Derek sees that a 24 foot flagpole casts a 10 foot shadow. At the same time of day, if a nearby tree casts

25 foot shadow, about how tall is the tree?

Answer:

The Answer is A. 252π ft3

Step-by-step explanation:

Hence volume of shaded sphere is  [tex]113.09734ft^{2}[/tex]

What is Volume?

Volume refers to part inside 3 d figure which tell how much space it occupies.

How to solve?

Given two concentric spheres  one with D=12 ⇒ R= 6 feet other with r=3feet.

volume of shaded part[tex]=\frac{4}{3} \pi R^{3}-\frac{4}{3} \pi r^{3}[/tex]

[tex]=\frac{4}{3} \pi (R-r)^{3}[/tex]

[tex]=\frac{4}{3} \pi 3^{3}[/tex]=[tex]113.09734[/tex][tex]ft^{2}[/tex]

Hence volume of shaded sphere is  [tex]113.09734ft^{2}[/tex]

Learn more about volume

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The length of the rectangle is 11 units

The width of the rectangle is 5 units.

Explanation:

The equation of the trinomial is [tex]r^{2}-6 r-55[/tex]

We need to find the length and the width of the rectangle.

The length and width of the rectangle can be determined by factoring the trinomial [tex]r^{2}-6 r-55=0[/tex]

Factoring using the quadratic formula, we have,

[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

where [tex]a=1, b=-6[/tex] and [tex]c=-55[/tex]

Substituting these in the above formula, we have,

[tex]r=\frac{-(-6) \pm \sqrt{(-6)^{2}-4 \cdot 1(-55)}}{2 \cdot 1}[/tex]

[tex]r=\frac{6\pm \sqrt{36+220}}{2}[/tex]

[tex]r=\frac{6\pm \sqrt{256}}{2}[/tex]

[tex]r=\frac{6\pm 16}{2}[/tex]

Hence, the two roots of the trinomial are

[tex]r=\frac{6+ 16}{2}[/tex] and [tex]r=\frac{6- 16}{2}[/tex]

Solving [tex]r=\frac{6+ 16}{2}[/tex] , we get,

[tex]r=\frac{22}{2}[/tex]

[tex]r=11[/tex]

Solving [tex]r=\frac{6- 16}{2}[/tex] , we get,

[tex]r=\frac{-10}{2}[/tex]

[tex]r=-5[/tex]

Thus, the solutions of the trinomial are 11 and -5

Since, the length of the rectangle is larger than the width, the length of the rectangle is 11 units.

Also, the width of the rectangle cannot be negative.

Thus, ignoring the negative sign, we have, [tex]r=5[/tex]

Hence, the width of the rectangle is 5 units.

Answer:

b,d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that

x²>18

So, let take the square root of both sides

Then,

√x²>√18

x> ± 4.24

So it is either

x>4.24 or x<-4.24

Either of the two will gives a square higher than 18. You should note that the square of any number is always positive.

The applicable answer are

A. 5

Because

5²=25 which is greater than 18

D. 8

Because

8²= 64 which is greater than 18

F. -18

Because

(-18)²=-18×-18=324 which is greater than 18.

Note : -×-=+

Well, there can be three different steps.

Rearrange the equation so "y" is on the left and everything else on the right.

Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

The average value of f(x) = 3x sin(x) on the interval [tex]\( 1 \leq x \leq 7 \) is approximately \( -1.6204 \).[/tex]

To find the average value of a function f(x) on a closed interval [a, b], we use the formula:

[tex]\[ \text{Average value} = \frac{1}{b - a} \int_{a}^{b} f(x) \, dx \]In this case, the function \( f(x) = 3x \sin(x) \) and the closed interval is \( 1 \leq x \leq 7 \).So, the average value of \( f(x) \) on the interval \( 1 \leq x \leq 7 \) is:\[ \text{Average value} = \frac{1}{7 - 1} \int_{1}^{7} 3x \sin(x) \, dx \][/tex]

[tex]\[ \text{Average value} = \frac{1}{6} \int_{1}^{7} 3x \sin(x) \, dx \][/tex]

Now, we need to compute the integral. We can do this using integration by parts:

[tex]Let \( u = 3x \) and \( dv = \sin(x) \, dx \).Then, \( du = 3 \, dx \) and \( v = -\cos(x) \).Using the integration by parts formula:\[ \int u \, dv = uv - \int v \, du \]\[ \int_{1}^{7} 3x \sin(x) \, dx = \left[ -3x \cos(x) \right]_{1}^{7} - \int_{1}^{7} (-\cos(x)) \cdot 3 \, dx \][/tex]

