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3 years ago

What is the surface area of this Square Pyramid? 10 in 5 in 5 in.

Mathematics

1 answer:

lidiya [134]3 years ago

6 0

Answer:

Base Surface Area: 25 in^2

Total surface area A = 128.07764064044 in^2

(PLEASE NOTE THIS IS BASED ON THE HEIGHT BEING 10 IN AND SIDE LENGTH A BEING 5 IN (IF THIS IS INCORRECT COMMENT AND ILL FLIP IT)

Step-by-step explanation:

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What is the slope of a line that passes through the points (-4,0) and (0,4)?

Schach [20]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

5 0

3 years ago

Find the volume of a cylinder with a diameter of 16 mm and a height of 5.7 mm

Mademuasel [1]

The volume formula for a cylinder is :
V= (pi)(r^2)(h)
So r= d/2 where d = 16mm so r= 8mm h is given as equaling 5.7mm
Now just plug it into the formula.
V=(pi)(8^2)(5.7) = 364.8 pi mm = 1146.053mm

3 0

3 years ago

Factor out the GCF from the terms of the polynomial –4y5 + 6y3 + 8y2 – 2y. A. –2y4 + 3y2 + 4y – 1 B. y(–4y4 + 6y2 + 8y – 2) C. 2

andreyandreev [35.5K]

Answer:

Option D) $-2y(2y^4-3y^2-4y+1)$ is correct

Therefore $-4y^5+6y^3+8y^2-2y=-2y(2y^4-3y^2-4y+1)$

Step-by-step explanation:

Given polynomial is $-4y^5+6y^3+8y^2-2y$

To factorise the given polynomial by taking out the common terms of the given polynomial :

$-4y^5+6y^3+8y^2-2y$
$=2y(-2y^4+3y^2+4y-1)$ ( here 2y is GCF common term so taking outside the terms of the polynomial )
$=-2y(2y^4-3y^2-4y+1)$ ( now taking (-) outside )