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stira [4]
3 years ago
10

What is the surface area in yards squared of the triangular prism shown below?

Mathematics
1 answer:
hichkok12 [17]3 years ago
7 0

Answer:

1,120 yd²

Step-by-step explanation:

Surface area of triangular prism = 2(BA) + P*H

✔️Triangular base area (BA) = ½bh

b = 15 yd

h = 8 yd

Base area (BA) = ½*8*15 = 60 yd²

✔️Perimeter of the base (P) = 17 + 15 + 8 = 40 yd

✔️Height or lenghtbor prism (P) = 25 yd

✔️Surface area = 2(60) + 40*25 = 120 + 1,000 = 1,120 yd²

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The area of the circle is 64pie cm. What is the radius in cm?
Vinil7 [7]

Answer: 8 centimeters

Step-by-step explanation: To find the radius of the circle, remember that the formula for the area of a circle is πr² and since we're given that the area of our circle is 64π, we can set up the equation 64π = πr².

To solve for <em>r</em>, we first divide both sides of the equation by π.

On the left side, the π's cancel and we're left with 64 and on the right side, the π's cancel and we're left with r².

So we have 64 = r².

Next, we take the square root of both sides to get 8 = r.

So the radius of our circle is 8 centimeters.

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3 years ago
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2 years ago
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△klm, lm=20 sqrt 3 m∠k=105°, m∠m=30° find: kl and km
Anarel [89]

Answer:

KL =  \frac{20\sqrt{6}}{1+\sqrt{3}} = 17.93

MK =  \frac{40\sqrt{3}}{1+\sqrt{3}} = 25.36


Explanation:

According to the Law of Sines:

\frac{a}{sinA}=\frac{b}{sinB}= \frac{c}{sinC}

where:

A, B, and C are angles

a, b, and c are the sides opposite to the angles


First of all, let's find m∠L: the sum of the angles of a triangle is 180°, therefore

m∠K + m∠L + m∠M = 180°

m∠L = 180° - m∠K - m∠M

m∠L = 180° - 105° - 30°

m∠L = 45°


Now, we can apply the Law of Sines to our case (see picture attached):

\frac{LM}{sinK}=\frac{MK}{sinL}=\frac{KL}{sinM}


Let's solve one side at the time:

\frac{LM}{sinK}=\frac{MK}{sinL}

\frac{20\sqrt{3}}{sin(105)}=\frac{MK}{sin(45)}

MK = \frac{20\sqrt{3} }{sin(105)} \cdot sin(45)

MK = \frac{40\sqrt{3} }{1+\sqrt{3} } = 25.36


Similarily:

\frac{LM}{sinK}=\frac{KL}{sinM}

\frac{20\sqrt{3}}{sin(105)}=\frac{KL}{sin(30)}

KL = \frac{20\sqrt{3} }{sin(105)} \cdot sin(30)

KL = \frac{20\sqrt{6}}{1+\sqrt{3}} = 17.93

8 0
3 years ago
Factorise the following
andreyandreev [35.5K]

Answer:

Below.

Step-by-step explanation:

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e) 3x⁴-54t = 3(x^4 - 18t)

f) x²+3x-10 = (x - 2)(x + 5)

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How do I condense each expression?
Ksivusya [100]

Answer:

  \log_5{\dfrac{x^5}{\sqrt[4]{8-x}}}

Step-by-step explanation:

Make use of the rules of logarithms:

  log(a/b) = log(a) - log(b)

  log(a^b) = b·log(a)

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3 years ago
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