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2 years ago

The radius of the circle on a basketball court is 6 feet. What are the approximate circumference and area of the circle?

1 answer:

4 0

Circumference formula - 2pi(r)
area formula - pi(r)^2
in both of the formulas r is the radius so

to find circumstance: 2(pi)(6) = 25.68 feet

to find area: pi(6)^2 = 113.04 feet

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Justin is saving money for a new gaming console. He currently has $200 in a saving account and each week $10 to his balance. In

Nikitich [7]

$500 - $200 = $300 dollars left.

$300 divided by $10 = 30 weeks.

8 0

3 years ago

Evaluate the interval (Calculus 2)

Darya [45]

Answer:

$2 \tan (6x)+2 \sec (6x)+\text{C}$

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{12}{1-\sin (6x)}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int a\:\text{f}(x)\:\text{d}x=a \int \text{f}(x) \:\text{d}x$\end{minipage}}$

If the terms are multiplied by constants, take them outside the integral:

$\implies 12\displaystyle \int \dfrac{1}{1-\sin (6x)}\:\:\text{d}x$

Multiply by the conjugate of 1 - sin(6x) :

$\implies 12\displaystyle \int \dfrac{1}{1-\sin (6x)} \cdot \dfrac{1+\sin(6x)}{1+\sin(6x)}\:\:\text{d}x$

$\implies 12\displaystyle \int \dfrac{1+\sin(6x)}{1-\sin^2(6x)} \:\:\text{d}x$

$\textsf{Use the identity} \quad \sin^2 x+ \cos^2 x=1:$

$\implies \sin^2 (6x) + \cos^2 (6x)=1$

$\implies \cos^2 (6x)=1- \sin^2 (6x)$

$\implies 12\displaystyle \int \dfrac{1+\sin(6x)}{\cos^2(6x)} \:\:\text{d}x$

Expand:

$\implies 12\displaystyle \int \dfrac{1}{\cos^2(6x)}+\dfrac{\sin(6x)}{\cos^2(6x)} \:\:\text{d}x$

$\textsf{Use the identities }\:\: \sec \theta=\dfrac{1}{\cos \theta} \textsf{ and } \tan\theta=\dfrac{\sin \theta}{\cos \theta}:$

$\implies 12\displaystyle \int \sec^2(6x)+\dfrac{\tan(6x)}{\cos(6x)} \:\:\text{d}x$

$\implies 12\displaystyle \int \sec^2(6x)+\tan(6x)\sec(6x) \:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$

$\boxed{\begin{minipage}{6 cm}\underline{Integrating $ \sec kx \tan kx$}\\\\$\displaystyle \int \sec kx \tan kx\:\text{d}x= \dfrac{1}{k}\sec kx\:\:(+\text{C})$\end{minipage}}$

$\implies 12 \left[\dfrac{1}{6} \tan (6x)+\dfrac{1}{6} \sec (6x) \right]+\text{C}$

Simplify:

$\implies \dfrac{12}{6} \tan (6x)+\dfrac{12}{6} \sec (6x)+\text{C}$

$\implies 2 \tan (6x)+2 \sec (6x)+\text{C}$

Learn more about indefinite integration here:

brainly.com/question/27805589

brainly.com/question/28155016

3 0

2 years ago

Please help what are the answers

krok68 [10]

Part b is 64 i think
hope this helps:))

4 0

2 years ago

NO LINKS!!!

allochka39001 [22]

Part A

Converse = "If corresponding angles are equal, then two lines are parallel"
Result = True

Explanation:

Refer to the converse of the corresponding angles theorem. The original version is stated as part A, and the converse is marked in bold above.

Conditional statements are of the form "if this, then that". Symbolically we can use the template "If P, then Q". The P and Q are placeholders for logical statements.

The converse of "if P, then Q" is "If Q, then P". We swap the positions of P and Q. Do not negate either piece.

========================================================

Part B

Converse = "If angle C is 70 degrees, then the sum of angles A and B is 110 degrees"
Result = True

Explanation:

Recall that for any triangle, the three interior or inside angles always add to 180 degrees. In short: A+B+C = 180. If C = 70, then A+B = 180-C leads to A+B = 180-70 and A+B = 110. This process can be reversed.

========================================================

Part C

Converse = "If two lines are not parallel, then alternate interior angles k and s are not equal"
Result = True

Explanation:

For more information, check out the converse of the alternate interior angles theorem. The regular version of the theorem is "If two lines are parallel, then the alternate interior angles are congruent".

The converse of this theorem flips things to say: "If alternate interior angles are congruent, then the lines are parallel".

========================================================

Part D

Converse = "If John loses his money, then he throws coins in the fountain"
Result = False

Explanation:

Throwing coins in a fountain is one way to lose money, but there are other ways. He could drop a coin somewhere, or leave the coin somewhere he forgot.

In other words, just because he lost his money does not mean he threw a coin in the fountain.

8 0

1 year ago

Emma has money in two savings accounts. One rate is 7% and the other is 8%. If she has $450 more in the 8% account and the total

hodyreva [135]

Answer:

420

Step-by-step explanation:

3 0

3 years ago