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3 years ago

Equation of the tangent line

Mathematics

1 answer:

GalinKa [24]3 years ago

5 0

Find the eqn. of the tangent line to the curve of f(x) = x^2 + 5x -5 at (0,-5).

Differentiate f(x) to obtain an expression for the derivative (slope of the tangent line):

f '(x) = 2x + 5

Subst. 0 for x here: f '(0) = 2(0) + 5 = 5 (at the point (0, -5))

Use the point-slope equation of a str. line to find the eqn of the tan. line:

y-k = m(x-h), where (h,k) is a point on the line and m is the slope:

y - [-5] = 5(x-0), or y+5 = 5x. Then y = 5x - 5 is the eqn. of the TL to the given curve at (0,-5).

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3 years ago

Read 2 more answers

If x and y satisfy both 9x+2y=8 and 7x+2y=4, then y=?

Alex

Answer:

The value of y is -5

Step-by-step explanation:

we have

$9x+2y=8$ ------> equation A

$7x+2y=4$ ------> equation B

we know that

If x and y satisfy both equations, then (x,y) is the solution of the system of equations

Using a graphing tool

Remember that

The solution of the systems of equations is the intersection point both graphs

The intersection point is (2,-5)

therefore

The solution of the system of equations is the point (2,-5)

The value of y is -5

7 0

3 years ago

Which inequalities correctly show the relationship between the numbers 13, −4, and −17?

lutik1710 [3]

Answer:

13 > -17 < -4

Step-by-step explanation

13 = postive number

-17 and -4 = negtive.

13 is greater than -17

Since negtive is oppistie of postive it goes backwards.

So -4 is greater than -17

(Im new to this so Im not sure if it is correct)

3 0

3 years ago

The Louvre is an art museum in Paris. A glass square base pyramid sits in front of the entrance to the museum. If the pyramid is

Sveta_85 [38]

Answer:

lateral area = 2320 m²

Step-by-step explanation:

The question wants us to calculate the lateral area of a square base pyramid. The square base pyramid has a side of 40 meters.The height is 21 meters.

Half of the square base is 40/2 = 20 meters . With the height it forms a right angle triangle. The hypotenuse side is the slant height of the pyramid.

Using Pythagoras's theorem

c² = a² + b²

c² = 20² + 21²

c² = 400 + 441

c² = 841

square root both sides

c = √841

c = 29 meters

The slant height of the pyramid is 29 meters.

The pyramid has four sided triangle. The lateral area is 4 multiply by the area of one triangle.

area of triangle = 1/2 × base × height

base = 40 meters

height = 29 meters

area = 1/2 × 40 × 29

area = 580

area of one triangle = 580 m²

Lateral area = 4(580)

lateral area = 2320 m²

5 0

3 years ago

Banabas must pay his ex-wife an amount of R350 000 in two years’ time. Calculate the amount that he must invest today to have th

White raven [17]

Answer:

He must invest R297 521 today.

Step-by-step explanation:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Banabas must pay his ex-wife an amount of R350 000 in two years’ time.

This means that $t = 2, A(t) = 350000$