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Leona [35]
3 years ago
8

How many minutes is 7:43 to 8:41

Mathematics
2 answers:
Arlecino [84]3 years ago
4 0
Between 7:43 and 8:41, there are 58 minutes.

frez [133]3 years ago
3 0
It is 58 minutes. :]
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Christina owns a café. The graph shows the number of cups of tea that were sold at her café each hour past noon. Based on the mo
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Where's the graph? I need the graph to answer

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3 years ago
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Match each figure with the number of edges it has.
Rashid [163]

Answer:

Rectangular prism- 12 edges

Rectangular pyramid- 8 edges

Triangular pyramid- 6 edges

Triangular prism- 9 edges

I hope this helps!

6 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
Complete the point-slope equation of the line through (-5,4) and (1,6). Use exact numbers.
BigorU [14]

ANSWER

y - 6 =  \frac{2}{7} (x - 1)

EXPLANATION

The point-slope equation of a straight line is given by:

y-y_1=m(x-x_1)

Where m is the slope.

The line goes through (-5,4) and (1,6).

The slope of this line is,

m =  \frac{6 - 4}{1 -  - 6}

m =  \frac{2}{7}

The point-slope equation is

y  - 6 =  \frac{2}{7} (x - 1)

7 0
3 years ago
PLEASE HELP ME!! #4 Suzan took out a $700 loan from the bank. At the end of 5 years, she pays back the principal, plus $105in si
Veseljchak [2.6K]

Answer:

3%

Step-by-step explanation:

105 = 700 x r x 5

r = 105 / ( 700 × 5 ) = 0.03

r = 0.03

0.03 in percent is 3%

3 0
2 years ago
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