what the volume of the soild

What The Volume Of The Soild

Answers

Answer 1

Answer:

A.264

Step-by-step explanation:

((Area Of triangle*height)=Volume

Area of triangle is the base of the triangle multiplied by height of triangle divided by 2

((8*6)/2)*11=264


Related Questions

Subtract (-2x4-4y3+4z3+6) - (-9x4-3y3+4z3+9)

Answers

Answer:

Step-by-step explanation:

-2x^4 - 4y^3 + 4z^3 + 6 + 9x^4 + 3y^3 - 4z^3 - 9

7x^4 - y^3 - 3

Answer:

28x-3y-3

Step-by-step explanation:

(-2x × 4 - 4v × 3 + 4z× 3 + 6) - (-9× × 4 - 3v× 3 + 4

Multiply the monomials

(-8×-4y×3+ 42×3+6)-(-9××4-3y×3+42×3+9

Multiply the monomials

(-8x-12y + 4z × 3 + 6) - (-9x× 4 - 3y × 3 + 4z × 3 + 9)

Multiply the monomials

(-8x - 12y + 12z +6) - (-9× × 4 - 3y × 3 + 4z × 3 + 9)

Multiply the monomials

(-8x-12y +12z +6) - (-36x -3y × 3+ 4z × 3 + 9)

Multiply the monomials

(-8x-12y + 12z + 6) - (-36x - 9y + 4z × 3 + 9)

8×-12y+122+6-(-36×-9y+122+9

Remove the parentheses for addition or

subtraction

-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9

-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9

Reorder and gather like terms

(-8x + 36x) + (-12y + 9y) + (12z - 12z) + (6 - 9) 3 steps

Collect coefficients of like terms

(-8+36) ××+ (-12 + 9) × y+ (12 - 12) × z+ (6 - 9)

Which expression is equivalent to -1/2 (1/4 x - 3/8). SHOW WORK

A. -1/8x + 3/16
B. -1/8 x + 3/8
C. 1/8x - 3/16
D. 1/8x - 3/8

Answers

Answer:

A. -1/8 x + 3/16

Step-by-step explanation:

Distribute -1/2 over the parentheses

-1/2 ( 1/4 x - 3/8 )

-1/2 (1/4 x) - 1/2 (-3/8 )

multiply fractions to simplify

-1/8 x + 3/16

A is correct

Need a little help!


Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for .
A sphere has a radius of 12 centimeters.
The volume of the sphere is about
cm³.

Answers

Answer = 7234.6 cm cu.
Reason
Volume of sphere
V= 4/3 x TT x r^3
V = 4/3 x 3.14 x 12^3
V= 7234.56
Rounded to 7234.6

rationalize the denominator of the fraction (6)/(4+\sqrt(5))

Answers

The rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

How to rationalize a fraction?

Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]

Then the conjugate of the denominator is given by b - c

Thus, rationalizing the fraction will give us

[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]

The given expression is

[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]

By rationalizing the denominator of the fraction

[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]

Thus, the rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

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Suppose y varies inversely with x, and y = 49 when x = 17. What is the value of x when y = 7 ?

Answers

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} y=49\\ x=17 \end{cases} \\\\\\ 49=\cfrac{k}{17}\implies 833=k~\hfill \boxed{y=\cfrac{833}{x}} \\\\\\ \textit{when y = 7, what is "x"?}\qquad 7=\cfrac{833}{x}\implies x=\cfrac{833}{7}\implies x=119[/tex]

Los disminuyentes de liquido normal en ula persona sana es de 0.6mL/kg/hr. Sabiendo que don pedro cuenta con 39 grados de fiebre y pesa82 kg. Calcule la perdida de liquido/h

Answers

The question requires the computation of loss body fluid. The results show that Don Pedro's loss of body fluid per hour is 54,234ml/hours. See computation below.

What is the loss of body fluid?

This refer to the rate at which a human being loses water on the hour. The formula for this is given as:

The Body weight in lb x percentage rate of dehydration (given in decimal form) x 500.

Hence, Don Pedro's loss of fluid per house is:

82 x 0.6 x 500;

Recall that in the formula, the weight is given in lb. So we convert Pedro's weight to Lb.

1kg = 2.20462Lb

Hence

80kg = 80 * 2.20462 = 176.37

Hence

Pedro's loss of fluid per house =

180.779 x 0.6 x 500

= 54,233.70

≈ 54, 234 ml/h


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PLEASE HELP!!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!!!!!!!!! A triangle has a base length of 3ac2 and a height 5 centimeters more than the base length. Find the area of the triangle if a = 4 and c = 5.

