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2 years ago

8

in order to prepare for building a brick patio, a rectangle measuring 8 feet by 10 feet must be marked off, then the dirt dug ou

t to a depth of 0.5 feet. what is the volume of sand needed, in feet, to feel up the space?

1 answer:

Gala2k [10]2 years ago

5 0

The sand makes up a rectangular prism of dimensions 8' by 10' by 0.5'.

The volume of sand is then V = L*W*H, or V = (10')(8')(0.5') = 40 cubic ft.

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Zara translates figure p to make figure q. If she translates figure q 4 units to right to make figure r where will figure r be l

Morgarella [4.7K]

Using translation concepts, considering the vertices (x,y) of figure p, the following rule is applied to find the vertices of figure r.

(x,y) -> (x + 4, y).

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

When a figure is shifted 4 units to the right, <u>4 is added to the x-coordinate</u>, hence, considering the vertices (x,y) of figure p, the following rule is applied to find the vertices of figure r.

(x,y) -> (x + 4, y).

More can be learned about translation concepts at brainly.com/question/28416763

#SPJ1

7 0

1 year ago

Find the directional derivative of f(x,y,z)=z3−x2yf(x,y,z)=z3−x2y at the point (−5,5,2)(−5,5,2) in the direction of the vector v

olga_2 [115]

We are given

$f=z^3 -x^2y$

Firstly, we can find gradient

so, we will find partial derivatives

$f_x=0 -2xy$

$f_x=-2xy$

$f_y=0 -x^2$

$f_y=-x^2$

$f_z=3z^2$

now, we can plug point (-5,5,2)

$f_x=-2*-5*5=50$

$f_y=-(-5)^2=-25$

$f_z=3(2)^2=12$

so, gradient will be

$gradf=(50,-25,12)$

now, we are given that

it is in direction of v=⟨−3,2,−4⟩

so, we will find it's unit vector

$|v|=\sqrt{(-3)^2+(2)^2+(-4)^2}$

$|v|=\sqrt{29}$

now, we can find unit vector

$v'=(\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })$

now, we can find dot product to find direction of the vector

$dir=(gradf) \cdot (v')$

now, we can plug values

$dir=(50,-25,12) \cdot (\frac{-3}{\sqrt{29} } , \frac{2}{\sqrt{29} } , \frac{-4}{\sqrt{29} })$

$dir=(-\frac{150}{\sqrt{29} } - \frac{50}{\sqrt{29} } - \frac{48}{\sqrt{29} })$

$dir=-\frac{248\sqrt{29}}{29}$ .............Answer

7 0

3 years ago

Read 2 more answers

Let f(x) = (5)^x+1 .Evaluate f (-3) without using a calculator

rewona [7]

Answer:

$f\left(-3\right)=\frac{126}{125}$

Step-by-step explanation:

Given

$f\left(x\right)\:=\:\left(5\right)^x+1$

Putting x = -3 to find f(-3)

$f\left(-3\right)\:=\:\left(5\right)^{\left(-3\right)}+1$

as

$5^{-3}=\frac{1}{125}$ ∵ $\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

so

$f\left(-3\right)=\frac{1}{125}+1$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:1=\frac{1\cdot \:125}{125}$

$f\left(-3\right)=\frac{1\cdot \:\:125}{125}+\frac{1}{125}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$f\left(-3\right)=\frac{1\cdot \:\:125+1}{125}$

$f\left(-3\right)=\frac{126}{125}$ ∵ $1\cdot \:125+1=126$

Thus,

$f\left(-3\right)=\frac{126}{125}$

6 0

3 years ago

HELP PLEASE FIND X AND SHOW YOUR WORK

PtichkaEL [24]

Answer:

34

Step-by-step explanation:

Straight lines are 180 degrees, so the angle inside of the triangle next to the 127, is 53 degrees. (180-127= 53)

So to find "x", we need to figure out what the full number is.

59+53 = 112.

180-112= 68.

Now that we have the degree of the full angle, we can make an equation to find x.

x*2 = 68

(Divide 2 from both sides to isolate the variable)

x = 34

I hope this helped!

7 0

2 years ago

The coordinates R(1, -3), S(3, -1) T(5,-7) form what type of polygon?

Reika [66]

- It's an obtuse triangle.

5 0

3 years ago

Read 2 more answers