge 3% commission how much nepali rupee should

timofeeve [1]

Answer:

356475Nrp

Step-by-step explanation:

$1=105Nrp

$3500=105×3500Nrp

=367500Nrp

Now,

Bank charges 3% commission

therefore, 3% of 367500Nrp

=3/100×367500Nrp

=11025Nrp

Then,

Required money =367500Nrp-11025Nrp

=356475Nrp

3 0

2 years ago

The length of one side of a triangle is 2 feet less than three times the length of its second side. The length of the third side

seropon [69]

Answer:

7 feet, 3 feet, 7.5 feet

Step-by-step explanation:

Let the sides be a, b and c.

<h3>Given</h3>

The length of one side of a triangle is 2 feet less than three times the length of its second side

a = 3b - 2

The length of the third side is 3/4 of the sum of the lengths of the first two sides:

c = (3/4)(a + b)

The perimeter of the triangle is 17.5 feet:

a + b + c = 17.5

<h3>Solution</h3>

Substitute a with b in the second equation:

c = (3/4)(3b - 2 + b) = (3/4)(4b - 2) = (3/4)(4b) - (3/4)(2) = 3b - 1.5

Now substitute a and c with b in the third equation and solve for b:

a + b + c = 17.5

3b - 2 + b + 3b - 1.5 = 17.5
7b - 3.5 = 17.5
7b = 17.5 + 3.5
7b = 21
b = 3

Find the value of a:

a = 3b - 2 = 3*3 - 2 = 9 - 2 = 7

Find the value of c:

c = 3b - 1.5 = 3*3 - 1.5 = 9 - 1.5 = 7.5

The sides of the triangle are:

a = 7 feet, b = 3 feet, c = 7.5 feet

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1 year ago