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2 months ago

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2 months ago

To find the total amount of floor covered add the amount of carpeting and tiling together. So 1/2 = 2/4, then 1/4 + 2/4 = (1 + 2) / 4 = 3/4. 3/4 of Captain Kirk's floor is covered.

Question

A holding pen for cattle must be square and have a diagonal length of 84 84 meters. a. find the length of a side of the pen.
b. find the area of the pen.

Solution 1

We know that

Applying the Pythagoras Theorem

cÂ²=aÂ²+bÂ²

in a square

a=b

c is the diagonal-----> 84 m

cÂ²=2aÂ²--------> aÂ²=cÂ²/2-----> aÂ²=84Â²/2-----> aÂ²=3528-----------> a=âˆš3528 m

the answer part a) is

âˆš3528 m or 59.40 m

the area of the pen is aÂ²------> 3528 mÂ²

**the answer Part b) isÂ **

**3528 mÂ²**

Applying the Pythagoras Theorem

cÂ²=aÂ²+bÂ²

in a square

a=b

c is the diagonal-----> 84 m

cÂ²=2aÂ²--------> aÂ²=cÂ²/2-----> aÂ²=84Â²/2-----> aÂ²=3528-----------> a=âˆš3528 m

the answer part a) is

âˆš3528 m or 59.40 m

the area of the pen is aÂ²------> 3528 mÂ²

Question

Sara loves to go hiking. This week she hiked 3 miles on Monday, 4 miles on Tuesday, and 3 miles on Thursday. Last week Sara hiked 8 miles. How many more miles did Sara hike this week than last week?*

Solution 1

This week, the total = 3 + 4 + 3 = 10 miles

Last week = 8 miles.

The number more = 10 - 8 = 2 miles.

2 miles more.

Last week = 8 miles.

The number more = 10 - 8 = 2 miles.

2 miles more.

Question

Use the intercept form to find the equation of the line with the given intercepts. the intercept form of the equation of a line with intercepts (a, 0) and (0, b.is

Solution 1

Assuming that the "given intercepts" are (a,0) and (0,b), the equation of the line thru these 2 pts. is easily found thru use of the point-slope formula:

Â Â Â Â Â b-0

m = -------- = -b/a

Â Â Â Â Â 0-a

Then y-0 = (-b/a)(x-a), or y = (-b/a)(x-a) (answer)

Â Â Â Â Â b-0

m = -------- = -b/a

Â Â Â Â Â 0-a

Then y-0 = (-b/a)(x-a), or y = (-b/a)(x-a) (answer)

Question

donovan bought 5 1/2 pounds of flour for $ 8.25. How much did the flour cost per pound? Give your answer in the correct dollar form.

Solution 1

Unit price per pound =Â Â $ 8.25 / 5.5 = $1.50

answer

the flour cost $ 1.50 per poundÂ

answer

the flour cost $ 1.50 per poundÂ

Solution 2

We want the unit rate:Â cost of flour per pound.

$8.25

--------- = $1.50/lb

5.5 lb

$8.25

--------- = $1.50/lb

5.5 lb

Question

A price of a new car was Â£12500
It was reduced to Â£11625
Work out the percentage reduction

Solution 1

Â£12500 -Â Â£11625 =Â Â£875

Â£875 /Â Â£12500 = 0.07 = 7%

answer

7%

Â£875 /Â Â£12500 = 0.07 = 7%

answer

7%

Question

How many ounces of water should you drink for every 20 minutes of activity? 12?

Solution 1

Yes because it a fact

Question

How to find an area of a circumbscribed hexagon using the diameter?

Solution 1

The formula for the area of a circumscribed hexagonÂ = 1/2 * 6 * a * rÂ Â where a = side length and r = radius of the circleÂ ( = 1/2 the diameter)Â so in terms of the diameter and side length its 1/2 * 1/2 * 6 *d * aÂ =Â Â 1.5 ad.

You can calculate the value of aÂ by using trigonometryÂ You consider one of the 6 isosceles triangles that make up the hexagon. The vertex angle of these triangles = 60 degrees so:-

tan 30Â =Â 1/2 a /Â rÂ =Â 1/2 a / 1/2 dÂ = a/d

a =Â d tan 30Â = sqrt3 d / 3

Substituting for a :-Â

So theÂ required formula for the area of the hexagon = 1.5 adÂ

= 1.5 * sqrt3 d * d / 3Â =Â 1/2 sqrt3 d^2Â Â Answer

You can calculate the value of aÂ by using trigonometryÂ You consider one of the 6 isosceles triangles that make up the hexagon. The vertex angle of these triangles = 60 degrees so:-

tan 30Â =Â 1/2 a /Â rÂ =Â 1/2 a / 1/2 dÂ = a/d

a =Â d tan 30Â = sqrt3 d / 3

Substituting for a :-Â

So theÂ required formula for the area of the hexagon = 1.5 adÂ

= 1.5 * sqrt3 d * d / 3Â =Â 1/2 sqrt3 d^2Â Â Answer

Question

How much money must be deposited today to become â€‹$1300 in 20 years at 7.5% compoundedâ€‹ continuously?

Solution 1

Use the formula for Amount for continuous compounding:

A = Pe^(rt)

Here A = $1300, r = 0.075 and t = 20 yrs.Â Thus,

1300 = P*e^(0.075*20), orÂ Â 1300 = P (4.482).

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â $1300

Solving for P:Â P = ----------------- = $290.07Â (answer)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4.482

A = Pe^(rt)

Here A = $1300, r = 0.075 and t = 20 yrs.Â Thus,

1300 = P*e^(0.075*20), orÂ Â 1300 = P (4.482).

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â $1300

Solving for P:Â P = ----------------- = $290.07Â (answer)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4.482

Question

How to find all values of x where the tangent line is horizontal?

Solution 1

Your question is a rather general one.Â However, it can be said that differentiating the given function of x with respect to x and setting the result = to 0, then solving for x, will produce all values of x where the t. l. is horizontal.

Question

If the discriminant is positive how many solutions are there

Solution 1

**Answer:**

yields 2 real roots

**Step-by-step explanation:**

To find the number of real roots for a quadratic, we apply the discriminate. The discriminate is the inside portion of the square root from the quadratic formula.

â€¢ yields 2 real roots

â€¢ yields 1 real root

â€¢ [tx]b^2-4ac<0[/tex] yields no real roots

Example:

where a=4, b=-7, and c=2

.

It has 2 real roots

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