[tex]\[ = \left[ -3x \cos(x) \right]_{1}^{7} + 3 \int_{1}^{7} \cos(x) \, dx \]\[ = \left[ -3x \cos(x) \right]_{1}^{7} + 3 \left[ \sin(x) \right]_{1}^{7} \]\[ = \left[ -21 \cos(7) + 3 \sin(7) \right] - \left[ -3 \cos(1) + 3 \sin(1) \right] \][/tex]

Now, let's compute these values:

[tex]\[ \text{Average value} = \frac{1}{6} \left[ \left( -21 \cos(7) + 3 \sin(7) \right) - \left( -3 \cos(1) + 3 \sin(1) \right) \right] \]\[ \text{Average value} = \frac{1}{6} \left[ (-21 \times 0.7539 + 3 \times 0.6560) - (-3 \times 0.5403 + 3 \times 0.8415) \right] \]\[ \text{Average value} = \frac{1}{6} \left[ (-15.8359 + 1.9680) - (-1.6209 + 2.5245) \right] \][/tex]

[tex]\[ \text{Average value} = \frac{1}{6} \left[ -13.8679 + 4.1454 \right] \]\[ \text{Average value} = \frac{1}{6} \times (-9.7225) \]\[ \text{Average value} \approx -1.6204 \][/tex]

So, the average value of f(x) = 3x sin(x) on the interval [tex]\( 1 \leq x \leq 7 \) is approximately \( -1.6204 \).[/tex]

The average value of [tex]\(f(x) = 3x \sin(x)\)[/tex] on the interval [tex]\(1 \leq x \leq 7\)[/tex] is approximately 1.879.

To find the average value of [tex]\( f(x) = 3x \sin(x) \)[/tex]on the closed interval [tex]\( 1 \leq x \leq 7 \)[/tex], we can use the formula for the average value of a function on a closed interval [a, b] :

[tex]\[ \text{Average value} = \frac{1}{b - a} \int_a^b f(x) \, dx \][/tex]

In this case, a = 1 and b = 7, so:

[tex]\[ \text{Average value} = \frac{1}{7 - 1} \int_1^7 3x \sin(x) \, dx \][/tex]

Now, we need to evaluate the integral:

[tex]\[ \int_1^7 3x \sin(x) \, dx \][/tex]

This integral can be evaluated using integration by parts or by using a software tool. After evaluation, we find that the average value is approximately 1.879.

So, the correct answer is 1.879.

Complete Question:

Let f be the function given by f(x)=3xsinx. What is the average value of f on the closed interval 1≤x≤7 ?

−14.764

−2.461

1.879

8.161

Answer:

D(4) = -18

Step-by-step explanation:

D(n) = D(n – 1)(-6)

D(1) = 1/12

D(2) = D(2 – 1)(-6)

D(2) = D(1)(-6)

D(2) = 1/12 * (-6)

D(2) = -6/12

D(2) = -1/2

D(3) = D(3 – 1)(-6)

D(3) = D(2)(-6)

D(3) = -1/2 * (-6)

D(3) = 6/2

D(3) = 3

D(4) = D(4 – 1)(-6)

D(4) = D(3)(-6)

D(4) = 3 * (-6)

D(4) = -18

Answer:

D(4) = -18

Step-by-step explanation:

Answer:15/8

Step-by-step explanation:

Answer:

15/8

Step-by-step explanation:

Cross multiply, 8x=15. Divide by 15 on both sides, 15/8 is your answer.

Answer:

[tex]2.25\ in^{2}[/tex]

Step-by-step explanation:

Area of a square is given by

[tex]A=b*b=b^{2}[/tex]

Where A is area and b is the length of any side. This question has only one thing that is square in shape, the mat hence the question directly requires its area.

Given that the mat has square shape and has dimensions of 1.5 in each then the area will be

A=1.5*1.5=2.25 square inches

Therefore, the area is 2.25 square inches.

Answer:

Step-by-step explanation:

Final answer:

To find the value of x, set the two expressions for the lengths of the sides of the rectangle equal to each other and solve. The value of x is 2. To find the length of each diagonal, use the Pythagorean Theorem with the lengths of the sides of the rectangle. The length of each diagonal is 13 * sqrt(2).

