All categories

3 years ago

Simplify: 7 exponent9 7 exponent3

Mathematics

1 answer:

Westkost [7]3 years ago

4 0

Answer:

7^9= 40,353,607

7*7*7*7*7*7*7*7*7=40,353,607

7^3 =343

7*7*7=343

You might be interested in

onyango wishes to fence a rectangular research plot using 100 m of wire .one end of the plot has a wall already erected .calcula

earnstyle [38]

Answer:

1250 m²

Step-by-step explanation:

Let x and y denote the sides of the rectangular research plot.

Thus, area is;

A = xy

Now, we are told that end of the plot already has an erected wall. This means we are left with 3 sides to work with.

Thus, if y is the erected wall, and we are using 100m wire for the remaining sides, it means;

2x + y = 100

Thus, y = 100 - 2x

Since A = xy

We have; A = x(100 - 2x)

A = 100x - 2x²

At maximum area, dA/dx = 0.thus;

dA/dx = 100 - 4x

-4x + 100 = 0

4x = 100

x = 100/4

x = 25

Let's confirm if it is maximum from d²A/dx²

d²A/dx² = -4. This is less than 0 and thus it's maximum.

Let's plug in 25 for x in the area equation;

A_max = 25(100 - 2(25))

A_max = 1250 m²

5 0

3 years ago

Mary has twice as many pencils as she has pens. Tom borrows a pen. Now, Mary has ten less pens than pencils. How many pencils do

I am Lyosha [343]

X - the number of pencils
y - the number of pens

She has twice as many pencils as she has pens.
$x=2y$

Tom borrows a pen, so she has y-1 pens. Now she has ten less pens than pencils.
$x-10=y-1 \\
x=y-1+10 \\
x=y+9$

Set 2y and y+9 equal to each other:
$2y=y+9 \\
2y-y=9 \\
y=9$
She has 9 pens.

3 0

3 years ago

Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate bo

Shalnov [3]

Looks like we're given

$\vec F(x,y)=\langle-x,-y\rangle$

which in three dimensions could be expressed as

$\vec F(x,y)=\langle-x,-y,0\rangle$

and this has curl

$\mathrm{curl}\vec F=\langle0_y-(-y)_z,-(0_x-(-x)_z),(-y)_x-(-x)_y\rangle=\langle0,0,0\rangle$

which confirms the two-dimensional curl is 0.

It also looks like the region $R$ is the disk $x^2+y^2\le5$ . Green's theorem says the integral of $\vec F$ along the boundary of $R$ is equal to the integral of the two-dimensional curl of $\vec F$ over the interior of $R$ :

$\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\iint_R\mathrm{curl}\vec F\,\mathrm dA$

which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of $R$ by

$\vec r(t)=\langle\sqrt5\cos t,\sqrt5\sin t\rangle\implies\vec r'(t)=\langle-\sqrt5\sin t,\sqrt5\cos t\rangle$

$\implies\mathrm d\vec r=\vec r'(t)\,\mathrm dt=\sqrt5\langle-\sin t,\cos t\rangle\,\mathrm dt$

with $0\le t\le2\pi$ . Then

$\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle-\sqrt5\cos t,-\sqrt5\sin t\rangle\cdot\langle-\sqrt5\sin t,\sqrt5\cos t\rangle\,\mathrm dt$

$=\displaystyle5\int_0^{2\pi}(\sin t\cos t-\sin t\cos t)\,\mathrm dt=0$

7 0

3 years ago

I need help with this question

julia-pushkina [17]

Answer:

I think its D

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Find the Diameter of the Circle with the following equation. Round to the nearest tenth.

Radda [10]

The diameter of the circle is 11.8 units

<h3>How to determine the diameter of the circle?</h3>

The circle equation is given as:

(x - 2)^2 + (y + 6)^2 = 35

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where

Diameter = 2r

By comparing both equations, we have

r^2 = 35

Take the square root of both sides

r = 5.9

Multiply by 2

2r = 11.8

Hence, the diameter of the circle is 11.8 units