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3 years ago

Want an equation in point slope form of the line through the given point and with the given slope

Mathematics

1 answer:

coldgirl [10]3 years ago

3 0

Answer:

<h3>The answer is option D</h3>

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

$y - y_1 = m(x - x_1)$

where

m is the slope

( x1 , y1) is the point

From the question the point is ( - 2 , -5) and slope 0 is

The equation of the line is

$y + 5 = 0(x + 2) \\$

We have the final answer as

Hope this helps you

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How to get the values of a and b? i need to differentiate first the equation?

Sidana [21]

Answer:

$a=-6$

$b=-\frac{31}{6}$

Step-by-step explanation:

We are given the equation of the curve:

$y=2x^{3}+bx-5$ (1)

And the equation of the line that is normal (perpendicular to that curve) in the point $(x,y)=(1,2)$ :

$y=\frac{a}{5}x+\frac{16}{5}$ (2)

Note this equation has the form $y=mx+B$ , where $m=\frac{a}{5}$ is the slope of the line that es normal to the curve and $B=\frac{16}{5}$ the intersection of that line with the y-axis.

Well, let’s begin by finding the slope of the line that is tangent to the curve by differentiating the equation (1):

$\frac{dy}{dx}=6x^{2}+b$ (3)

Then, we have to evaluate that when $x=1$ (remember we are given the point $(1,2)$ ):

$\frac{dy}{dx}_{x=1}=6(1)^{2}+b=6+b$ (4) This is the slope of the line that is tangent to the curve

And the slope of the line that is perpendicular to that tangent line is its negative reciprocal. Hence:

$m=-\frac{1}{6+b}$ (5) This is the slope of the line normal to the curve

Then:

$m=\frac{a}{5}=-\frac{1}{6+b}$

$a=\-frac{5}{6+b}$ (6)

Rewritting (2):

$y=-\frac{5}{5(6+b)}x+\frac{16}{5}$ (7)

Evaluating in the point $(1,2)$ :

$2=-\frac{5}{5(6+b)}1+\frac{16}{5}$ (8)

Finding $b$ :

$b=-\frac{31}{6}$ (9) This is the value of $b$

Substituting (9) in (6):

$a=\-frac{5}{6-\frac{31}{6}}$ (10)

$a=\-frac{31}{6}$ (11) This is the value of $a$

8 0

3 years ago

How do you right <br> 0.125 as a whole number

LenaWriter [7]

Step-by-step explanation:

divide 1 by 0.1 to 5 and this will tell you what you need to multiply it by in order to make 0.125

1/0.125=8

thus : 8 *0.125 =1

8 0

3 years ago

Suppose you observe a spot exchange rate of $1.50/€. if interest rates are 5% apr in the u.s. and 3% apr in the euro zone, what

Varvara68 [4.7K]

The no-arbitrage 1-year forward rate in $/€, F($/<span>€) is given by

$F(\$/euro)=S(\$/euro)\times \frac{1+i_\$}{1+i_{euro}}$

where S(</span>$/euro) is the spot exchange rate in $/€, $i_\$$ is the interest rate in the US and $i_{euro}$ <span> is the exchange rate in the Euro zone.

Thus, given that </span>the <span>spot exchange rate is $1.50/€ and interest rates are 5% apr in the u.s. and 3% apr in the euro zone.

The no-arbitrage 1-year forward rate is given by:

$F(\$/euro)=1.50\times \frac{1+0.05}{1+0.03} \\ \\ =1.50\times \frac{1.05}{1.03} =1.50\times1.019 \\ \\ =\bold{\$1.5291}$ </span>

4 0

3 years ago

A bakery has one 200 kg bag of sugar. The bakery uses 6.25 kg of sugar each day. How much sugar will it use in 8 days? How many

Nookie1986 [14]

Answer:

BOO!

Step-by-step explanation:

AHH!

7 0

3 years ago

Kamal is buying supplies for a science lab. He needs a piece

V125BC [204]

Answer:

kamal needs to buy 84 in of wire.

Step-by-step explanation:

multiply the length value by 12:

if he wants 7 feet, and the store only sells it in inches, then we know what a foot is twelve inches so 12x7=84.

hope this helped! :D <3

8 0

3 years ago

Read 2 more answers