Answers

Answer:

the Area = 100in^2

Step-by-step explanation:

pls mark brainiest

Area of triangle is 10 square cm.

What is area of triangle?

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Given

Base = 4

Height = 5

Area of triangle = [tex]\frac{1}{2}[/tex] × b × h

=  [tex]\frac{1}{2}[/tex] × 4 × 5

= 2 × 5

= 10

Hence, area of triangle is 10 square cm.

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what are the amounts of interest and maturity value of a loan for 25,000 at 12% simple interest for 5 years

Answers

Answer:

Interest= 15,000

Maturity Value=40,000

Step-by-step explanation:

Simple Interest

V= (principal) * (rate) * (# of periods)

=(25,000)*(0.12)*(5)

=15,000

Maturity Value

V= P*(1+rt)

=25,000*(1+(.12)(5))First, converting R percent to r a decimal

r = R/100 = 12%/100 = 0.12 per year.

Solving our equation:

V = 25000(1 + (0.12 × 5)) = 40000

V = 40,000.00

hope it will help you

thank u

i needs help with it please ​

Answers

Answer:

(i)  (0, -32)

(ii)  (-4, 0) and (8, 0)

(iii)  x = 2

(iv)  (2, -36)

(v)  (2, -36) minimum

Step-by-step explanation:

Given quadratic equation:

[tex]y=x^2-4x-32[/tex]

Part (i)

The y-intercept is the point at which the curve crosses the y-axis.

To find the y-intercept, substitute x = 0 into the given equation:

[tex]\implies (0)^2-4(0)-32=-32[/tex]

Therefore, the y-intercept is at (0, -32)

Part (ii)

The zeros are the points at which the curve crosses the x-axis.

To find the zeros, substitute y = 0 into the given equation and factor:

[tex]\implies x^2-4x-32=0[/tex]

[tex]\implies x^2-8x+4x-32=0[/tex]

[tex]\implies x(x-8)+4(x-8)=0[/tex]

[tex]\implies (x+4)(x-8)=0[/tex]

Therefore:

[tex](x+4)=0 \implies x=-4[/tex]

[tex](x-8)=0 \implies x=8[/tex]

So the zeros are (-4, 0) and (8, 0)

Part (iii)

The axis of symmetry is a vertical straight line that divides the curve into two symmetrical parts.  The axis of symmetry is the x-value of the mid-point of the zeros.

[tex]\sf \implies midpoint=\dfrac{8+(-4)}{2}=2[/tex]

Therefore, the axis of symmetry is:  x = 2

Part (iv)

The vertex is the turning point of the parabola.

If the leading coefficient is positive, the parabola opens upwards and the vertex is the minimum point.  

If the leading coefficient is negative, the parabola opens downwards and the vertex is the maximum point.

The axis of symmetry is the x-value of the vertex.

To find the y-value, substitute x = 2 into the equation:

[tex]\implies (2)^2-4(2)-32=-36[/tex]

Therefore, the vertex is (2, -36)

Part (v)

The optimal value is also known as the vertex.

Therefore, the optimal value is (2, -36).  

As the leading coefficient of the given quadratic equation is positive, the parabola opens upwards and so the optimal value is a minimum.

Two complementary angles are in the ratio 5 to 7 find the angles

Answers

Answer:

37.5°, 52.5°

Step-by-step explanation:

Let the two angles be 5x and 7x

Total ratio= 5+7 =12

5x = (5/12) ×90° ( sum of complementary angles = 90°)

= (5/2)×15°

75/2= 37.5°

Similarly

7x = (7/2)×15°

=105/2= 52.5°

Verification

37.5°+52.5°=90° (sum of complementary angles= 90°)

What is angle Data please help

Answers

Answer:

C.  74°

Step-by-step explanation:

Cosine Rule (for finding angles)

[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

where:

C = anglea and b = sides adjacent the anglec = side opposite the angle

Given:

C = [tex]\theta[/tex]a = 5b = 11c = [tex]\sf \sqrt{115}[/tex]

Substitute these values into the formula:

[tex]\implies \sf \cos(\theta)=\dfrac{5^2+11^2-(\sqrt{115})^2}{2(5)(11)}[/tex]

[tex]\implies \sf \cos(\theta)=\dfrac{25+121-115}{110}[/tex]

[tex]\implies \sf \cos(\theta)=\dfrac{31}{110}[/tex]

[tex]\implies \sf \theta=\cos^{-1}\left(\dfrac{31}{110}\right)[/tex]

[tex]\implies \sf \theta=74^{\circ} \quad (nearest\:degree)[/tex]

how do you get 14 divided by 9 as a decimal

Answers

Answer:

14 divided by 9 = 1.5

The result of 14/9 is a non-terminating, repeating decimal.

