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3 years ago

Joy wants to create a box with a volume of 8 cubic units. which dimensions would work

Mathematics

1 answer:

N76 [4]3 years ago

4 0

Answer:

The dimensions of the box is 2 units.

Step-by-step explanation:

Volume of cube, V = 8 cubic units

Let the length of the side is a.

So,

The volume of the cube is

$V = a^3\\\\8 = a^3\\\\a = 2 units$

So, the dimensions of the box is 2 units.

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Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2

pshichka [43]

$a_n_+_1=-4a_n_+_2$

dividing both sides by -4, we get:

$a_n_+_2=- \frac{a_n_+_1}{4}$

this means, each term is its previous term divided by -4.

now we can construct the sequence as follows:

$a_1=2$

$a_2=- \frac{a_1}{4}= - \frac{2}{4}= -\frac{1}{2}$

$a_3=- \frac{a_2}{4} =- \frac{ \frac{1}{2} }{4}=- \frac{1}{8}$

$a_4=- \frac{a_3}{4}=- \frac{ \frac{1}{8} }{4}=- \frac{1}{32}$

Answer: the last term is -1/32

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3 years ago

A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8 degrees when staring at the top of t

borishaifa [10]

The height of the statue is 19.5 feet.

Why?

We can solve the problem using trigonometric formulas. In this case, we are going to use the trigonometric formula of the tangent.

We know that the person is standing 50ft from the statue, so, it will be the base of the two triangles formed by both angles (elevation and depression)

Using the trignometric formula, we have:

First triangle:

$tg(\alpha )=\frac{h_{1}}{base} \\\\tg(8\°)=\frac{h_{1}}{50ft}\\\\0.14*50ft=h_1\\\\h_1=7ft$

Second triangle:

$tg(\alpha )=\frac{h_{2}}{base} \\\\tg(14\°)=\frac{h_{1}}{50ft}\\\\0.25*50ft=h_1\\\\h_1=12.5ft$

Now, the total height of the statue will be:

$TotalHeight=h_1+h_2=7ft+12.5ft\\\\TotalHeight=19.5ft$

Have a nice day!

8 0

3 years ago

The measure of an angle is 8 times the measure of its complement. tina writes an equation and finds the correct measure of each

pogonyaev

One of the unknown angles (let's called it n) has a complement (meaning their sum adds up to 90 degrees) and the other angle is 8 times the unknown angle (8n)

With all this information, you should have the equation:

n + 8n = 90

To solve, combine like terms to get:

9n = 90

Divide by 9 on both sides to isolate the variable n.

n = 10

Now we plug back in to find our angle measurements. The first angle, n, is 10 degrees. The second angle, 8n, is 8 * 10 which is 80; the second angle is 80 degrees.

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3 years ago

Can someone help wit this just find the value of x

Romashka-Z-Leto [24]

2x-2+x+5=90
3x+3=90
-3 -3
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x=29

6 0

3 years ago

Find the equation of the axis of symmetry and the coordinates of vertex of the functions =2x^2+4x-3

SVEN [57.7K]

Hello,

Find the equation of the axis of symmetry is like find the maximum or minimum point of this function.

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The equation of the axis of symmetry is then : $x=-1$

$\beta=f(\alpha)=2(-1)^2+4(-1)-3=2-4-3=-5$

Coordinates of vertex : $(\alpha,\beta)=(-1;-5)$

8 0

3 years ago