Explanation:

To find the value of x, we can set the two expressions for the lengths of the sides of the rectangle equal to each other, since opposite sides of a rectangle are congruent. So, we have:

6x + 1 = 9x - 5

To solve for x, we can subtract 9x from both sides and add 5 to both sides:

1 + 5 = 9x - 6x

6 = 3x

x = 2

Therefore, the value of x is 2. To find the length of each diagonal, we can use the Pythagorean Theorem. The diagonal of a rectangle acts as the hypotenuse of a right triangle formed by the sides of the rectangle. In this case, the length of one side is 6x + 1, and the length of the other side is 9x - 5. So, the length of each diagonal is:

d = sqrt((6x + 1)^2 + (9x - 5)^2)

d = sqrt((6(2) + 1)^2 + (9(2) - 5)^2)

d = sqrt(13^2 + 13^2)

d = sqrt(2 * 13^2)

d = 13 * sqrt(2)

Answer:

60ft

Step-by-step explanation:

you havent multiplied it by [tex]\pi[/tex] yet do it would just be the radius multiplied by two so it would be 60, becuase the radius is 30.

C= 2[tex]\pi[/tex]r

The volume of the given rectangular prism is option C. [tex]24 un^{3}[/tex].

Step-by-step explanation:

Step 1:

The dimensions of the given rectangular prism are 4 units × 3 units × 2 units.

So we take the length equals 4 units, the width is equal to 3 units and the height is 2 units.

Step 2:

The volume of this rectangular prism is calculated by multiplying the given prism's length, its width, and its height.

The Volume of the given rectangular prism = [tex]( Length) (Width) (Height) = (4units) (3units) (2 units) = 24 unit^{3} .[/tex]

So the given right rectangular prism's volume is [tex]24 unit^{3}[/tex] which is option C.

Answer:

D

Step-by-step explanation:

To find two unknowns, you need atleast two different equations.

Answer:

[tex]\large \boxed{2}[/tex]

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.

[tex]\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}[/tex]

Check:

[tex]\begin{array}{rcl}16384 & = & 4(2)^{12}\\16384 & = & 4(4096)\\16384 & = & 16384\\\end{array}[/tex]

It checks.

Answer:

4ft

Step-by-step explanation:

A) This is a Pythagorean Triple.

B) 3^2 +x^2=5^2

9+x^2=25

x^2=16

x=4

Answer:

It is 4

Step-by-step explanation:

Answer:

0.2+sqrt3/10

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, if I'm reading it correctly, it could be simplified to (1/5)+(sqrt3/10) or 0.2+sqrt3/10.

(っ◔◡◔)っ ♥ Hope this helped, have a great day! ♥

˜”*°•.˜”*°• ~Star •°*”˜.•°*”˜

Answer:

Here the degree of the polynomial is 11.

Step-by-step explanation:

To find the degree of the multivariate polynomials, we need to add up the powers of all the variables.   So the total degree is given by the sum of all the powers of the highest powers terms.

Now in the given polynomial [tex]-3w+x^6y^5-2+5y^4w^3x^2[/tex]

the term with the highest total powers is [tex]x^6y^5[/tex] and thus the total power is 6+5=11.

And hence the degree of this polynomial is 11.

Answer:

150000

Step-by-step explanation:

Answer:

150,000‬

Step-by-step explanation:

Answer:

-2/3

[tex]\sqrt50[/tex]

-1

-2.3145

Step-by-step explanation:

Answer:

-2/3

\sqrt50

-1

-2.3145

Step-by-step explanation:

please brainlist!

Answer:

75

Step-by-step explanation:

(92+8)-(22+3)

Add the terms inside of the parentheses because of PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction)

(100)-(25)

Then subtract 25 from 100

75

Answer:

20 1/2

Step-by-step explanation:

its 20 and a half because 16+20=36 and you just need to add a half to 20 since your taking it away

Answer:

c=20.5 or 41/2

Step-by-step explanation:

c- 1/2 + 16=36

Make C the subject

c=36-16+1/2

c=20+1/2

Using LCM

c=(40+1)/2

c=41/2

c=20.5

To check if we are correct, we substitute c with 41/2. and then both sides of the equation must be equal

c- 1/2 + 16=36

41/2-1/2+16=36

20+16=36

36=36

Answer:

[tex]\frac{-19}{2}[/tex]