Answer:

1.56 [?]

this question's wording was slightly confusing but I think this is what you meant

Step-by-step explanation:

by dividing the two numbers, (you can use long division or a calculator) while they are not in a fraction state (don't rewrite it as [tex]\frac{14}{9}[/tex], actually divide

14 by 9) you will end up with a number:

1.55555556

(repeating decimal)

So, you can either write this as 1.5 with a little dash over the 5

Or, you can round the decimal to 1.56 .

(method: by actual division)

Find the height of a trapezium below with are 90cm and parallel sides 6 and 19.

Answers

Answer:

  7.2 cm

Step-by-step explanation:

The height of the trapezium can be found by making use of the area formula with known values filled in.

__

solve for height

The area of a trapezium is given by ...

  A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height

Using the given values, we have ...

  90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values

  (90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h

The height of the trapezium is 7.2 cm.

Which of the following is the graph of y = |x - 3|?

Answers

Answer:

D

Step-by-step explanation:

with this functional definition y can never have a negative value.

so, A and C are automatically out.

and then find some core points (like x = 0 and y = 0).

for x = 0 we get y = 3. ok, that fits to both B and D.

for y = 0 x must be 3.

and that leaves only D as right answer.

Answer:

the answer is a on my test

Step-by-step explanation:

E Homework: 3.1 Homework
Evaluate the following function at the values 2, -3, and x-2.
f(x) = x² +5
f(2)= (Type an integer or a simplified fraction.)

Answers

Answer:

Question 13 of 16 Evaluate the following function at the values 2, -4, and x-1. f(x)=x2-5 = ..... f(2)= (Type an integer or a simplified fraction.) f(-4)=L(Type an integer or a simplified fraction.) f(x-1)= (Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)

Given that these simultaneous equations
x-y=k
2x²+y²-15
have exactly one pair of solutions, find k.

The answer is supposedly (±3√10)/2, but I don't know how to get to the answer

Answers

The value of k is[tex](3\sqrt{ 10})/2[/tex]

How to solve the simultaneous equation?

Given:

x-y=k.............(eq i)

2x²+y²-15..............(eq ii)

We would make y the subject formula in eq ii

2x²+y²-15= 0

2x² + y²= 15

y²= 15-2x²

y= [tex]\sqrt{15-2x^2}[/tex]...........(eq iii)

Substitute the value of y into eq i

x-([tex]\sqrt{15-2x^2}[/tex]= k

x- ([tex]\sqrt{15} - 2x[/tex]= k

k= [tex](3\sqrt{ 10})/2[/tex]

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A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. The figure shows both designs.

please help

Answers

The height and the base area of both the design must be equal. Then the correct option is A.

What is a cylinder?

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers.

Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder.

The figure shows both designs.

The volume of the cylinder will be given as

V = πr² h

If the volume of the oblique cylinder and right cylinder is the same.

Then the height of both the designs must be equal and the base area of both the design must be equal.

Then the correct option is A.

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Answer:

D

Step-by-step explanation:

did the test on edmentum

[Worth 30 Points] NEED HELP!!!

To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level) b=740meters from the base of the mountain to the top of the mountain is β=60∘. The students then walk a=1850 meters straight back and measure the angle of elevation to now be α=37∘. If we assume that the ground is level, use this information to estimate the height of the mountain.

The height of the mountain is: ______ Meters.

Explain how your answer measure below. Be sure to show all of your work.

Answers

The height of the mountain estimated by two students is 2,467.98 meters.

Height of the mountain

The height of the mountain is calculated as follows;

tanα = h/( a + b + x)

where;

x is the distance between end of b and h

tan37 = h/(1850 + 740 + x)

tan37 = h/(2590 + x)

h = tan37(2590 + x)

h =1,951.82 +  0.7536x  ---- (1)

tanβ = h/(b + x)

tan60 = h/(740 + x)

h = tan60(740 + x)

h = 1,281.68 + 1.732x ---- (2)

Solve (1) and (2) together

1,951.82 +  0.7536x = 1,281.68 + 1.732x

1,951.82  -  1,281.68 = 1.732x  -  0.7536x

670.14 = 0.9784x

x = 684.93 m

h = 1,281.68 + 1.732x

h = 1,281.68 + 1.732(684.93)

h = 2,467.98 m

Thus, the height of the mountain estimated by two students is 2,467.98 meters.

