Math Answers

The first term in the arithmetic sequence is 1 and the fifth is 3. What is the tenth term in the sequence?

Let it be f (x) = 2x³ - 9x² - 10.

a) specify the zeros of the f derivate of the function.

b) with what variable x values does f on grow?

c) determine between the maximum and the minimum value of the function f and [-4, 4].

Find a basis for the following subspace of

R

5

.

J

=

{

⃗

x

∈

R

5

∣

x

1

=

x

2

=

x

5

,

x

3

+

x

4

=

}

What is the dimension of

J

?

(a) Rowanberries contain 6,2% sugar. Nine-tenths of the rest of the material is water. The container contains 500 g of rowanberries. How many grams of water do the berries in the container contain? 

b) Up to 32.7% of the fox's hair may be on the fox's tail. If the fox's tail has a total of 15,400 hairs, how many hairs are there elsewhere in the fox's turkey? 

c) A small entrepreneur sells the jewelry he or she makes at a price of 12 euros per piece, which means that the average sales are 340 pieces per month. He will lower the price of jewelery by 11%, increasing his monthly jewelery sales by 5%. What percentage of an entrepreneur’s income will change? 

Is the interaction variation significant in case of the following information concerning mileage based on

different brands of gasoline and cars?

Find the solution of (3x-y+6)dx +(6x-2y-6)dy=0 using Case 1

6. Ship A is travelling south at the rate of 2 km/hr, at the instant that ship B, which is 32

miles south of ship A, is travelling east at rate of 4 km/hr.

a) Are they separating or approaching at the end of 2 hrs, and at what rate?

b) At what time are they nearest together?

c) What is their minimum distance apart?

5. A spherical snowball with an outer layer of ice melts, so that the radius of the snowball

decreases at the rate of 1/5 cm/sec. Find the rate at which the volume decreases when the

diameter is 50 cm.

3. An open rectangular box w/ square ends to hold 6400 cu ft, is to be built at a cost of

Php 75.00 per sq ft. for the base and

Php 25.00 /sq ft for the sides. Find the most economical dimensions.

2. A boy is flying a kite at a height of 150 ft. If the kite moves horizontally away from the

boy at the rate of 20 ft/sec, how fast is the string being paid out when the kite is 250 ft from him?