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riadik2000 [5.3K]
3 years ago
12

Find the value of c such that y= x + c is a tangent to the parabola y = x squared - x - 12

Mathematics
1 answer:
Bond [772]3 years ago
5 0

Answer:

c = –13

Step-by-step explanation:

by property of tangent line, equation

x² – x – 12 = x + c

x² – 2x – 12 – c = 0

has only one solution, which mean

– 12 – c = 1

c = –13

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A magazine currently has 8700 subscribers for its online web version. It is adding members at the rate of R(t) = 190e0.03t subsc
aleksklad [387]

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<u>Solution:</u>

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\begin{array}{l}{\mathrm{R}(\mathrm{t})=190 \mathrm{e}^{0.03 \mathrm{t}} \text { subscribers/month }} \\\\ {\mathrm{S}(\mathrm{t})=\mathrm{e}^{-0.06 \mathrm{t}}}\end{array}

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\begin{array}{l}{\mathrm{R}(36)=190 \mathrm{e}^{0.03 \times(36)}=190 \times(2.944)} \\\\ {\mathrm{R}(36) \approx 560} \\\\ {\mathrm{S}(36)=\mathrm{e}^{-0.06 \times(36)}=0.12}\end{array}

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