Tangent line of f(x) = sec x @ (pi/3, 2)

1 answer:

3 0

The derivitive of sec(x) is sec(x)tan(x)

find the slope at pi/3

sec(pi/3)=2
tan(pi/3)=√3

sec(x)tan(x) at x=pi/3 is 2√3

for slope=m and a point is (x1,y1)
the equation is
y-y1=m(x-x1)
slope=2√3
point=(pi/3,2)

equation is
y-2=2√3(x-pi/3)

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Verify sin^4 x - sin^2 x = cos^4 x - cos^2 x is an identity

Citrus2011 [14]

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

sin(x)^4 - sin(x)^2 = cos(x)^4 - cos(x)^2

sin(x)^2 = 1 - cos(x)^2:

sin(x)^4 - 1 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2

-(1 - cos(x)^2) = cos(x)^2 - 1:

cos(x)^2 - 1 + sin(x)^4 = ^?cos(x)^4 - cos(x)^2

sin(x)^4 = (sin(x)^2)^2 = (1 - cos(x)^2)^2:

-1 + cos(x)^2 + (1 - cos(x)^2)^2 = ^?cos(x)^4 - cos(x)^2

(1 - cos(x)^2)^2 = 1 - 2 cos(x)^2 + cos(x)^4:

-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = ^?cos(x)^4 - cos(x)^2

-1 + cos(x)^2 + 1 - 2 cos(x)^2 + cos(x)^4 = cos(x)^4 - cos(x)^2:

cos(x)^4 - cos(x)^2 = ^?cos(x)^4 - cos(x)^2

The left hand side and right hand side are identical:

Answer: (identity has been verified)

3 0

3 years ago

A department store sells a pair of shoes with an 87% markup. If the store bought the pair of shoes for $55.25, what is the selli

kolbaska11 [484]

Markup means they sell it for that percentage more than they bought it for. First let's calculate how much they will mark it up for:

$\sf 55.25\cdot 87\%$

Convert 87% into a decimal(87/100):

$\sf 55.25\cdot 0.87$

Multiply:

$\sf\approx 48$

This is how much they'll mark it up, now let's add it to how much they bought it for to find out the selling price:

$\sf 48+55.25\approx\boxed{\sf \$ 103}$