a boy is standing 180 metres from the base of a tree. the angle of elevation to the top of the tree is 40°. what is the height of the tree?​

The vector v (-6, 6, -5) points in the direction of itself, so we start there.

We can capture all points on the line through the origin and the point (-6, 6, -5) by scaling v by an arbitrary real number t.

The line through point P and pointing in the same direction as v is parallel to the other line that passes through the origin. Then the line we want can be obtained by translating the line through the origin by a vector p that points to (-4, 5, 2), so the vector equation for this line is

r (t ) = p + t v

r (t ) = (-4, 5, 2) + t (-6, 6, -5)

r (t ) = (-4 - 6t, 5 + 6t, 2 - 5t )

To get the parametric equations, simply take out the components:

x (t ) = -4 - 6t

y (t ) = 5 + 6t

z (t ) = 2 - 5t

Answer:

2083.33 trouts

Step-by-step explanation:

Total population of fish in the pond is unknown, therefore, let's us represent this using letter Z

The ratio of banded , caught and released trout to the total trout population is represented as 250 : Z

We can solve this type of problem with a proportion:

Total number of fishes that was tagged and caught/ Total number of fishes that was caught = Total number of tagged fishes in the pond/ Total number of fishes in the pond.

In the question, we were given this values:

Total number of banded trout's that was caught and released into the pond = 250

Total number of trouts that was caught and had bands in the lake= 30

Total number of trouts that was caught in the lake = 250

Total number of fishes in the pond = Z

Hence we have:

30/250 = 250/ Z

We cross mulitply

30× Z = 250 × 250

30Z = 62500

We divide both sides by 30

30Z/ 30 = 62500/30

Z = 2083.33

Therefore, the expected population of trout is 2083.33 trouts

Answer:

the answer is 10 i think

Answer:

1) 943.895 mm3

2) 144 cm3

Step-by-step explanation:

1)

First we need to find the volume of the rectangular prism:

Volume_1 = 9 * 11 * 6 = 594 mm3

Then, we can find the volume of the half cylinder above the prism:

Volume_2 = 0.5*(pi * (4.5^2) * 11) = 349.895 mm3

So the volume of the figure is the sum of both volumes:

Volume_total = Volume_1 + Volume_2 = 943.895 mm3

2)

The volume of a pyramid is one third of the base area multiplied by the height, so we have:

Volume = (1/3) * 6 * 8 * 9 = 144 cm3

Answer:

1. Volume of the composite figure is 943.89 mm³

2. The volume, of the is 144 cm³

Step-by-step explanation:

1. The composite figure comprises of a cube and a half cylinder;

Volume of a cube = 9 mm × 11 mm × 6 mm = 594 mm³

Volume of the half cylinder = area of base × length = (π·r²)/2 × l

Where:

r = (Diameter of base)/2 = 9/2 = 4.5 mm

l = 11 mm

Therefore, plugging the values, gives;

Volume of the half cylinder = (π × 4.5²)/2 × 11 = 349.89 mm³

Hence, volume of the composite figure = Volume of the cube + Volume of the half cylinder

Volume of the composite figure = 594 mm³ + 349.89 mm³ = 943.89 mm³

2. The volume, V of a pyramid is given by the following relation;

[tex]V = \frac{l \times w \times h}{3}[/tex]

Where:

l = Length of base = 8 cm

w = Width of the base = 6 cm

h = Height of the pyramid = 9 cm

[tex]V = \frac{8 \times 6 \times 9}{3} = 144 \ cm^3[/tex]

Here we have that a cube of side x, therefore, the area = x·x, integrating we have;

[tex]\int\limits^x_0 {x \cdot x} \, dx = \frac{x^3}{3}[/tex]

Where:

Length, height width of the pyramid = x

It can therefore be shown, that for a pyramid of length, l, width, w, and height, h, the volume, [tex]V = \frac{l \times w \times h}{3}[/tex] .

Answer: So, an Engineer will use a topography while working to locate the elevation for a given region. They provide the numerical value of an elevation. So from the list of options the closest to it is to determine the best location for a new road.

I hope this is helpful.

Answer:

B

Step-by-step explanation:

Answer:

5.(345)=1,780/333

Step-by-step explanation:

5.(345)=(5,345-5)/999=5,340/999=1,780/333

The fraction corresponds to given decimal is 1780/333.

What is fraction form?

A fraction is used to show how much of something is left over. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Let x=5.345

The repeating number is 345

Multiply both sides by 1000

1000x=5345.345

Subtract x=5.345 from the obtained equation,

999x=5340

Solve for x,

x=5340/999

x=1780/333

Therefore, the fraction corresponds to given decimal is 1780/333.

