Miguel is flying a kite, holding his hands a distance of 3.5 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 25^{\circ} ∘ . If the string from the kite to his hand is 150 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer:

The answer is 50.

Step-by-step explanation:

Set up a proportion: [tex]\frac{41}{y} =\frac{82}{100}[/tex]
Step 2- Multiply 41 by 100 to get 4100
Step 3. Divide 4100 by 82 to get 50.
Hope this helps! :)

The area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

To find the area of the bounded region by the curves(refer to attached picture):

[tex]\rm A= \int\limits^2_1 {(\frac{1}{x}-\frac{1}{x^2}) } \, dx[/tex]

After solving:

A = 0.193 square units

Thus, the area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.

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Answer:

[tex]\dfrac12 < p < 5[/tex]

Step-by-step explanation:

To solve this, we need to use the discriminant.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

If the given equation has 2 real roots, then we need to use:

[tex]b^2-4ac > 0[/tex]

Given equation:  [tex]8x^2-4x+1-p=0[/tex]

[tex]\implies a=8, \quad b=-4, \quad c=(1-p)[/tex]

Substituting these values into [tex]b^2-4ac > 0[/tex] and solve for p:

[tex]\implies (-4)^2-4(8)(1-p) > 0[/tex]

[tex]\implies 16-32(1-p) > 0[/tex]

[tex]\implies 16-32+32p > 0[/tex]

[tex]\implies -16+32p > 0[/tex]

[tex]\implies 32p > 16[/tex]

[tex]\implies p > \dfrac{16}{32}[/tex]

[tex]\implies p > \dfrac12[/tex]

For the roots to be less than 1, first find the value of p when the root is 1.

If the root is 1, then [tex](x-1)[/tex] will be a factor, so [tex]f(1)=0[/tex]

Substitute [tex]x=1[/tex] into the given equation and solve for p:

[tex]\implies 8(1)^2-4(1)+1-p=0[/tex]

[tex]\implies 5-p=0[/tex]

[tex]\implies p=5[/tex]

Therefore, the values of p for which the given equation has two different real roots less than 1 are:

[tex]\dfrac12 < p < 5[/tex]

Answer:

Tama po

Yan

Step-by-step explanation:

Enjoy po

Godbless

Answer:

4,569,760 different passwords

Step-by-step explanation:

[tex]26 \times 26 \times 26 \times 26 \times 10 = 4569760[/tex]

Digits can be repeated means repeatation is allowed

So

Total ways

Answer:

Answer:

16 inches

Step-by-step explanation:

2 1/4 = 9/4 inches

Number of pieces = 36 / 9/4

= 36 + 4/9

= 16 inches

Answer:

Step-by-step explanation:

Formula

Volume = L * w * h

Givens

L = 7 feet

w = 4 feet

h = 5 feet

Solution

V = L * w * h             Substitute values into the formula

V = 7 * 4 * 5

V = 140 cubic feet.

Answer

140 ft^3

Answer:

D) 140 cubic feet

Step-by-step explanation:

The given information is,

→ Length (l) = 7 ft

→ Breadth (b) = 4 ft

→ Height (h) = 5 ft

Formula we use,

→ Volume of cuboid = l × b × h

Let's solve the problem,

→ l × b × h

→ 7 × 4 × 5

→ [ 140 ft³ ]

Hence, the volume is 140 ft³.

Answer: D

Step-by-step explanation:

Answer:

D. 95 ≤ u ≤ 155

Step-by-step explanation:

3 cm/h easy peasy

Step-by-step explanation:

[tex]10^3 = 10 \times 10 \times 10 = 1000[/tex]

Answer: 28 yards

You just have to multiple the 7 by the 4. :)

Answer:

See below

Step-by-step explanation:

z  = uncle's age

1/2z +3   = Sam's age

Answer:

Step-by-step explanation:

This exercise is about optimization and seeks to prove that if the new strategy of packing the discs is adopted, then h/r = [tex]\sqrt[4]{3}[/tex]/n ≈2.21.

We must determine the amount of metal consumed by each end, or the area of each hexagon.

The hexagon is divided into six congruent triangles, each of which has one side (s in the diagram) in common with the hexagon.

Step I

Next, let's derive the length of s = 2r tan π/6 = (2/([tex]\sqrt{3}[/tex])r². From this we can state that the area of each of the triangles are 1/2(sr) = (1/[tex]\sqrt{3}[/tex])r²

while the total area of the hexagon is 6 * (1/[tex]\sqrt{3}[/tex])r² = (2/[tex]\sqrt{3}[/tex])r².

From the above, we can state that the quantity we want to minimize is given as:

A =  2πrh + 2* (2/[tex]\sqrt{3}[/tex])r²

Step 2

Next, we substitute for h and differentiate. This gives us:

da/dr = - (2V/r²) + [tex]\sqrt[8]{3r}[/tex].

Let us equate the above to zero.

[tex]\sqrt[8]{3r} ^{3}[/tex] = 2V = 2πr²h ⇒  h/r =[tex]\sqrt[4]{3}[/tex]/n  

The above is approximately 2.21

Because d²A/dr²=[tex]\sqrt[8]{3}[/tex] + 4V/r[tex]^{3}[/tex] > 0 the above minimizes A.

