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umka2103 [35]
3 years ago
5

What is 1.08 to the power of

\frac{1}{5}" align="absmiddle" class="latex-formula">? Show your steps
Mathematics
2 answers:
lord [1]3 years ago
8 0

Answer:

1.01551

Step-by-step explanation:

1.08^1/5 = 1.01551

There's really no way of showing work for this problem unless you wanna convert 1/5 to a decimal and multiply that way.

I just did it on the calculator because most schools allow you to do exponents this way.

Vesna [10]3 years ago
6 0

Step-by-step explanation:

a^\frac{1}{n}=\sqrt[n]{a}\\\\1.08^\frac{1}{5}=\sqrt[5]{1.08}\qquad\text{convert the decimal to the fraction}\\\\=\sqrt[5]{\dfrac{108}{100}}=\sqrt[5]{\dfrac{108\cdot1000}{100\cdot1000}}=\sqrt[5]{\dfrac{108000}{100000}}=\dfrac{\sqrt[5]{108000}}{\sqrt[5]{100000}}=\dfrac{\sqrt[5]{108000}}{10}\\\\\text{You can use a calculator:}\\\\1.08^\frac{1}{5}=\sqrt[5]{1.08}\approx1.015511

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Given the figure below, find the values of x and z.
aleksandrvk [35]

Answer: x = 2 and z=78

Step-by-step explanation:

Opposite angles are non-adjacent angles formed by two intersecting lines. Opposite angles are congruent (equal in measure). Z is Opposite to 78 angle, so z=78.

Adjacent angles add up to 180 degrees, and 78 and (5x + 92) are adyacents so:

5x + 92 + 78 = 180

5x + 170 = 180

5x = 180 - 170

5x = 10

x = 10/5

x = 2

7 0
3 years ago
Jose's football weighs 7/8 of a pound. His football helmet weighs 4 1/6 of a pound. Estimate how much more the helmet weighs tha
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5 0
3 years ago
Are these linear or nonlinear?<br> 1. y-4=-8(x-1)<br> 2. y=x^4<br> 3. y-x^2=4.5<br> 4.3x+5y=15
olya-2409 [2.1K]
1st is linear
2nd is nonlinear
3rd is nonlinear
4th is linear
7 0
3 years ago
Please help me with this
satela [25.4K]
Area of the trapezoid:
\frac{12.8 + 4.2}{2} (4.9) = 41.65 cm^2

Area of the rectangle:
4.2 x 3.1 = 13.02 cm^2

Area of each quarter circle:
\frac{ \pi  (3.1)^{2} }{4} = 7.54 cm^2

We have two quarter circles:
7.54 + 7.54 = 15.08

41.65 + 13.02 + 15.08 = 69.75 cm^2
5 0
3 years ago
Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y
professor190 [17]

Answer:

Required total charge is 256\pi coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

x^2=y^2\leq 16 so that the charge density at (x,y) is,

\rho (x,y)=2x+2y+2x^2+2y^2

To find total charge on the disk let Q be the total charge and x=r\cos\theta,y=r\sin\theta so that,

Q={\int\int}_Q\rho(x,y) dA                where A is the surface of disk.

=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA

=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta

=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta

=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta

=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta

=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi

=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi

=256\pi

Hence total charge is 256\pi coulombs per square meter.

3 0
3 years ago
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