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how to graph
f(x) = x² + 5x + 2

Answers

This is what I got, please tell me if it’s wrong or right, thank you!!

Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 14 cm.
(1) How many equilateral triangles are there? _____

(2) What is the measure of each of the three angles in the equilateral triangle? _____

(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____

(4) What is the vocabulary word for the segment a? _____

(5) What is the length of the short side of one of the 30-60-90 triangles? _____

(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____

(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____

(8) What is the height of one of the the equilateral triangles? _____

(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____

(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____

Answers

Find answers to the questions in the attached file.

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5x+3
Write the fraction below as a sum or difference.
=?
4
(Simplify your answer. Use integers or fractions for any numbers in the
expression.)

Answers

To write this sum as a fraction, you can use the following formula: 5x/4 + 3/4.

How to transform a fraction into a sum?

To transform a fraction into a sum we must perform the following procedure:

[tex]\frac{5x + 3}{4}[/tex] = [tex]\frac{5x}{4} + \frac{3}{4}[/tex]

According to the above, all we have to do is divide the fraction using each digit of the numerator and put the same denominator.

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The sum of a number and 64 is no more than 36.

Answers

i believe the answer is 64+(-28)

[tex]\text{Let the number be x,}\\\\~~~~~~~~x+64\leq 36\\\\\implies x \leq 36 - 64\\\\\implies x \leq -28[/tex]

Question 1: 5 pts
Bill wants to plant roses in his triangular plot. There will be 1 plant at a corner. Each row will have 6
additional plants. He wants the plot to have as many lows as possible with 150 rose plants. How many
rows will Bill's plot have?
O 7 rows
O 8 rows
O 6 rows
O 5 rows

Answers

The arrangement of the rose plants on the triangular plot is such that they

form a series or progression that is defined.

The number of rows on Bill's plot is; 8 rows

The given parameters for the triangular plot are;

Number of plants at the corner = 1 plant

Number of additional plants per row = 6 plants

Number of rose plants = 150 rose plants

The number of rows in the plot.

The difference between successive rows, d = 6

The number rose at the top vertex, a = 1

Therefore, the rose in the garden forms an arithmetic progression

The first term, a = 1

The common difference, d = 6

The number of rows Bill's plot will have, n is given by the sum of n in terms of

an arithmetic progression, Sn, is given as follows;

[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]

When Sn = 150, we get;

[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]

150 = 3·n² - 2·n

3·n² - 2·n - 150 = 0

Taking only the positive solution for n, we have;

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]

[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]

[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]

The number of rows Bill's plot has, n ≈ 7.3965

Given that the 7th row is completed, an 8th row will be present on Bill's plot

The number of rows Bill's plot will have = 8 rows

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What is the product of 4/15 and 3/8?

Answers

Hi there.

[tex]= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =[/tex]

What we should do here is multiply the fractions. We know this information because it says in our problem - "the product".

.

If ever we come across the word "the product of" in any mathematics problems, we should know that the operation we should use is "multiplication".

.

.

This is how we multiply fractions:

.

First, we check: Is there any way we can reduce the fractions?

.

.

We cannot divide the top and bottom of these two fractions by the same number, but there is some reducing that can be done:

.

.

Notice that 4 and 8 have a common factor - 2.

.

Since 4 and 8 have a 2 in common, we divide 8 and 4 by 2:

.

[tex]\bf{\displaystyle\frac{4}{15} *\frac{3}{8}}[/tex]

.

[tex]\bf{\displaystyle\frac{1}{15} *\frac{3}{2}}[/tex]

.

.

Now, 15 and 3 also have a common factor - 3:

.

[tex]\bf{\displaystyle\frac{1}{5} *\frac{1}{2}}[/tex]

.

.

What we should do now is multiply 1 by 1 and 5 times 2:

.

[tex]\bf{\displaystyle\frac{1}{10}}[/tex]

.

I hope that this helps clear your doubts; if any are left, please ask.

.

I wish you a nice rest of your day.

.

