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2 years ago

The tangent ratio is the ratio of the side _ the acute angle over the side __ to the acute angle.

1 answer:

8 0

For this case what you have to take into account is the following trigonometric definition:
Tan (x) = (C.O) / (C.A)
Where,
x: angle
C.O: opposite leg
C.A: Adjacent cateto.
We have then:
The tangent ratio is the ratio of the side opposite the angle of the side to the angle.
Answer:
opposite, adjacent

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Find the dimensions of the rectangle with area 289 square inches that has minimum perimeter, and then find the minimum perimeter

nalin [4]

<span>To minimize the perimeter you should always have a square.
sqrt(289) = 17
The dimensions should be 17 X 17

To see , try starting at length 1, and gradually increase the length.
The height decreases at a faster rate than the length increases, up until you reach a square.

Or if you want to use algebra, Say the width is 17-x
Then the length is 289/(17-x)

Now, this is bigger than 17+x, as shown here:
289/(17-x) > 17+x
289 > 289 - x^2
which is true.
so the perimeter would be bigger than 2 * (17- x + 17 + x) = 2 * (2 * 17) = 4 * 17

Again, the dimensions should be a square. 17 X 17.</span>

4 0

2 years ago

Jace has consumed 1,500 calories so far today. He has also burned off 400 calories at the gym. He would like to keep his daily c

maksim [4K]

Answer:

Step-by-step explanation:

Consumed = 1500

Burned = 400

Calorie Count total = 1500 - 400 = 1100

His target is 1900, so he will need 1900 - 1100 = 800 calories to consume more

So, 1100 is NOT a viable solution because he will go over 1900 if that happens. Hence, C is the correct choice.

7 0

2 years ago

Read 2 more answers

The 8th term of a GP is -7/32 find its common ratio if its first term is 28

Ugo [173]

<h2>Common ratio = -1/2</h2>

Step-by-step explanation:

$\text{8}^{th}$ term of a Geometric progression is given as $\dfrac{-7}{32}$ . The first term is given as $28$ .

Any general Geometric progression can be represented using the series $a,ar,ar^{2},ar^{3},ar^{4}...\text{ }ar^{n-1}$ .

The first term in such a GP is given by $a$ , common ratio by $r$ , and the $n^{th}$ term is given by $ar^{n-1}$ .

In the given GP, $a=28;t_{8}=ar^{7}=\dfrac{-7}{32}\\\\28r^{7}=\dfrac{-7}{32}\\\\r^{7}=\dfrac{-1}{128}\\\\r=\dfrac{-1}{2}$

∴ Common ratio is $\dfrac{-1}{2}$ .

5 0

2 years ago

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

den301095 [7]

Answer:

The maximum height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> the height of the prism

we know that

the area of the rectangular base of the prism is equal to

$A=L*W$

$A\leq 27\ m^{2}$

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Substitute equation B in equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substitute equation B and equation D in the inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The solution for x is the interval----------> $[0,12]$

see the attached figure

but remember that

The width of the base must be $9$ meters less than the height of the prism

the solution for x is the interval ------> $(9,12]$

The maximum height of the prism is $12\ m$

8 1

2 years ago

Read 2 more answers

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

5 0

2 years ago

The tangent ratio is the ratio of the side _____ the acute angle over the side ______ to the acute angle.

The tangent ratio is the ratio of the side _ the acute angle over the side __ to the acute angle.