MATHEMATICS
COLLEGE

B. du/dx = 2x + 2

C. dv/dx = 4xe4x

D. du/dx = 2x

Answer:

Answer:

D. du/dx = 2x

Step-by-step explanation:

Given to find dy/dx where;

Then when you let;

u=x²+2 and

Then

In u=x²+2 du/dx = 2x------------------------step 1

In e^4x, dv/dx = e^4x * d/dx (4x)

=e^4x *4 = 4e^4x------------------------------------step 2

HIGH SCHOOL

Evaluate cotθ if sinθ= √6/5

Answer: .

Step-by-step explanation: Given sinθ= √6/5.

We know radio of .

Therefore,

.

Let us apply Pythagoras Theorem to find the third side(Adjacent side) of the triangle .

Subtracting 6 from both sides, we get

Therefore, adjacent side =

We know,

Or

.

HIGH SCHOOL

An advisor to the mayor of a large city wants to estimate, within 3 minutes, the mean travel time to work for all employees who work within the city limits. He knows that the standard deviation for all travel times is 12.25 minutes. He also wants to achieve a 95% confidence interval. He will poll a random sample of city employees. At least how many employees should he poll?

Answer:

64

Step-by-step explanation:

Given that an advisor to the mayor of a large city wants to estimate, within 3 minutes, the mean travel time to work for all employees who work within the city limits.

Let X be the random variable denoting the time for employees to travel within city limit

Std dev of X

For 95% confidence interval Z critical 1.96 is used because population std dev is known

Margin of error

i.e.

where n is the desired sample size.

Simplify to get

Hence atleast 64 employees should he poll

MIDDLE SCHOOL

A label covers the lateral surface area of a can. The can has a diameter of 2.6 inches and a height of 4 inches. What is the lateral surface area of the label?

Answer:

First of all, lateral means the sides of the can in this case.

Calculate the surface area of the can, subtract the area of the top and bottom which are two circles, and theres the answer!

Step-by-step explanation:

1. SA= 2πrh+2πr^2

= 2(π)(1.3)(4) + 2(π)(1.3^2)

= 43.29- (π1.3^2)^2

=15.09

Please note that ^(a number) means to the power of (that number). Hope this helps!

Answer:

32.68

Step-by-step explanation:

Now we need the circumference of the circle, with the formula 2 pi r

2 times pi is about 6.28 that times the radius, (1.3) Which is 8.17.

So the circumference of the circle is 8.17, and the height is 4.

Multiply those together to get the surface area around the can. Not including the top and bottom.

8.17 * 4 = 32.68

The surface area of the label of the can is 32.68

HIGH SCHOOL

Which congruence theorem can be used to prove △ABR ≅ △ACR

The answer:

according to the figure, the sides of the two triangles △ABR and △ACR have specific congruence.

the congruences are:

AB≅ BC and AR ≅ CR, these mean that the sides are proportional

such triangles are called similar

so to prove that △ABR ≅ △ACR , we can use SSS theorem

side-side -side Similarity theorem

according to the figure, the sides of the two triangles △ABR and △ACR have specific congruence.

the congruences are:

AB≅ BC and AR ≅ CR, these mean that the sides are proportional

such triangles are called similar

so to prove that △ABR ≅ △ACR , we can use SSS theorem

side-side -side Similarity theorem

HL - Hypotenuse Leg

SAS - Side Angle Side

SSS - Side Side Side