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3 years ago

56.25% of what number is 168.75

Mathematics

2 answers:

Alenkasestr [34]3 years ago

5 0

Answer:

300

Step-by-step explanation:

The information we have is:

Number percentage

168.75 → 56.25%

and we want to know what number will be the 100%, in such a way that the 56.25% is 168.75, so we update the last table:

Number percentage

168.75 → 56.25%

x → 100%

Using the information we have, to find x we must multiply 168.25 by 100% and then divide by 56.25%:

$x=\frac{168.75*100}{56.25}=\frac{16875}{56.25} =300$

thus, 168.75 is 56.25% of 300.

Anastaziya [24]3 years ago

3 0

Set up a ratio
56.25/100 = 168.75/x
cross multiply and get that x = 300

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The surface area of a square pyramid 360 square meters. The base length is 12 meters. Determine the slant height.

garri49 [273]

Answer:

The slant height is 9 meters.

Step-by-step explanation:

To determine the slant height, we will follow the steps below;

First, write down the formula:

Surface area = 2bs + b²

where b= the length of the base of the square pyramid

s = the slant height of the square pyramid

From the question given,

surface area of a square pyramid = 360 square meters

base length = 12 meters

We can now proceed to insert the values into the formula and then solve for s

Surface area = 2bs + b²

360 = 2(12)s + (12)²

360 = 24s + 144

subtract 144 from both-side of the equation

360 - 144 = 24s

216 = 24s

Divide both-side of the equation by 24

216/24 = 24s/24

9 = s

s = 9 meters

The slant height is 9 meters.

7 0

3 years ago

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balandron [24]

Answer:

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Step-by-step explanation:

7 0

3 years ago

Use Gauss's approach to find the following sums (do not use formulas) a 1+2+3+4 998 b. 1+3+5 7+ 1001 a The sum of the sequence i

valkas [14]

Answer:

(a) 498501

(b) 251001

Step-by-step explanation:

According Gauss's approach, the sum of a series is

$sum=\frac{n(a_1+a_n)}{2}$ .... (1)

where, n is number of terms.

(a)

The given series is

1+2+3+4+...+998

here,

$a_1=1$

$a_n=998$

$n=998$

Substitute $a_1=1$ , $a_n=998$ and $n=998$ in equation (1).

$sum=\frac{998(1+998)}{2}$

$sum=499(999)$

$sum=498501$

Therefore the sum of series is 498501.

(b)

The given series is

1+3+5+7+...+ 1001

The given series is the sum of dd natural numbers.

In 1001 natural numbers 500 are even numbers and 501 are odd number because alternative numbers are even.

$a_1=1$

$a_n=1001$

$n=501$

Substitute $a_1=1$ , $a_n=1001$ and $n=501$ in equation (1).

$sum=\frac{501(1+1001)}{2}$

$sum=\frac{501(1002)}{2}$

$sum=501(501)$

$sum=251001$

Therefore the sum of series is 251001.

8 0

3 years ago

Suppose a > 0 is constant and consider the parameteric surface sigma given by r(phi, theta) = a sin(phi) cos(theta)i + a sin(

Gnom [1K]

$\Sigma$ should have parameterization

$\vec r(\varphi,\theta)=a\sin\varphi\cos\theta\,\vec\imath+a\sin\varphi\sin\theta\,\vec\jmath+a\cos\varphi\,\vec k$

if it's supposed to capture the sphere of radius $a$ centered at the origin. ( $\sin\theta$ is missing from the second component)

a. You should substitute $x=a\sin\varphi\cos\theta$ (missing $\cos\theta$ this time...). Then

$x^2+y^2+z^2=(a\sin\varphi\cos\theta)^2+(a\sin\varphi\sin\theta)^2+(a\cos\varphi)^2$

$x^2+y^2+z^2=a^2\left(\sin^2\varphi\cos^2\theta+\sin^2\varphi\sin^2\theta+\cos^2\varphi\right)$

$x^2+y^2+z^2=a^2\left(\sin^2\varphi\left(\cos^2\theta+\sin^2\theta\right)+\cos^2\varphi\right)$

$x^2+y^2+z^2=a^2\left(\sin^2\varphi+\cos^2\varphi\right)$

$x^2+y^2+z^2=a^2$

as required.

b. We have

$\vec r_\varphi=a\cos\varphi\cos\theta\,\vec\imath+a\cos\varphi\sin\theta\,\vec\jmath-a\sin\varphi\,\vec k$

$\vec r_\theta=-a\sin\varphi\sin\theta\,\vec\imath+a\sin\varphi\cos\theta\,\vec\jmath$

$\vec r_\varphi\times\vec r_\theta=a^2\sin^2\varphi\cos\theta\,\vec\imath+a^2\sin^2\varphi\sin\theta\,\vec\jmath+a^2\cos\varphi\sin\varphi\,\vec k$

$\|\vec r_\varphi\times\vec r_\theta\|=a^2\sin\varphi$

c. The surface area of $\Sigma$ is

$\displaystyle\iint_\Sigma\mathrm dS=a^2\int_0^\pi\int_0^{2\pi}\sin\varphi\,\mathrm d\theta\,\mathrm d\varphi$

You don't need a substitution to compute this. The integration limits are constant, so you can separate the variables to get two integrals. You'd end up with

$\displaystyle\iint_\Sigma\mathrm dS=4\pi a^2$

# # #

Looks like there's an altogether different question being asked now. Parameterize $\Sigma$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k$

with $\sqrt2\le u\le\sqrt6$ and $0\le v\le2\pi$ . Then

$\|\vec s_u\times\vec s_v\|=u\sqrt{1+4u^2}$

The surface area of $\Sigma$ is

$\displaystyle\iint_\Sigma\mathrm dS=\int_0^{2\pi}\int_{\sqrt2}^{\sqrt6}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$

The integrand doesn't depend on $v$ , so integration with respect to $v$ contributes a factor of $2\pi$ . Substitute $w=1+4u^2$ to get $\mathrm dw=8u\,\mathrm du$ . Then

$\displaystyle\iint_\Sigma\mathrm dS=\frac\pi4\int_9^{25}\sqrt w\,\mathrm dw=\frac{49\pi}3$

# # #

Looks like yet another different question. No figure was included in your post, so I'll assume the normal vector points outward from the surface, away from the origin.

Parameterize $\Sigma$ by

$\vec t(u,v)=u\,\vec\imath+u^2\,\vec\jmath+v\,\vec k$

with $-1\le u\le1$ and $0\le v\le 2$ . Take the normal vector to $\Sigma$ to be

$\vec t_u\times\vec t_v=2u\,\vec\imath-\vec\jmath$

Then the flux of $\vec F$ across $\Sigma$ is

$\displaystyle\iint_\Sigma\vec F\cdot\mathrm d\vec S=\int_0^2\int_{-1}^1(u^2\,\vec\jmath-uv\,\vec k)\cdot(2u\,\vec\imath-\vec\jmath)\,\mathrm du\,\mathrm dv$