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2 years ago

Which statement about determining the quotient 1/8 ÷ 2 is true?

Mathematics

1 answer:

NISA [10]2 years ago

7 0

Answer:

A. Because 1/16 x 2 = 1/8, 1/8 divided by 2 is 1/16.

Step-by-step explanation:

I put it into decimals to figure it out. 1/16 as a decimal is 0.0625, which I multiplied by two to get 0.125. Converting that into 1/8.

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In one grade of 150150 students, the ratio of boys to girls is 2 : 3 . How many boys are in that grade?

Serjik [45]

2 + 3 =5

150/5=30

30 x 2 is 60

There are 60 boys

4 0

3 years ago

Evaluate (−23)×(−23)3 by using the Laws of Exponents

Nikolay [14]

Given:

$\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3$

To find:

The value of given expression by using the Laws of Exponents.

Solution:

We have,

$\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3$

Using the Laws of Exponents, we get

$=\left(-\dfrac{2}{3}\right)^{1+3}$ $[\because a^ma^n=a^{m+n}]$

$=\left(\dfrac{-2}{3}\right)^{4}$

$=\dfrac{(-2)^4}{(3)^4}$ $[\because \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}]$

$=\dfrac{(-2)\times (-2)\times (-2)\times (-2)}{(3)\times (3)\times (3)\times (3)}$

$=\dfrac{16}{81}$

Therefore, the value of given expression is $\dfrac{16}{81}$ .

3 0

2 years ago

Ellus<br> If f(x) = x2, and<br> g(x) = x - 1, then<br> f(g(x)) = [ ? ]x2 +[ ]x+]

Nostrana [21]

Answer:

x^2-2x+1

Step-by-step explanation:

f(x)=x^2

g(x)=x-1

f(g(x))=f(x-1)=(x-1)^2=x^2-2x+1

8 0

2 years ago

Which side of A DEF is the longest?

Cloud [144]

Answer:

show

Step-by-step explanation:

8 0

2 years ago

Compute the line integral with respect to arc length of the function f(x, y, z) = xy2 along the parametrized curve that is the l

SIZIF [17.4K]

Answer:

$\displaystyle\frac{15\sqrt{3}}{4}-90\sqrt{146}$

Step-by-step explanation:

The line integral with respect to arc length of the function f(x, y, z) = xy2 along the parametrized curve that is the line segment from (1, 1, 1) to (2, 2, 2) followed by the line segment from (2, 2, 2) to (−9, 6, 5) equals the sum of the line integral of f along each path separately.

Let

$C_1,C_2$

be the two paths.

Recall that if we parametrize a path C as $(r_1(t),r_2(t),r_3(t))$ with the parameter t varying on some interval [a,b], then the line integral with respect to arc length of a function f is

$\displaystyle\int_{C}f(x,y,z)ds=\displaystyle\int_{a}^{b}f(r_1,r_2,r_3)\sqrt{(r'_1)^2+(r'_2)^2+(r'_3)^2}dt$

Given any two points P, Q we can parametrize the line segment from P to Q as

r(t) = tQ + (1-t)P with 0≤ t≤ 1

The parametrization of the line segment from (1,1,1) to (2,2,2) is

r(t) = t(2,2,2) + (1-t)(1,1,1) = (1+t, 1+t, 1+t)

r'(t) = (1,1,1)

and

$\displaystyle\int_{C_1}f(x,y,z)ds=\displaystyle\int_{0}^{1}f(1+t,1+t,1+t)\sqrt{3}dt=\\\\=\sqrt{3}\displaystyle\int_{0}^{1}(1+t)(1+t)^2dt=\sqrt{3}\displaystyle\int_{0}^{1}(1+t)^3dt=\displaystyle\frac{15\sqrt{3}}{4}$

The parametrization of the line segment from (2,2,2) to

(-9,6,5) is

r(t) = t(-9,6,5) + (1-t)(2,2,2) = (2-11t, 2+4t, 2+3t)

r'(t) = (-11,4,3)

and

$\displaystyle\int_{C_2}f(x,y,z)ds=\displaystyle\int_{0}^{1}f(2-11t,2+4t,2+3t)\sqrt{146}dt=\\\\=\sqrt{146}\displaystyle\int_{0}^{1}(2-11t)(2+4t)^2dt=-90\sqrt{146}$

Hence

$\displaystyle\int_{C}f(x,y,z)ds=\displaystyle\int_{C_1}f(x,y,z)ds+\displaystyle\int_{C_2}f(x,y,z)ds=\\\\=\boxed{\displaystyle\frac{15\sqrt{3}}{4}-90\sqrt{146}}$

8 0

3 years ago