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Answer:

B represents area of the right triangle

Step-by-step explanation:

Given;

Area of a triangle is A = 0.5bh

where;

b is the base of the triangle

h is the height of the triangle

Given, formula for the volume of a prism is V = Bh

For a right triangle prism, the formula for the volume is, V = Bh

Where;

B is the area of the right triangle

h is the height of the prism

Therefore, B represents area of the right triangle

Answer:

The percentage of the surveyed that preferred Lirt juice is 40%

Step-by-step explanation:

In this question, we are asked to calculate the percentage of beings that preferred Lirt juice

Let’s look at the survey presented in the question. 10 beings preferred out of a total of 25

The percentage that preferred Lirt juice will thus be;

10/25 * 100%

= 10 * 4 = 40%

Answer:

11 cm

Step-by-step explanation:

The strip of paper is 66 cm and it is folded into 6 different parts. It is used to form a model of a honeycomb cell.

To find the length of one side of the model, all we have to do is divide 66 cm by 6. That is:

66 / 6 = 11 cm

The length of one side of the model is 11 cm.

Answer:

17 is added to both numerator and denominator.

Step-by-step explanation:

Given:

Fraction = 1/10

New fraction = 2/3

Find:

Number added to both numerator and denominator.

Computation:

Assume,

a is added to both numerator and denominator.

[tex]\frac{1+a}{10+a}=\frac{2}{3}\\\\3 + 3a=20+2a\\\\3a-2a=20-3\\\\a=17[/tex]

Therefore, 17 is added to both numerator and denominator.

Answer:

x = -2.67

Step-by-step explanation:

6.8x + 9.3 = -9.4 + 3.4(-3x)

6.8x + 10.2x = -9.4 - 9.3

17x = -18.7

x = -2.67

Answer:

1.47070788E36

Step-by-step explanation:

Answer:

20 %

Step-by-step explanation:

$10/100%    $2/?

10/ what to get 2 so you do 10/5=2 so 100/5= 20.

x^2 + 16 - 46 = x^2 + 16 + 8^2 - 46 - 8^2 = (x + 8)^2 - 110

Answer:

[tex]f(x)=(x+8)^{2}-110[/tex]

Step-by-step explanation:

[tex]f(x)=x^{2}+16x-46 \\=x^{2}+2\times 8\times x-46 \\=x^{2}+16x+8^2-8^2-46 \\=(x+8)^{2}-64-46\\f(x)=(x+8)^{2}-110[/tex]

Answer:

1. B

2. A

3. B

4. ???

5. A

6 ???

7. I can't see it

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The rule for negative exponents is:

[tex]a^{-n} = \frac{1}{a^n}[/tex]

We have:

[tex]5^{-2}[/tex]

So, we can create a fraction with 1 as the numerator, and our exponent raised to a positive number as the denominator, and rewrite it as:

[tex]\frac{1}{5^2}[/tex]

Evaluate the exponent in the denominator

[tex]\frac{1}{5*5}\\\frac{1}{25}[/tex]

Therefore, choice A, 1/25 is correct.

Answer:

4 times

Step-by-step explanation:

Answer:

4.8333333 or 4 5/6 times

Step-by-step explanation:

29/6 = 4.83333333

Answer:

The answer is 66 ways .

Step-by-step explanation:

You have to use Combination because it says choosing 10 out of 12 as the position is not important :

12C10 = 66 ways of arrangements

The number of different 10-person teams are 66.

A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

We have out of the 12 girls who tried out for the softball team, 10 will be chosen for the team.

Using Combination

C(n, r) = n!/ r! (n- r)!

Here n = 12, r= 10

So, C(12, 10)= 12! / 10! (12- 10)!

                   = 12 x 11 x 10! / 10! x 2

                   = 6 x 11

                   = 66

There are 66 10-person teams.

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Answer:

The result for the equation is [tex]x = -8[/tex] .

Step-by-step explanation:

-Solve the equation:

[tex]0.75x -0.5 =x +1.5[/tex]

-Subtract [tex]x[/tex] from [tex]0.75x[/tex] :

[tex]0.75x -0.5-x =x -x+1.5[/tex]

[tex]-0.25x -0.5 = 1.5[/tex]

-Add both sides by 0.5 :

[tex]-0.25x -0.5 +0.5 =1.5 +0.5[/tex]

[tex]-0.25x = 2[/tex]

-Divide both sides by 0.25 :

[tex]\frac{-0.25x}{-0.25} =\frac{2}{-0.25}[/tex]

[tex]x = -8[/tex]

So, the answer for the equation is [tex]x = -8[/tex] .

