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3 years ago

15

Adam let out 18 feet of string to fly his kite. He then let out 19 feet more before reeling back in 8 feet. How long was his str

ing after reeling back?

1 answer:

shusha [124]3 years ago

3 0

29 feet long after reeling back

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A special liquid is held in a tank described as (x 2 + y 2 ) ≤ z ≤ 1 in a Cartesian coordinate system. Assume that the density o

vivado [14]

Since $\rho=\dfrac mV$ (density = mass/volume), we can get the mass/weight of the liquid by integrating the density $\rho(x,y,z)$ over the interior of the tank. This is done with the integral

$\displaystyle\int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{x^2+y^2}^1(2-z^2)\,\mathrm dz\,\mathrm dy\,\mathrm dx$

which is more readily computed in cylindrical coordinates as

$\displaystyle\int_0^{2\pi}\int_0^1\int_{r^2}^1(2-z^2)r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{3\pi}4}$

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3 years ago

What is the smallest of three consecutive positive integers if the product of the smaller two integers is 10 more than 4 times t

r-ruslan [8.4K]

The smallest is 6
Three consecutive integers
X. Smallest 6
X+1. 7
X+2. Largest 8

X(X+1)= 4(X+2)+10
X^2+X= 4x+8+10
X^2+X-4x-18=0
X^2-3x-18=0

( X+3)(X-6)
X=-3. X=6
Don't use the negative

Check 6(7)= 4(8)+10
42=42

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3 years ago

Select all the situations that can be represented by the tape diagram. 99 W W W W W 4 Clare buys 4 bouquets, each with the same

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Answer:

Third one 33333333333333333

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3 years ago

Read 2 more answers

Which is a pair of equal expressions

ZanzabumX [31]

Answer:

C

Step-by-step explanation:

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3 years ago

The diagonals of a rhombus measures 6cm and 8cm, what is the perimeter of this rhombus?

Kamila [148]

<h2><u>Diagram</u><u>:</u><u>-</u></h2>

$\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(6,1)\qbezier(1,1)(1,1)(1.6,4)\qbezier(1.6,4)(1.6,4)(6.6,4)\qbezier(6,1)(6,1)(6.6,4)\qbezier(6.6,4)(6.6,4)(1,1)\qbezier(1.6,4)(1.6,4)(6,1)\put(0.7,0.5){\sf A}\put(6,0.5){\sf B}\put(1.4,4.3){\sf D}\put(6.6,4.3){\sf C}\end{picture}$

<h3><u>Required Answer</u><u>:</u><u>-</u></h3>

The diagonals of the Rhombus= d1 & d2=6cm and 8cm

Let the Side=a

As we know that in a Rhombus

${\boxed{\sf side=\sqrt {\left ({\dfrac{d1}{2}}\right)^2+\left ({\dfrac {d2}{2}}\right)^2}}}$

Substitute the values

${:}\longmapsto$ $\sf a=\sqrt {\left ({\dfrac {6}{2}}\right)^2+\left ({\dfrac {8}{2}}\right)^2 }$

${:}\longmapsto$ $\sf a=\sqrt {(3)^2+(4)^2}$

${:}\longmapsto$ $\sf a=\sqrt {9+16}$

${:}\longmapsto$ $\sf a=\sqrt{25}$

${:}\longmapsto$ $\sf a=5cm$

<h2>_____________</h2><h3>Again </h3>

we know that in a Rhombus

$\boxed{\sf Perimeter=4a}$

Substitute the values

${:}\longmapsto$ $\sf Perimeter=4×5$

${:}\longmapsto$ $\sf Perimeter=20cm$

$\therefore$ Perimeter of the rectangle is 20cm.

5 0

3 years ago