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2 years ago

Find an equation of the tangent line to the graph of

Mathematics

2 answers:

lakkis [162]2 years ago

6 0

Answer:

y + 4 = -3 (x - 5)

In other words,

y = -3 x + 11

Step-by-step explanation:

The slope of the tangent line to y = g(x) at x = 5 is the same as the value of g'(x). g'(5) = 3. Therefore, 3 will be the slope of the tangent line.

The tangent line goes through the point of tangency (5, g(5)). g(5) = -4. Therefore, the tangent line passes through the point (5, -4).

Apply the slope-point form of the line. The equation for a line with slope m that goes through point (a, b) will be y - b = m(x - a). For the tangent line in this question,

m = 3,
a = 5, and
b = -4.

What will be the equation of this line?

Darina [25.2K]2 years ago

5 0

Answer: y = 3x - 19

Step-by-step explanation:

y = g(x)

g(5) = -4

⇒ y = -4 when x = 5 ⇒ (5, -4)

g'(5) = 3 means that when x = 5, the tangent slope (m) = 3

because the first derivative gives the tangent slope

Use the Point-Slope formula to find the equation of the line that passes through the point (5, -4) with slope (m) of 3:

y - y₁ = m(x - x₁)

y -(-4) = 3(x - 5)

y + 4 = 3x - 15

y = 3x - 19

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3 years ago

Convert 15°C to Fahrenheit. Use the formula F = 9/5C + 32.

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3 years ago

Read 2 more answers

Without using your calculator, decide which of these is larger: log8 62 or log7 50. How confident are you of your answer? Explai

nataly862011 [7]

Answer:

Step-by-step explanation:

log8 62 = x1

8^x1= 62

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6 0

3 years ago

Plz help me with this

AnnZ [28]

Answer: $\bold{A)\quad y=5sin\bigg(\dfrac{6}{5}x-\pi\bigg)-4}$

Step-by-step explanation:

The general form of a sin/cos function is: y = A sin/cos (Bx-C) + D where the period (P) = 2π ÷ B

In the given function, $B=\dfrac{6}{5}$ → $P=2\pi \cdot \dfrac{5}{6}=\dfrac{10\pi}{3}$

Half of that period is: $\dfrac{1}{2}\cdot \dfrac{10\pi}{3}=\large\boxed{\dfrac{5\pi}{3}}$

Calculate the period for each of the options to find a match:

$A)\quad B=\dfrac{6}{5}:\quad 2\pi \div \dfrac{6}{5}=2\pi \cdot \dfrac{5}{6}=\dfrac{5\pi}{3}\quad \leftarrow\text{THIS WORKS!}\\\\\\B)\quad B=\dfrac{6}{10}:\quad 2\pi \div \dfrac{6}{10}=2\pi \cdot \dfrac{10}{6}=\dfrac{10\pi}{3}\\\\\\C)\quad B=\dfrac{5}{6}:\quad 2\pi \div \dfrac{5}{6}=2\pi \cdot \dfrac{6}{5}=\dfrac{12\pi}{5}\\\\\\D)\quad B=\dfrac{3}{10}:\quad 2\pi \div \dfrac{3}{10}=2\pi \cdot \dfrac{10}{3}=\dfrac{20\pi}{3}$

7 0

3 years ago

Evelyn has $524.96 in her checking account. She must maintain a $500 balance to avoid a fee. She wrote a check for $32.50 today.

cupoosta [38]

A linear inequality to represent the algebraic expression is given as 492.46 - x ≥ 500

<h3>Linear Inequality</h3>

Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1.

In this problem, her minimum balance must not decrease beyond $500 or she will pay a fee.

where

x = withdrawals

The inequality to represent this can be written as

524.96 - 32.50 - x ≥ 500

Simplifying this;

492.46 - x ≥ 500

The linear inequality is 492.46 - x ≥ 500

Learn more on linear inequality here;

brainly.com/question/23093488

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4 0

1 year ago