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3 years ago

What is the slant height x of this square pyramid? (Express your answer in radical form.)

Mathematics

1 answer:

Kitty [74]3 years ago

8 0

This is a 30,60,90° triangle where the hypotenuse is equal to 4 meters and the slant height is opposite the 60° angle

The ratios of the sides and their opposite angle for this type of triangle are:

1,30°, √3, 60°, and 2, 90° so the relationship we need is:

x/4=√3/2 multiply both sides by 4

x=2√3

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Power (denoted by PPP) can be defined as a function of work (denoted by WWW) and time (denoted by ttt) using this formula: P=\df

Amanda [17]

Answer:

$\dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^3}$

Step-by-step explanation:

Power (denoted by P) can be defined as a function of work (denoted by W) and time (denoted by t) using this formula:

$P=\dfrac{W}{t}$

Unit of Work = $\dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^2}$

Unit for Time = s

Therefore, the Unit of Power

$=$Unit for W \times \dfrac{1}{\text{Unit for time}}$

$=\dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^2} \times \dfrac{1}{s} \\=\dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^3}$

An appropriate unit for power is: $\dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^3}$

3 0

3 years ago

Solve for x.<br> 21x + 11 - 5 = 5

Reil [10]

Answer:

x= -1/21

Step-by-step explanation:

21x + 11 - 5 = 5

21x + 6 = 5

(-6 each side)

21x = -1

(divide 21 each side)

x= -1/21

3 0

3 years ago

Read 2 more answers

2+17+8 rewritten correctly using the commutative property and then simplified correctly

zheka24 [161]

Answer:

Step-by-step explanation:

I am sorry this is to confusing for me

7 0

3 years ago

Read 2 more answers

A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it tak

IgorC [24]

Answer

According to newton law of cooling

$\dfrac{d T}{dt} = k (T - T_a)$

and

$T = Ce^{kt} + T_a$

now At Ta = 100

T₀ = 10 °C

T₁ = 12° C

$T(0) = Ce^{0} + T_a$

10 = C + 100

C = -90

now,

$12 = -90e^k + 100$

$e^k = \dfrac{88}{90}$

$k = ln{\dfrac{88}{90}}$

at time equal to t

T(t) = 70

$T(t) = -90 (\dfrac{88}{90})^t + 100$

$70 = -90(\dfrac{88}{90})^t + 100$

$(\dfrac{88}{90})^t = \dfrac{1}{3}$

$t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{3})$

t = 48.88 s

hence, after 48.88 s the temperature of the body will be 70°C

b) time taken to reach 98°C

$T(t) = -90 (\dfrac{88}{90})^t + 100$

$98 = -90(\dfrac{88}{90})^t + 100$

$(\dfrac{88}{90})^t = \dfrac{1}{45}$

$t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{45})$

t = 390 s

hence, after 390 s the temperature of the body will be 98°C

5 0

3 years ago

Find x when y = 32, given that x varies inversely as y, and x = 132 when y = 4.

gizmo_the_mogwai [7]

Answer:

When y=32, x=16.5

Step-by-step explanation:

Find x when y = 32, given that x varies inversely as y, and x = 132 when y = 4.

We are given:

x varies inversely with y

We can write it as: $x\:\alpha \:\frac{1}{y}$

$x=\frac{k}{y}$

We have x = 132, when y=4

We can find value of k by using these values

$x=\frac{k}{y}\\132=\frac{k}{4}\\k=132*4\\k=528$

We need to find x when y=32

$x=\frac{k}{y}\\x=\frac{528}{32}\\x=16.5$

So, when y=32, x=16.5

6 0

3 years ago