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3 years ago

What is the number of times a base is multiplied by its self indicated by an exponent

1 answer:

5 0

The question is worded a bit strangely (in my opinion anyway), but I think your teacher wants you to describe how exponents work.

Let's say we had the expression $5^3$

The base is 5 as its the bottom most value (think of something like the base of a tree or building). The exponent is 3.

The exponent of 3 tells the reader to multiply the base 5 by itself 3 times like so

$5^3 = 5*5*5 = 125$

With larger exponents, it becomes more tedious to write out all the repeated multiplications, which is why many calculators have an exponent button to save time.

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Consider f and c below. f(x, y) = (3 + 4xy2)i + 4x2yj, c is the arc of the hyperbola y = 1/x from (1, 1) to 3, 1 3 (a) find a fu

irga5000 [103]

We want to find a scalar function $f(x,y)$ such that $\nabla f(x,y)=\mathbf f(x,y)=\dfrac{\partial f}{\partial x}\,\mathbf i+\dfrac{\partial f}{\partial y}\,\mathbf j$ .
So we need to have
$\dfrac{\partial f}{\partial x}=3+4xy^2$
Integrating both sides with respect to $x$ gives
$f(x,y)=3x+2x^2y^2+g(y)$
Differentiating with respect to $y$ gives
$\dfrac{\partial f}{\partial y}=4x^2y+\dfrac{\mathrm dg}{\mathrm dy}=4x^2y$ $\implies\dfrac{\mathrm dg}{\mathrm dy}=0$ $\implies g(y)=C$
So we find that
$f(x,y)=3x+2x^2y^2+C$
By the fundamental theorem of calculus, we then know the line integral depends only on the values of $f(x,y)$ at the endpoints of the path. Therefore

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f\left(3,\frac13\right)-f(1,1)=11-5=6$

4 0

3 years ago

HELP ME ASAP! BRAINLIEST UP FOR GRABS

natita [175]

Answer:

-5 ≤ x≤ 3

Step-by-step explanation:

The domain is the values for x

x starts and -5 and includes -5 since the circle is closed

and goes to 3 and includes 3 since the circle is closed

-5 ≤ x≤ 3

8 0

3 years ago

Read 2 more answers

Enter the equation of the circle in standard form with center and radius given.\\\\\\\\\\\Center (8,0), radius = sqrt 3/////////

ehidna [41]

Answer:

(x - 8)^2 + y^2 = 3.

Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

Here h = 8, k = 0 and r^2 = (√3)^2 = 3

The answer is (x - 8)^2 + (y - 0)^2 = 3

or (x - 8)^2 + y^2 = 3.

4 0

3 years ago

Evaluate 3{5 + 3[10 + 4 · 8]}

VMariaS [17]

393 is the answer to the question

8 0

3 years ago

A cube has side length

lilavasa [31]

900 : 1

The linear ratio = a : 30a = 1 : 30

volume ratio = 1³ : 30³ = 1 : 900

ratio of larger to smaller = 900 : 1

3 0

3 years ago