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Answer:

ALL RED = 19/5000

Two Red = 3831/10000

No red marbles = 16/26

Step-by-step explanation:

1. Find the total number of marbles

7+10+9= 26

2. There are 10 red marbles so the probability that the first marble is red 10/26

3. When the second marble there are 25 marbles so the probability that it is red is 9/25

4. Third Marble probability

8/24

5. Fourth Marble probablity

7/23

6. Fifth marble probability

6/22

7. Now to find that ALL the marbles are red you multiply all the fractions above

10/26 * 9/25 * 8/24 * 7/23 * 6/22 = 0.0038

8. Convert to fraction form

19/5000

9. Two marbles are red

5!/(3!*2!) * 10/26 * 9/25 * 16/24 * 15/23 * 14/22 = 0.3831

10. Convert to fraction

3831/10000

If it's a regular nonagon, each exterior angle has measure 360°/9 = 40°, so the supplementary interior angles each have measure 180° - 40° = 140°.

We can split up the nonagon into 9 congruent isosceles triangles whose longer side coincides with the radius of the circle. (The language in the question is a bit ambiguous; I think it's clearler to say the nonagon is itself circumscribed by the circle, so that each of its vertices lie on the circle. See attached image - not mine, but it's in public domain.)

As the image suggests, each triangle will have interior angles measuring 70°, 70°, and 40°.

We can use trigonometry to find the side length of the nonagon, i.e. the length of the shortest side of each triangle - I'll call it x. For example, using the law of cosines,

x² = 4² + 4² - 2 • 4 • 4 cos(40°)   ⇒   x = 4√2 √(1 - cos(40°))

Then the perimeter of the nonagon is

9x = 36√2 √(1 - cos(40°)) in ≈ 24.623 in

The area of a triangle is 1/2 the product of its base and height. The base will be b = x, but to get the height we cut the isosceles triangle in half to produce a right triangle. We use trig again to determine its height h:

tan(70°) = h/(b/2)   ⇒   h = 1/2 x tan(70°)

so each triangle contributes an area of

a = 1/2 bh = 1/4 x² tan(70°) ≈ 5.142 in²

and so the area of the nonagon is

9a = 9x²/8 tan(70°) ≈ 46.281 in²

Answer:

4r ^2 +9r + 12

Step-by-step explanation:

Hope this helps! :)

Answer:

38

Step-by-step explanation:

|-7|×|5|+18÷|-6|

First take the absolute value of each number, which means take the positive value

7×5+18÷6

Multiply and divide from left to right

35 + 3

Then add

38

Length x width x price
8x2 = 16

16x$3 = $48

the total cost is $48

Answer:

Yes the one you clicked on is the right answer.

Answer:

350 divided by 70

Step-by-step explanation:

350 by 5= 70  350 by 70 = 5

Hope this helps

Answer:

70

Step-by-step explanation:

Answer:

The area of figure is 29.

Step-by-step explanation:

By counting the square box.

Answer:

28.5 square units

Step-by-step explanation:

Spit it into a triangle and a rectangle.

The Triangle is

(3 * 3) / 2

= 9 / 2

= 4.5

The Rectangle is

3 * 8

=24

The total is 4.5 + 24 = 28.5

Answer:

(Chairs):C=29−8t/3

(Tables):T=87/8−3c/8

Step-by-step explanation:

For C: Move all terms that don't contain c to the right side and solve.

For T: Move all terms that don't contain t to the right side and solve.

(Do the same thing with the other numbers as well)

(CHeck your work for each one)

Expanding the cube, we have

[tex]\dfrac1{(a+b+c)^3} = \left(\dfrac1{a+b+c}\right)^3 \\\\ = \dfrac1{a^3} + \dfrac1{b^3} + \dfrac1{c^3} + 3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc}[/tex]

so it remains to be shown that

[tex]3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc} = 0[/tex]

Factorize the grouped sum on the left as

[tex]\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2} = \dfrac1{abc} \left(\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac\right)[/tex]

so that with simplification, it remains to be shown that

[tex]\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac + 2 = 0[/tex]

With a little more manipulation, we have

[tex]\dfrac ba + \dfrac ca = \dfrac{a+b+c}a - 1[/tex]

[tex]\dfrac cb + \dfrac ab = \dfrac{a+b+c}b - 1[/tex]

[tex]\dfrac bc + \dfrac ac = \dfrac{a+b+c}c - 1[/tex]

so that our equation simplifies to

[tex]\dfrac{a+b+c}a + \dfrac{a+b+c}b + \dfrac{a+b+c}c - 1 = 0[/tex]

which we can factorize as

[tex](a+b+c)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]

Finish up by using the hypothesis:

[tex]\left(\dfrac1{\frac1{a+b+c}}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]

[tex]\underbrace{\left(\dfrac1{\frac1a+\frac1b+\frac1c}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right)}_{=1} - 1 = 0[/tex]

and the conclusion follows.

Answer:

7x^3 -24x^2 +6x +37

Step-by-step explanation:

Step 1:

Expand (2x-3)^3

(2x)^3 - 3(2x)^2 * 3+3 * 2x * 3^2 -3

(8x^3 -36x^2 +54x -27)

Step 2:

Expand (x-4)^3

x^3 -3x^2 *4 +3x *4^2 -4^3

(x^3 -12x^2 +48x -64)

Step 3: Subtract and add like terms

(8x^3 -36x^2 +54x -27) - (x^3 -12x^2 +48x -64)

7x^3 -24x^2 +6x +37

Ans: 7x^3 -24x^2 +6x +37

Answer:

E. 4/6 = 18/x

Step-by-step explanation:

4 hour using 6 logs

18 hours using x logs