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3 years ago

Polygon ABCDE rotates 45° clockwise about point F to produce polygon FGHIJ as shown. What is mBCD?

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

5 0

Polygon FGHIJ is the result of the rotation of ABCDE.

A = F ⇒ 117°
B = G ⇒ 90°
C = H ⇒ 127°
D = I ⇒ 90°
E = J ⇒ 117°

The measure of angle BCD remains the same because the rotation involves the whole polygon. Thus, it is still 127°

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Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with dia

Mademuasel [1]

An hemispherical dome is half a sphere. If the diameter is 60 m, then the radius is 30 m.

We can use differentials to solve this problem because we are adding a thin layer to the original dome, so the volume of the dome in increased by a differential of itself.

This differential volume that the dome is increased is equal to the volume of the coat of paint.

The volume of the dome can be written as:

$\begin{gathered} V=\frac{4\pi}{3}r^3 \\ \frac{dV}{dr}=\frac{4\pi}{3}\cdot3r^2\Rightarrow dV=\frac{4\pi}{3}\cdot3r^2\cdot dr=4\pi r^2\cdot dr \end{gathered}$

Now, we can calculate dV as:

$\begin{gathered} dV=4\pi r^2\cdot dr \\ dV\approx4\cdot3.14\cdot(30m)^2\cdot0.07\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}} \\ dV\approx12.57\cdot900m^2\cdot0.0007m \\ dV\approx7.92m^3 \end{gathered}$

Answer: the paint needed for this coat is approximately 7.92 m^3

5 0

1 year ago

Find an explicit rule for the nth term of the sequence. 3, -12, 48, -192, ...

Nimfa-mama [501]

Hello,
$u_{1}=3$
$u_{2}=3*(-4)$
$u_{3}=3*(-4)^2$

$u_{n}=3*(-4)^{n-1}$

6 0

3 years ago

Read 2 more answers

Translate this sentence into an equation.

motikmotik

Answer:

g = 61.

Step-by-step explanation:

g + 9 = 70 Subtract 9 from both sides of the equation:

g + 9 - 9 = 70 - 9

g = 61.

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3 years ago

You invest $3000 in an account at 3.5% per year simple interest. How much will

Schach [20]

Answer:

Option "D" is correct $3630

Step-by-step explanation:

At the beginning of the 7th year, the money has been in the account for 6 years.

The simple interest on $3000 at 3.5% for 6 years is I = prt:

(3000) = (.035) = (6) = 360

he amount in the account at the beginning of the 7th year is then the original amount plus the interest $3630.

3 0

2 years ago

Which equation can be used to solve the following word problem? Seth has 8 more nickels than dimes, and the total value of his c

9966 [12]

Answer:

Seth has 21 nickels

Step-by-step explanation:

Let n represent the number of nickels. Since Seth has 8 more nickels than dimes, then (n-8) is the number dimes.

Nickel is worth 5 cents and dime is worth 10 cents. Thus, n nickels are worth 5n cents and (n-8) dimes are worth 10(n-8) cents. The total value of Seth's coins is $2.35 that is 235 cents, then

$5n+10(n-8)=235.$

Solve this equation:

$5n+10n-80=235,\\ \\15n=235+80,\\ \\15n=315,\\ \\n=21.$

6 0

3 years ago