All categories

2 years ago

Please help and give explanation

Mathematics

1 answer:

sertanlavr [38]2 years ago

3 0

The percent of discount on the backpack was 42.30%.

Step-by-step explanation:

Step 1:

From the given data, the original cost was $52 and it decreased to $30 due to a discount.

First, we need to determine the difference in values between the original price and the discounted price.

The difference between the prices $= 52-30 = 22.$

Step 2:

The percent decrease is given by dividing the difference in values by the original value multiplied by 100.

Percent decrease $= \frac{difference in values}{original value}(100) .$

Percent decrease $= \frac{22}{52} (100) = 0.4230(100) = 42.30 \%$

So there was a 42.30% discount on the backpack.

You might be interested in

What figure is a dilation of Figure A by a factor of 1/2 ?

lora16 [44]

A dilation of figure A by a factor of 1/2 is the last figure with sides 1in, 2 in, 0.5 in and 2.5 inch. Since dilation means becoming larger, smaller or wider from one figure, this is also same with similar figures where the ratios of corresponding sides should be the same. In this problem, the ratio is 0.5 or 1/2. Therefore figure A is similar to the last figure.

7 0

3 years ago

Read 2 more answers

Graphs which present the values on the horizontal axis and the number of times this occurs on the vertical axis are known as wha

Ivanshal [37]

Answer:

The horizontal axis represents TIME

Step-by-step explanation:

In a time-series plot, the horizontal axis represents time, and the vertical axis represents the value of the variable we are measuring. -The values of the variable are plotted at each of the times, then the points are connected with straight lines.

3 0

2 years ago

Problem 4: Let F = (2z + 2)k be the flow field. Answer the following to verify the divergence theorem: a) Use definition to find

Viktor [21]

Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk $x^2+y^2\le3$ , I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere $x^2+y^2+z^2=3$ .

a. Let $C$ denote the hemispherical <u>c</u>ap $z=\sqrt{3-x^2-y^2}$ , parameterized by

$\vec r(u,v)=\sqrt3\cos u\sin v\,\vec\imath+\sqrt3\sin u\sin v\,\vec\jmath+\sqrt3\cos v\,\vec k$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take the normal vector to $C$ to be

$\vec r_v\times\vec r_u=3\cos u\sin^2v\,\vec\imath+3\sin u\sin^2v\,\vec\jmath+3\sin v\cos v\,\vec k$

Then the upward flux of $\vec F=(2z+2)\,\vec k$ through $C$ is

$\displaystyle\iint_C\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^{\pi/2}((2\sqrt3\cos v+2)\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm dv\,\mathrm du$

$\displaystyle=3\int_0^{2\pi}\int_0^{\pi/2}\sin2v(\sqrt3\cos v+1)\,\mathrm dv\,\mathrm du$

$=\boxed{2(3+2\sqrt3)\pi}$

b. Let $D$ be the disk that closes off the hemisphere $C$ , parameterized by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le\sqrt3$ and $0\le v\le2\pi$ . Take the normal to $D$ to be

$\vec s_v\times\vec s_u=-u\,\vec k$

Then the downward flux of $\vec F$ through $D$ is

$\displaystyle\int_0^{2\pi}\int_0^{\sqrt3}(2\,\vec k)\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv=-2\int_0^{2\pi}\int_0^{\sqrt3}u\,\mathrm du\,\mathrm dv$

$=\boxed{-6\pi}$

c. The net flux is then $\boxed{4\sqrt3\pi}$ .

d. By the divergence theorem, the flux of $\vec F$ across the closed hemisphere $H$ with boundary $C\cup D$ is equal to the integral of $\mathrm{div}\vec F$ over its interior:

$\displaystyle\iint_{C\cup D}\vec F\cdot\mathrm d\vec S=\iiint_H\mathrm{div}\vec F\,\mathrm dV$

We have

$\mathrm{div}\vec F=\dfrac{\partial(2z+2)}{\partial z}=2$

so the volume integral is

$2\displaystyle\iiint_H\mathrm dV$

which is 2 times the volume of the hemisphere $H$ , so that the net flux is $\boxed{4\sqrt3\pi}$ . Just to confirm, we could compute the integral in spherical coordinates:

$\displaystyle2\int_0^{\pi/2}\int_0^{2\pi}\int_0^{\sqrt3}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=4\sqrt3\pi$

4 0

3 years ago

If h(x) = -5x -10 find (h-2)

gizmo_the_mogwai [7]

H(x) = -5x - 10
h(-2) = -5(-2) - 10
h(-2) = 10 - 10
h(-2) = 0

8 0

3 years ago

What is the y- intercept of: y=-2x

shusha [124]

Answer:

it is Zero 0

Step-by-step explanation:

7 0

3 years ago