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2 years ago

Question 5 (1 point)

Mathematics

1 answer:

RoseWind [281]2 years ago

7 0

Answer:c

Step-by-step explanation:

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Last year 80 students signed up for a summer trip to Washington, D.C. This summer 50 students have signed up to go. What is the

Fynjy0 [20]

Given:

Last year 80 students signed up for a summer trip to Washington, D.C.

This summer 50 students have signed up to go.

To find:

The percent decrease in the number of students.

Solution:

We have,

Students in last year = 80

Students in this year = 50

Now,

$\text{Decrease}\%=\dfrac{\text{Students in last year - Students in this year }}{\text{Students in last year }}\times 100$

$\text{Decrease}\%=\dfrac{80-50}{80}\times 100$

$\text{Decrease}\%=\dfrac{30}{80}\times 100$

$\text{Decrease}\%=\dfrac{3}{8}\times 100$

$\text{Decrease}\%=37.5$

Therefore, the correct option is B.

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3 years ago

If 60 is 75% of s value, what is that value

ohaa [14]

Let's write it down:
<span>"60 is 75% of s" means:

60=75%*s

75% is $\frac{75}{100}= \frac{3}{4}$ , (percent just means "out of 100" so we just divide it by 100) so we can also write:

60=</span><span> $\frac{3}{4}$ s

now, let's multiply both sides by 4:

240=3s

and divide by 3:
80=s

So we have the result that the original value, s, is 80!
</span>

3 0

3 years ago

NEED HELP ASAPPP

Serjik [45]

The answers is a because the radius must be 5

6 0

3 years ago

Read 2 more answers

A(-5,-4) ——> A’ is a glide reflection where the translation is (x,y)—->(x+6,y), and the line of reflection is y=3. What ar

Nastasia [14]

Solution:

The Point in the coordinate plane is A(-5,-4).

Perpendicular or shortest Distance from line y=3 that is (-5,3) to point (-5,-4) is

$=\sqrt{(-5+5)^2+(3+4)^2}\\\\=7$

When it is reflected through the line, y=3, the coordinate of point A (-5,-4) changes to (-5,3+7)= B(-5,10).

Now, the Point B is translated by the rule , (x,y)—->(x+6,y),

So,the point B is translated to, (-5+6,10)=(1,10)

Option C: (1,10) is the glide reflection of point A(-5,-4).

8 0

3 years ago

Read 2 more answers

For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such f

butalik [34]

$\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k$

Let

$\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k$

The curl is

$\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)$

where $\partial_\xi$ denotes the partial derivative operator with respect to $\xi$ . Recall that

$\vec\imath\times\vec\jmath=\vec k$

$\vec\jmath\times\vec k=\vec i$

$\vec k\times\vec\imath=\vec\jmath$

and that for any two vectors $\vec a$ and $\vec b$ , $\vec a\times\vec b=-\vec b\times\vec a$ , and $\vec a\times\vec a=\vec0$ .

The cross product reduces to

$\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k$

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

$\nabla\times\vec f=\vec0$

which means $\vec f$ is indeed conservative and we can find $f$ .

Integrate both sides of

$\dfrac{\partial f}{\partial y}=2xze^{2xyz}$

with respect to $y$ and

$\implies f(x,y,z)=e^{2xyz}+g(x,z)$

Differentiate both sides with respect to $x$ and

$\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}$

$2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}$

$4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}$

$\implies g(x,z)=4\sin(xz^2)+h(z)$

Now

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)$

and differentiating with respect to $z$ gives

$\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}$

$2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}$

$\dfrac{\mathrm dh}{\mathrm dz}=0$

$\implies h(z)=C$

for some constant $C$ . So

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C$

3 0

3 years ago