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3 years ago

How do I find the value of theta given to area of the sector and the radius

Mathematics

1 answer:

stira [4]3 years ago

7 0

$\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=24\\
A=90
\end{cases}\implies 90=\cfrac{\theta \pi 24^2}{360}\implies 90=\cfrac{\theta \pi 576}{360}
\\\\\\
90=\cfrac{8\theta \pi }{5}\implies 450=8\theta \pi \implies \cfrac{450}{8\pi }=\theta \implies \cfrac{225}{4\pi }=\theta \\\\\\ 17.904931 \approx \theta$

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The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their sum?

Serjik [45]

Answer:

2√5

Step-by-step explanation:

Using the formula for calculating resultant

R = √Fx + Fy

\sum Fx = -2sin 45 + 4 cos 45

\sum Fx = 2cos45

\sum Fx = 2(1/√2)

\sum Fx = 2/√2

Similarly;

\sum Fy = 2 cos 45 + 4 sin45

\sum Fx = 2(1/√2) + 4(1/√2)

\sum Fx = 6/√2

Magnitude = √(2/√2)²+6/√2)²

Magnitude = √4/2 + 36/2

Magnitude = √2+18

Magnitude = √20

Magnitude = 2√5

Hence the magnitude of their sum is 2√5

6 0

3 years ago

Read 2 more answers

Carlos and his friends are going to out to bowl, eat dinner, and see a movie. The starts at 8:10 p.M. And they want to arrive 20

Fantom [35]

Answer:

They should leave Carlo's house by 4:20 PM

Step-by-step explanation:

The movie starts at 8:10 pm, they want to arrive 20 minutes before the movie starts

20 minutes before 8:10 pm = 7:50 pm.

Hence, they should arrive by 7:50 pm

Duration of their activities before the movie is calculated as:

They will bowl for one hour and dinner will take 1 hour and 15 minutes. Travel time is 20 minutes to the bowling alley, 45 minutes ta the restaurant, and ten minutes to the theater.

: 1 hour + 1 hour 15 minutes + 20 minutes + 45 minutes + 10 minutes

= 2 hour 15 minutes + 75 minutes

= 2 hour 15 minutes +1 hour 15 minutes

= 3 hours 30 minutes in total.

The time they are meant to leave is calculated as:

7:50 pm - 3 hours 30 minutes

= 4:20pm

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3 years ago

I WILL GIVE ALL MY POINTS AND BRAINIEST FOR THE RIGHT ANSWER !!!!!!

arsen [322]

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3 years ago

PLEASE HELP ME GUYS OR I WONT PASS this calculus!!!!

KonstantinChe [14]

Answer:

b. $\displaystyle \frac{1}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

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f(x) = cxⁿ
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Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle H(x) = \sqrt[3]{F(x)}$

Step 2: Differentiate

Rewrite function [Exponential Rule - Root Rewrite]: $\displaystyle H(x) = [F(x)]^\bigg{\frac{1}{3}}$
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Simplify: $\displaystyle H'(x) = \frac{F'(x)}{3}[F(x)]^\bigg{\frac{-2}{3}}$
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Step 3: Evaluate

Substitute in x [Derivative]: $\displaystyle H'(5) = \frac{F'(5)}{3[F(5)]^\bigg{\frac{2}{3}}}$
Substitute in function values: $\displaystyle H'(5) = \frac{6}{3(8)^\bigg{\frac{2}{3}}}$
Exponents: $\displaystyle H'(5) = \frac{6}{3(4)}$
Multiply: $\displaystyle H'(5) = \frac{6}{12}$
Simplify: $\displaystyle H'(5) = \frac{1}{2}$