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3 years ago

Can someone help me with this and answer asap.

Mathematics

2 answers:

Ber [7]3 years ago

7 0

Answer:

Length of the pendulum will be 254 centimeters.

Step-by-step explanation:

In this question the formula to calculate the time period is given and we have to measure the length of new pendulum to be replaced with.

Formula is $T= 2\pi \sqrt\frac{L}{980}$ centimeters

Given parameters is T = 3.2 seconds

By putting the value of T in the formula

$3.2 = 2\pi \sqrt{\frac{L}{980} }$

$\frac{3.2}{2\pi } =\sqrt{\frac{L}{980} }$

$(\frac{1.6}{\pi })^{2} = \frac{L}{980}$

$L = (\frac{1.6}{\pi })^{2}(980) = \frac{2508.8}{(3.14)^{2} }$

L = 254 centimeters.

Karo-lina-s [1.5K]3 years ago

6 0

Answer:

Choice B is correct answer.

Step-by-step explanation:

We have given the time period of pendulum.

We have to find the the length of pendulum.

We have given the formula for time period of new pendulum.

T = 2π√L/980

Separating the length from above formula, we have

T² = 4π²(L/980)

980×T² = 4π²× L

L = 980T² / 4π²

Putting the given value of T, we have

L = 980(3.2)² / 4π²

L = 980(10.24) / 4π²

L = 254 centimeters

Hence, the length of new pendulum is 254 centimeters.

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14^2 - square root o f 144

stealth61 [152]

Answer:

184

Step-by-step explanation:

The sqrt(144) = 12

14^2 = 196

196 - 12 - 184

7 0

3 years ago

Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

$b^{2} = a^{2} + c^{2} - 2\;a\cdot c\cdot \cos{B}$ .

$\displaystyle \cos{B} = \frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}$ .

$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

7 0

3 years ago

If a monopolist supplies goods at a price; P = 170 - Q, with marginal cost; MC = 52. Find the quantity and price

Arada [10]

Answer:

Quantity = 59 units

Price = $111

Step-by-step explanation:

The Demand function is given by

$P = 170 - Q$

The Marginal cost is given by

$MC = 52$

We are asked to find the quantity and price of goods.

Firstly, obtain the Marginal revenue function from the demand function

The Total revenue is given by

$TR = P \times Q \\\\TR = (170 - Q) \times Q \\\\TR = 170Q - Q^2$

The Marginal revenue is the derivative of the Total revenue,

$MR = \frac{d}{dQ} (TR) = 170Q - Q^2 \\\\MR = \frac{d}{dQ} (TR) = 170 - 2Q \\\\$

Assuming that the monopolist maximizes profits,

$MR = MC \\\\170 - 2Q = 52\\\\2Q = 170 - 52\\\\2Q = 118\\\\Q = 118/2\\\\Q = 59$

Therefore, the quantity is 59 units.

The price of each good is

$P = 170 - Q \\\\P = 170 - 59 \\\\P = 111$

Therefore, the price is $111.

3 0

3 years ago

3<br> What is the difference of<br> 21<br> ?<br> 4

PilotLPTM [1.2K]

Answer:

The difference is 4–3. If you want the difference between 3 and -4, then the difference is 7.

Step-by-step explanation:

6 0

3 years ago

(tap the picture in order to see the hole thing) guys i really need help plz its so annoying that i cant answer it

vlabodo [156]

David's total income is ($8/hr)x + ($11/hr)y.

This problem requires us to write and solve an inequality:

8x + 11(15)<$200

Solving for x: 8x < $200-$165, or 8x < $35. Strictly speaking, x = 4.375 hrs, but if we assume that David must work an integer # of hours, then x=5 full hours.

6 0

3 years ago