Step-by-step explanation:

[tex]\frac{5}{4}[/tex] + [tex]\frac{-43}{4}[/tex] = [tex]\frac{-19}{2}[/tex]

Step-by-step explanation:

[tex] {6}^{2} - 10 \\ = 36 - 10 \\ = 26 \\ so \: kurt \: forgot \: to \: write \: units \: place \: \\ number \: 6 \: after \: 2.[/tex]

Answer:

10 bows

Step-by-step explanation:

Each bow is 0.5 yards and you have 5 yards of ribbon. In equation form (where x = number of bows), that looks like: 0.5 * x = 5. Solve for x and you'll get x = 10.

This mathematics problem can be solved by multiplication. Since each bow requires half a yard of ribbon, each yard can produce two bows. Therefore, five yards of ribbon can produce 10 bows.

The question requires us to determine how many bows we can make with a given number of yards of ribbon. Since it takes half a yard of ribbon to make a bow, you can fit two bows in a single yard. To find how many bows can be made with 5 yards, you can perform multiplication.

To do this, you would multiply the number of yards by 2, since each yard can create two bows: 5 yards × 2 = 10 bows. So, you can make 10 bows out of 5 yards of ribbon.

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Answer:

Part 1) Vertical line : [tex]x=1[/tex]

Part 2) Horizontal line :  [tex]y=-4[/tex]

Step-by-step explanation:

Part 1) Write the equation for the vertical line passing through the point (1,-4)

we know that

The equation of a vertical line (parallel to the y-axis) is equal to the x-coordinate of the point that passes through it

so

The x-coordinate is 1

therefore

The equation of the line is

[tex]x=1[/tex]

Part 2) Write the equation for the horizontal line passing through the point (1,-4)

we know that

The equation of a horizontal line (parallel to the x-axis) is equal to the y-coordinate of the point that passes through it

so

The y-coordinate is -4

therefore

The equation of the line is

[tex]y=-4[/tex]

Answer:

It would be A:likely

Step-by-step explanation:

let's take rounding decimals for example; when you 5.86 and you were rounding to the nearest tenth it would be 5.9. That is because the 6 is greater than 5, so for the weather the highest the percentage it can be is 100% and 50% is half and since it is more than half then it would be more likely.

Answer: 30 min.

Step-by-step explanation: for this, you have to find the gcf of 5 and 6, which is 30.

Final answer:

Mike and Sam will both cross the starting line together after 30 minutes of running, as 30 minutes is the least common multiple of their individual lap times of 5 and 6 minutes.

Explanation:

To find out how long it will take for Mike and Sam to cross the starting line together again, we need to determine the least common multiple (LCM) of their lap times. Mike runs a lap in 5 minutes and Sam runs a lap in 6 minutes. The LCM of 5 and 6 will give us the first time they both cross the starting line at the same time after they start running.

To calculate the LCM of 5 and 6, we list the multiples of each number until we find a common one:

5, 10, 15, 20, 25, 30, ...

6, 12, 18, 24, 30, ...

The smallest common multiple of 5 and 6 is 30. Therefore, Mike and Sam will both cross the starting line together after 30 minutes of running.

Answer:

1hr=60minutes

ATQ,20 minutes/60 minutes=1/n

1/3=1/n

so the value of n is 3...

Step-by-step explanation: Hope i helped please give brainliest!

Answer: 33a+19

Step-by-step explanation:

11a+7+10a+3+12a+9

Collect like terms.

(11a+10a+12a)+(7+3+9)

Simplify.

33a+19

Answer:

33a+9

Step-by-step explanation:

11a+10a+12a= 33a

7+3+9= 19

To determine the length of ZY for it to be a tangent to circle X at point Y, we must know additional measurements, such as the radius of the circle, because a tangent is perpendicular to the radius at the point of tangency.

To determine the length of ZY so that it is tangent to circle X at point Y, we need to apply properties of tangents to a circle. A tangent to a circle forms a right angle with the radius at the point of tangency. Therefore, in a right-angled triangle, with the radius XY being one side and ZY being the hypotenuse, we could use the Pythagorean theorem if we know the length of the radius and any other segment connected to the radius or tangent.

Without further information, such as the length of radius XY or any other segment, it's not possible to calculate the exact length of ZY. However, the essential condition is that radius XY must be perpendicular to the tangent ZY at point Y for ZY to be a proper tangent.