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SpyIntel [72]
3 years ago
5

Jean drove 70 miles per hour for a total of 420 miles on a trip. She used the equation below to calculate the time, t, it would

take her to complete the trip.
What is the constant of proportionality in the equation?
A.
6
B.
420
C.
t
D.
70
Mathematics
2 answers:
Ket [755]3 years ago
8 0

Answer:

D because she is constantly going 70 MPH

Step-by-step explanation:

hope this helps

il63 [147K]3 years ago
8 0

Answer:

D. 70

Step-by-step explanation:

Distance = k × time

70 = k(1)

k = 70

Distance = 70 × time

time to complete the journey:

420 = 70 × time

time = 420 ÷ 70

time = 6 hours

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Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?
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Step-by-step explanation:

\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}

\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}

\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}

\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}

\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}

\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}

Taking sin²θ common in both numerator & denominator, We get :

\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}

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\mathsf{Given :\;cot\theta = \dfrac{1}{\sqrt{5}}}

\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}

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\mathsf{\implies \dfrac{5 - 1}{5 + 1}}

\mathsf{\implies \dfrac{4}{6}}

\mathsf{\implies \dfrac{2}{3}}

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