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3 years ago

Find an equation of he tangent line to the curve at the given point y= sinx+sin^2 x , (0,0)

1 answer:

4 0

Y = sin x + sin² x
y ` = f ` ( x ) = cos x + 2 sin x cos x
f `( 0 ) = cos 0 + 2 sin 0 cos 0 = 1
The tangent line formula:
y - y0 = f ` ( x0 ) ( x - x0 )
y - 0 = 1 · ( x - 0 )
Answer: y = x

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The owner of a 4000-gal oil truck loads the truck with gasoline and keroseno. The profit on each gallon of gasoline is 16e and o

lilavasa [31]

Answer:

There were 35 gallons of gasoline and 500 gallons of kerosene.

Step-by-step explanation:

Step 1: Write data for equation 1

Let gallons of kerosene be x

Let gallons of gasoline be y

Total capacity of truck is 4000

Step 2: Form equation 1

x + y = 4000

Step 3: Write data for equation 2

Profit of total gallons of kerosene is 0.12x

Profit of total gallons of gasoline is 16y

Total profit is $620

Step 4: Form equation 2

0.12x + 16y = 620

Step 5: Find x in terms of y from equation 1

x + y = 4000

x = 4000 - y

Step 6: Substitute value of x in equation 2

0.12x + 16y = 620

0.12 (4000 - y) + 16y = 620

480 - 12y + 16y = 620

4y = 620 - 480

y = 140/4

y = 35

Step 7: Substitute value of y in equation 1 to find x

0.12x + 16y = 620

0.12x + 16 ( 35 ) = 620

0.12x = 60

x = 500

There were 35 gallons of gasoline and 500 gallons of kerosene.

6 0

3 years ago

In triangle $abc$, $m\angle a = 90^\circ$, $m\angle b = 75^\circ$, and $bc = \sqrt {3}$ units. what is the area of triangle $abc

andrey2020 [161]

As we can see from the angles given, one is 90 degrees, the triangle should be a right triangle. We are given the two angles and one side which would represent the hypotenuse or the longest side. The area of a triangle is calculated from one half the product of its base and its height. From the given values, we need to calculate for the height and base. We do as follows:

sin 75 = height / √3
height = 1.67

cos 75 = base / √3
base = 0.45

Area = bh/2
Area = (0.45) (1.67) / 2
Area = 0.37 square units

Therefore, the area of the triangle is about 0.37 square units.

3 0

4 years ago

The range of the function is to because 4x is always positive

dem82 [27]

Answer:

NANIIIIIIIIIIII?

Step-by-step explanation:

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3 years ago

Read 2 more answers

A town has a population of 13,000 and grows at 4.5% every year what will be the population after 13 years to the nearest whole n

Vlad [161]

Answer:

23,039

Step-by-step explanation:

13,000×1.045¹³ ≅ 23,039

3 0

3 years ago

There are 4 chairs, but only 3 tables. Write the ratio of chairs to tables

lana66690 [7]

Answer:

4:3

Step-by-step explanation:

4:3 ratio of chairs to tables

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3 years ago