Answer:

The initial amount of money Tyra has is $90

Step-by-step explanation:

Let the initial money Tyra has be equal to y

She spent ⁴/₅ of her initial money on gas for her car = ⁴/₅ of y

She spent ¹/₂ of the remainder on sandwiches;

the remainder = 1 -  ⁴/₅  = ¹/₅

¹/₂ of the remainder = ¹/₂ x ¹/₅ = ¹/₁₀

Thus, she spent ¹/₁₀ of her money on sandwiches = ¹/₁₀ of y

Amount she spent on sandwiches = $9 = ¹/₁₀ of y

[tex]\frac{y}{10} = \$ 9\\\\y = \$ 90[/tex]

Therefore, the initial amount of moneyTyra has is $90

Answer:

The answer is sandy

Step-by-step explanation:

18/3= 6 why? because each glass of lemonade he drink he puts 3 table spoons, and a table spoon is the big spoon

hope this helped <3

Answer:

The scale factor to transform DEF to D'E'F' is 1/2

Step-by-step explanation:

DEF is

D(-8, 6), E(-8, 14), F(2, 3)

D'(-3, 6), E'(-3, 10), F'(2, 4.5)

Therefore;

DE = √((-8-(-8))²+(6-14)²) = 8

D'E' = √((-3 -(-3))² + (6 - 10)²) = 4

Similarly,

EF = √((-8 - 2)² + (14 - 3)²) = √(100 + 121) = √221

E'F' = √((-3 - 2)² + (10 - 4.5)²) = √(100/4 + 121/4) = (√221) × 1/2

Also

DF = √(-8 - 2)² + (6 - 3)² = √(100 + 9 =√109

D'F' = √(-3 - 2)² + (6 - 4.5)² = √(5² + 3²) = √((10/2)² + (3/2)²) = √(100/4 + 9/4) = (√109)×1/2

Therefore the ratio of DEF to D'E'F' = DE/D'F' = EF/E'F' = DF/D'F' = √221/(√221) × 1/2 = 2

That is the scale factor of DEF to D'E'F'  = 1/2.

Multiplying a negative number by a negative number will give you a positive product.

When multiplying two negative integers, it comes out as positive.

For example, we are given the equation -4 * -4.

Using the rule [ -(-a) = a ], the answer for the equation is 16.

Best of Luck!

Answer:

1.2 units

Step-by-step explanation:

2.6(d + 1.4) - 2.3d = 4

2.6d + 3.64 - 2.3d = 4

0.3d + 3.64 = 4

0.3d = 0.36

d = 1.2

Answer:

393.75 m^3

Step-by-step explanation:

to find the volume, u need to multiply the length by the width by the height . when u multiply the 3 numbers u will get 393.75 m^3

Answer:

y' = y

Step-by-step explanation:

The slopes are independent of x.  So the only possible answer is y' = y.

Answer:

D

Step-by-step explanation:

-4 x 3/2 = -12/2; which equals -6

so -6x.

-4 x -1/2 = 4/2; which equals 2

This means that:

-6x + 2 = 15; so 'D' is the answer

Answer:

D

Step-by-step explanation:

The distributive property states that a(b+c)=ab+ac. In this problem -4 is a, 3/2x is b, and -1/2 is c. -4(3/2) is 6, and -4(-1/2) is 2. So we have -6x+2=-15.

Answer:

125.6 cubic meters

Step-by-step explanation:

To calculate the volume of the cylinder, we will do it as follows:

Vc = Base area * Height

We know that the base of the cylinder is a circle, therefore:

Base area: pi * r ^ 2

replacing we have:

Vc = pi * (r ^ 2) * h

We have r = 2 and h = 10, we replace:

Vc = pi * (2 ^ 2) * 10

Vc = 40 * pi

pi = 3.14

Vc = 40 * 3.14

Vc = 125.6

Which means that the volume of the cylinder is 125.6 cubic meters

Answer:

It is 40

Step-by-step explanation:

I filled it in the blank and I got it correct edge 2020!

hope this helps :)

The quadratic has one root with multiplicity 2 if the discriminant is 0, which is

[tex](2m+4)^2-4(4-m)(8m+1)[/tex]

(That is, for a quadratic [tex]ax^2+bx+c[/tex], the discriminant is [tex]b^2-4ac[/tex].)

Set the discriminant equal to 0 and solve for [tex]m[/tex]:

[tex](2m+4)^2-4(4-m)(8m+1)=0[/tex]

[tex]4m^2+16m+16+32m^2-124m-16=0[/tex]

[tex]36m^2-108=0[/tex]

[tex]36m(m-3)=0[/tex]

[tex]\implies m=0\text{ or }m=3[/tex]