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3 years ago

5

A moon's physical diameter is about 3800.0 km, and its orbital distance from its planet varies between 360,000 km and 430000.0 k

m. What is the moon's angular size in degrees at maximum distance from the planet?

1 answer:

Paul [167]3 years ago

8 0

Answer:

c

Step-by-step explanation:

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A person casts a shadow that aligns with a shadow of a tree. the person is 5.5 feet tall and casts a shadow 8.25 feet long. the

SOVA2 [1]

An equation that can be used to determine the tree's height is 22.5/8.25 = x/5.5.

The height of this tree is equal to 15 feet.

The distance of this person from the tree is equal to 14.25 feet.

<h3>What are the properties of similar triangles?</h3>

In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Additionally, two (2) geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Now, we can write an equation that can be used to determine the tree's height. Since the ratio of the corresponding sides of similar triangles are equal in magnitude, we have the following mathematical expression (equation):

22.5/8.25 = x/5.5

Where:

x represents the height of the tree.

<h3>How tall is the tree?</h3>

22.5/8.25 = x/5.5

Cross-multiplying, we have:

8.25x = 22.5 × 5.5

8.25x = 123.75

x = 123.75/8.25

x = 15 feet.

<h3>How far is the person standing from the tree?</h3>

The distance of this person from the tree can be calculated as follows;

Distance = Length of tree's shadow - Length of person's shadow

Distance = 22.5 - 8.25

Distance = 14.25 feet.

Read more on corresponding side here: brainly.com/question/11920446

#SPJ1

7 0

1 year ago

50 pts!!! Given: x - 6 1/3 ≤ 1 1/2. Choose the solution set.

maw [93]

Answer:

{x | x R, x ≤ 7 5/6 }

Step-by-step explanation:

we have

$x-6\frac{1}{3} \leq 1\frac{1}{2}$

Convert mixed number to an improper fraction first

$6\frac{1}{3}=\frac{6*3+1}{3}=\frac{19}{3}$

$1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2}$

substitute

$x-\frac{19}{3} \leq \frac{3}{2}$

Multiply by 6 both sides to remove the fractions

$6x-38 \leq 9$

Adds 38 both sides

$6x \leq 9+38$

$6x \leq 47$

Divide by 6 both sides

$x\leq \frac{47}{6}$

convert to mixed number

$\frac{47}{6}=\frac{42}{6}+\frac{5}{6}=7\frac{5}{6}$

substitute

$x\leq 7\frac{5}{6}$

therefore

{x | x R, x ≤ 7 5/6 }

4 0

4 years ago

Write an equation for each description.

olga2289 [7]

Answer:

4x =16

a - 11 =12

9/10x + 6 =51

3(1/3 + 8) =11

Step-by-step explanation:

5 0

4 years ago

HELPP MEEE PLEASEEEEE!

snow_lady [41]

Let $a=x+\tfrac{5}{2}$. Then the expression $(x+1)(x+2)(x+3)(x+4)$ becomes $\left(a-\tfrac{3}{2}\right)\left(a-\tfrac{1}{2}\right)\left(a+\tfrac{1}{2}\right)\left(a+\tfrac{3}{2}\right)$.

We can now use the difference of two squares to get $\left(a^2-\tfrac{9}{4}\right)\left(a^2-\tfrac{1}{4}\right)$, and expand this to get $a^4-\tfrac{5}{2}a^2+\tfrac{9}{16}$.

Refactor this by completing the square to get $\left(a^2-\tfrac{5}{4}\right)^2-1$, which has a minimum value of $-1$.

Similar to Solution 1, grouping the first and last terms and the middle terms, we get $(x^2+5x+4)(x^2+5x+6)+2019$.

Letting $y=x^2+5x$, we get the expression $(y+4)(y+6)+2019$. Now, we can find the critical points of $(y+4)(y+6)$ to minimize the function:

$\frac{d}{dx}(y^2+10y+24)=0$

$2y+10=0$

$2y(y+5)=0$

$y=-5,0$

To minimize the result, we use $y=-5$. Hence, the minimum is $(-5+4)(-5+6)=-1$, so $-1+2019 = \boxed{\textbf{(B) }2018}$.

Note: We could also have used the result that minimum/maximum point of a parabola $y = ax^2 + bx + c$ occurs at $x=-\frac{b}{2a}$.

Solution 4

The expression is negative when an odd number of the factors are negative. This happens when $-2 < x < -1$ or $-4 < x < -3$. Plugging in $x = -\frac32$ or $x = -\frac72$ yields $-\frac{15}{16}$, which is very close to $-1$. Thus the answer is $-1 + 2019 = \boxed{\textbf{(B) }2018}$.

Solution 5 (using the answer choices)

Answer choices $C$, $D$, and $E$ are impossible, since $(x+1)(x+2)(x+3)(x+4)$ can be negative (as seen when e.g. $x = -\frac{3}{2}$). Plug in $x = -\frac{3}{2}$ to see that it becomes $2019 - \frac{15}{16}$, so round this to $\boxed{\textbf{(B) }2018}$.

We can also see that the limit of the function is at least -1 since at the minimum, two of the numbers are less than 1, but two are between 1 and 2.

5 0

3 years ago

You are given a rectangular sheet of cardboard that measures 11 in. by 8.5 in. (see the diagram below). A small square of the sa

Stells [14]

We can solve for the value of x using the formula:

V = l w h

where,

h = x the size of the cut since it would form the walls of the rectangle

<span>w = 8.5 – 2x = it is subtracted by 2x since two sides will be cut</span>

l = 11 – 2x

Substituting:

V = x (8.5 − 2x) (11 − 2x)

Expanding the expression:

V = 93.5 x – 39 x^2 + 4 x^3

To solve the maxima, we have to get the 1st derivative dV / dx then equate to 0. dV / dx = 0:

dV / dx = 93.5 – 78 x + 12 x^2

0 = 93.5 – 78 x + 12 x^2

We get:

x ≈ 1.585 in and x ≈ 4.915 in

Therefore Anya’s suggestion of 1.5 inches would create the larger volume since it is nearer to 1.585 inches.

There can be different volumes since volume refers to the amount of space inside the rectangle. They can only have similar perimeter and surface area, but not volume.

It is restricted to <span>0 in. < x < 4.25 in. because our w is 8.5 – 2x. Going beyond that value will give negative dimensions.</span>

7 0

3 years ago