[tex]\bf{W}\sf{r}\bf{i}\sf{t}\bf{i}\bf{n}\sf{g}\:\bf{A\:\sf{L}\bf{e}\sf{t}\bf{t}\sf{e}\bf{r}.[/tex]

--

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What does \boxed{product} mean?}[/tex]
[tex]\bullet\large\text{ Product simply means multiplication/multiply}[/tex]


[tex]\huge\textbf{So, what are we doing in the equation?}[/tex]

[tex]\bullet\large\text{ We are multiplying! :)}[/tex]

[tex]\huge\textbf{What should our equation look like?}[/tex]

[tex]\rm{\dfrac{4}{15}\times\dfrac{3}{8}}[/tex]


[tex]\huge\textbf{What are the steps?}[/tex]

[tex]\mathsf{\dfrac{4}{15}\times\dfrac{3}{8}}[/tex]

[tex]\mathsf{= \dfrac{4\times 3}{15\times 8}}[/tex]

[tex]\mathsf{= \dfrac{12}{120}}[/tex]

[tex]\mathsf{= \dfrac{12\div2}{120\div2}}[/tex]

[tex]\mathsf{= \dfrac{6}{60}}[/tex]

[tex]\mathsf{= \dfrac{6\div3}{60\div3}}[/tex]

[tex]\mathsf{= \dfrac{2}{20}}[/tex]

[tex]\mathsf{= \dfrac{2\div2}{20\div2}}[/tex]

[tex]\mathsf{= \dfrac{1}{10}}[/tex]


[tex]\huge\textbf{What is your answer to the question?}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{1}{10}}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]


~[tex]\frak{Amphitrite1040:)}[/tex]

PLS PLS PLS HELP!!!

The perimeter of a square is given as 6c - 4(c-5) Which expression give the length of one side of the square?

A 2c + 20
B 1/2c + 20
C 1/2c+5
D 8c+20

Are the two expressions, 6c-4(c-5) and the answer you chose to the
question above equivalent?
Explain why or why not in 1 to 2 sentences.

Answers

Answer:

( we know that square of perimeter is 4L now,4L=6c-4(c-5),4L=6c-4c+20,4L=2c+20,then L=(c+10)/2

The side of a given square is c/2+5. Therefore, option C is the correct answer.

What is the perimeter?

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, the perimeter of a square is 6c-4(c-5).

We know that, the perimeter of a square is 4a, where a is the side.

Now, 4a=6c-4(c-5)

4a=6c-4c+20

4a=2c+20

a=c/2+5

Therefore, option C is the correct answer.

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Is the integer below prime or composite?
26

Answers

composite xx it's not prime

A circle has four sections. Only three sections are labeled. The labels are 29.78% 24.73% and 19.49%. What is the missing section should be?

Answers

Answer:

26

Step-by-step explanation:

You would add the 3 numbers and then minus that from 100

an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E. The wind velocity is 30 kilometers per hour in the direction N30 degrees W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?

Answers

For an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E,  the ground speed of the plane and its direction is mathematically given as

Vg=556.10km/hr[tex]\theta=52.99East[/tex]

What is the ground speed of the plane and its direction?

Generally, the equation for the velocity of the plane is mathematically given as

[tex]Vp=Fcos\thetai+Fsin\theta j[/tex]

Therefore

Vp=530cos45i+530sin45j

Vp= 374.76i+374.76j

For wind speed

Vm=80cos(90+30)i+80sin(90+30)j

Vm=-40i+69.28j

Hence, there resultant is

Vr=Vm +Vp

Vr=374.76i+374.76j + 40i+69.28j

Vr=334.77i+1444.05j

In conclusion, the Ground speed is

[tex]Vg=\sqrt{334.77^2+1444.05^2}[/tex]

Vg=556.10km/hr

Direction

[tex]Tan \theta=\frac{444.05}{334.77}[/tex]

[tex]\theta=52.99East[/tex]

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Which of the following is equal to 5 1/3?

Answers

The answer is 10 2/6 i think
10 2/6 is the correct answer


pls help me out with this question​

Answers

Height be h

[tex]\\ \rm\Rrightarrow tan\Theta=\dfrac{Perpendicular}{Base}[/tex]

[tex]\\ \rm\Rrightarrow tan54=\dfrac{h}{60}[/tex]

[tex]\\ \rm\Rrightarrow h=60tan54[/tex]

[tex]\\ \rm\Rrightarrow h=82.6\approx 83m[/tex]

Answer:

83 m  (nearest metre)

Step-by-step explanation:

This can be modeled as a right triangle, where the base is 60 m and the height is the height of the building.

Alternate Interior Angles Theorem (Z-angles)

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Using the Alternate Interior Angles theorem, the angle between the ground and the dashed line (angle of elevation) is 54°.

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angle

Given:

[tex]\theta[/tex] = 54°O = height of building (h)A = 60

Substituting the given values into the formula and solving for h:

[tex]\implies \sf \tan(54^{\circ})=\dfrac{h}{60}[/tex]

[tex]\implies \sf h=60 \tan(54^{\circ})[/tex]

[tex]\implies \sf h=82.58291523...[/tex]

[tex]\implies \sf h=83\:\:m\:(nearest\:metre)[/tex]

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