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2 years ago

Find the surface area of a pyramid with a square base with dimensions 100 mm by 100 mm and height of 75 mm.

Mathematics

1 answer:

Reil [10]2 years ago

8 0

To solve for the surface area of the pyramid, we make use of the formula:

A= l w + l [sqrt ((w / 2)^2 + h^2)] + w [sqrt ((l / 2)^2 + h^2))

where,

l and w are the base of the pyramid = 100 mm

h is the height of the pyramid = 75 mm

Substituting the given values into the equation:

A= 100 * 100 + 100 [sqrt ((100 / 2)^2 + 75^2)] + 100 [sqrt ((100 / 2)^2 + 75^2))

A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)

A = 20,148.90 mm^2

Therefore the surface area of the pyramid is about 20,149 mm^2.

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What is the substitution of -6x-8y=-20 and x+6y=-6

ale4655 [162]

Substitution doesn't work for this, but elimination does.

-6x-8y=-20 +6( x+6y=-6)

-6x-8y=-20 + 6x+36y=-36

-6x and 6x cancel each other, add -8 and 36 to get 28, and -20 and -36 to get -56.

28y=-56

divide by 28 on both sides.

Y= -2

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2 years ago

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Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125

Savatey [412]

we have that

$300 + 150 + 75 +...$

Let

$a1=300\\ a2=150\\ a3=75$

we know that

$\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50$

$\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50$

$a(n+1)=an*0.50$

Is a geometric sequence

Find the value of $a4$

$a(4)=a3*0.50$

$a(4)=75*0.50$

$a(4)=37.5$

Find the value of $a5$

$a(5)=a4*0.50$

$a(5)=37.5*0.50$

$a(5)=18.75$

Find $S5$

$S5=a1+a2+a3+a4+a5\\ S5=300+150+75+37.5+18.75\\ S5=581.25$

therefore

the answer is

$581.25$

Alternative Method

Applying the formula

$S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25$

therefore

the answer is

$581.25$

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2 years ago

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torisob [31]

Answer:

21/2

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$3\frac{3 - 8}{10}$

$2\frac{5}{10}$

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Molodets [167]

Take half of the coefficient of x (which is 2/5) and square it:

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x^2 + (2/5)x = x^2 + (2/5)x + (1/5)^2 - (1/5)^2, or

(x+1/5)^2 - (1/5)^2, or (x + 1/5)^2 - 1/25

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Nesterboy [21]

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3 years ago