MATHEMATICS HIGH SCHOOL

Find two rational numbers between -1 and 0

Answers

Answer 1

Answer:

Answer:

-1/2 and -3/4

Step-by-step explanation:

rational numbers are numbers that can be expressed in a fraction

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A 109 ft tree casts a shadow that is 130 ft long. what is the angle of elevation of the sun?

Answers

The angle of elevation of the sun is approximately 40 degrees

The scenario forms a right angle triangle.

The height of the tree is the opposite side of the right angle triangle formed .

The shadow casted on the ground is the adjacent side of the triangle.

Therefore, using trigonometric ratio, the angle of elevation can be found as follows:

height of the tree = 109 ft

length of the shadow = 130 ft

let

the angle = ∅

tan ∅ = opposite / adjacent

tan ∅ = 109 / 130

∅ = tan⁻¹ 0.83846153846

∅ = 39.978520842

∅ ≈ 40°

learn more on trigonometry here: brainly.com/question/24303045

Answer: 40°

Explanation:

$\tan(\theta) = \cfrac{109}{130}$

$\theta = 40 \textdegree$

The Wise Orange wonders about the purpose of knowing the degree of elevation.

County X has a population density of 250 people per square mile. The totalpopulation of the county is 150,000. Which geometric model could be the shape of
county X?
A a parallelogram with a base of 25 miles and a height of 25 miles
B a rectangle that is 15 miles long and 45 miles wide
C a right triangle with a leg that is 30 miles long and a hypotenuse that is
50 miles long
D a trapezoid with base lengths of 10 miles and 30 miles and a height of
25 miles

Answers

Answer:

Option C. is the correct option.

Step-by-step explanation:

County X has a population density of 250 people per square mile.

Total population of the county is 150000.

Total area which represents the population = $\frac{\text{Total population}}{\text{Population density}}$ = $(150000)/(250)=600$ square mile.

So geometric model which has the same area as 600 square miles will be the answer.

A). Area of a parallelogram = Base × height

= 25×25

= 625 square miles

which is not equal to 600 square miles so it's not the correct option.

B). Area of a rectangle = Length×width

= 15×45 = 675 square miles ≠ 600 square miles

Therefore, not the correct option.

C). Area of a right triangle = $(1)/(2)(Base)(height)$

Since length of hypotenuse is given so we will find the length of height.

Height = √[(Hypotenuse)²- (Base)²] = $\sqrt{50^(2)-30^(2)}$

= $√(2500-900)$

= $√(1600)$

= 40 miles

So area of the right triangle = $(1)/(2)(40)(30)$

= $(1200)/(2)$

= 600 square miles

Which matches the area of County X, so it's a correct option.

D). area of trapezoid = $(1)/(2)[(base1 + base2)](height)$

= $(1)/(2)(10+30)(25)$

= $(1)/(2)(40)(25)$

= 20×25

= 500 square miles ≠ 600 miles

Therefore, this option is not correct.

C. with a 150,000 person population at 250 persons per square mile the country would be 600 square miles. The last leg would equal 40 miles and therefore making the area equal 600 square miles.

A 1500 kg hippo is completely submerged, standing on the bottom of a lake. What is the approximate value of the upward normal force on the hippo?

Answers

Answer:

About 428 N

Step-by-step explanation:

Weight = 1,500 * 9.8 = 14,700 N

Density = Mass ÷ Volume

1,030 = 1,500 ÷ V

V = 1,500 ÷ 1,030 = 1.46 m^3.

Buoyant force = Density * g * V

Buoyant force = 1,000 * 9.8 * (1,500 ÷ 1,030)

Buoyant force = 9,800 * (1,500 ÷ 1,030) = 14,272 N.

Net force = 14,700 – [(9,800 * (1,500 ÷ 1,030)]

Final answer:

The upward normal force on a 1500 kg submerged hippo is approximately equal to its weight, calculated as its mass times the acceleration due to gravity (1500 kg × 9.81 m/s²), resulting in a force of 14715 N.

Explanation:

The question is asking about the upward normal force on a submerged hippo in a lake. To find this force, we must understand that the upward normal force that the ground (or in this case, the lake bed) exerts on the hippo is equal to the weight of the hippo, which is the product of the hippo's mass (m) and the acceleration due to gravity (g).

In equation form: Normal Force = m × g. Plugging in the values, we have a 1500 kg hippo and the acceleration due to gravity is approximately 9.81 m/s². Therefore, the upward normal force is:

Normal Force = 1500 kg × 9.81 m/s² = 14715 N.

This is the approximate value of the upward normal force exerted on the hippo standing on the bottom of the lake.

Learn more about normal force here:

brainly.com/question/18799790

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How do i solve this problem 4s -12 = -5s + 51

Answers

$4s-12=-5s+51\ \ \ \ /+12\n\n4s-12+12=-5s+51+12\n\n4s=-5s+63\ \ \ /+5s\n\n4s+5s=-5s+5s+63\n\n9s=63\ \ \ /:9\n\n9s:9=63:9\n\ns=7$

4s-12=-5s+51
+12= +12
4s=-5s+63
+5s =+5s
9s=63
9/9=63/9
s=7

A 4.0-kg cart moving due east at 9.0 m/s collides with a 3.0-kg cart moving due west. The carts stick together and come to rest after the collision. What was the initial speed of the 3.0-kg cart?