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3 years ago

9

Hey need some help with this problem, its trigonometry with right triangles using SohCahToa if you can give me a hand it would b

e greatly appreciated

1 answer:

Firlakuza [10]3 years ago

6 0

For the given triangle, the value of x equals 30.9892 units.

Step-by-step explanation:

Step 1:

In the triangle, the angle is 40°, the opposite side has a length of 26 units, the adjacent side has a length of x units while the hypotenuse is not given.

To determine the value of x, we determine the value of the tan of the given triangle.

To calculate the tan of angle A we divide the opposite side's length by the the adjacent side's length.

$tan A = \frac{oppositeside}{adjacent side}.$

Step 2:

The length of the opposite side = 26 units.

The length of the adjacent side = x units.

$tan A = \frac{oppositeside}{adjacent side}, tan 40 = 0.8390, tan A = \frac{26}{x} .$

$0.8390 = \frac{26}{x} , x = \frac{26}{0.8390} = 30.9892.$

So x measures 30.9892 units.

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Consider the following. f(x) = x5 − x3 + 6, −1 ≤ x ≤ 1 (a) Use a graph to find the absolute maximum and minimum values of the fu

kykrilka [37]

ANSWER

See below

EXPLANATION

Part a)

The given function is

$f(x) = {x}^{5} - {x}^{3} + 6$

From the graph, we can observe that, the absolute maximum occurs at (-0.7746,6.1859) and the absolute minimum occurs at (0.7746,5.8141).

b) Using calculus, we find the first derivative of the given function.

$f'(x) = 5 {x}^{4} - 3 {x}^{2}$

At turning point f'(x)=0.

$5 {x}^{4} - 3 {x}^{2} = 0$

This implies that,

${x}^{2} (5 {x}^{2} - 3) = 0$

${x}^{2} = 0 \: or \: 5 {x}^{2} - 3 = 0$

$x = - \frac{ \sqrt{15} }{5} \: or \: x = 0 \: \: or \: x =\frac{ \sqrt{15} }{5}$

We plug this values into the original function to obtain the y-values of the turning points

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} +750)) \:and \: (0, - 6) \: and\: ( \frac{ \sqrt{15} }{5} , \frac{1}{125} ( - 6 \sqrt{15} +750))$

We now use the second derivative test to determine the absolute maximum minimum on the interval [-1,1]

$f''(x) = 20 {x}^{3} - 6x$

$f''( - \frac{ \sqrt{15} }{5} ) \: < \: 0$

Hence

$( - \frac{ \sqrt{15} }{5} , \frac{1}{125} ( 6 \sqrt{15} + 750))$

is a maximum point.

$f''( \frac{ \sqrt{15} }{5} ) \: > \: 0$

Hence

$( \frac{ \sqrt{15} }{5} , \frac{1}{125} (- 6 \sqrt{15} + 750))$

is a minimum point.

$f''(0) \: =\: 0$

Hence (0,-6) is a point of inflexion

4 0

3 years ago

What are the intercepts of 2x + 3y – 6z = 30?

ycow [4]

Intercept of equation 2x + 3y - 6z = 30 is (15, 0, 0) , (0, 10, 0) and (0, 0, -5)

<h3><u>Solution:</u></h3>

Given equation is:

2x + 3y - 6z = 30

We have to find the intercepts

Intercept are the point where equations cut the x- axis, y- axis and z- axis.

<em><u>Thus, at x- axis :</u></em>

y and z both are zero

So substitute y = 0 and z = 0 in given equation

2x + 3(0) - 6(0) = 30

2x = 30

x = 15

<h3>Thus the intercept is (15, 0, 0)</h3>

<em><u>Thus at y - axis:</u></em>

x and z both are zero

So substitute x = 0 and z = 0 in given equation

2(0) + 3y -6(0) = 30

0 + 3y + 0 = 30

3y = 30

y = 10

<h3>Thus the intercept is (0, 10, 0)</h3>

<em><u>Thus at z - axis:</u></em>

x and y are both zero

So substitute x = 0 and y = 0 in given equation

2(0) + 3(0) - 6z = 30

-6z = 30

z = -5

<h3>Thus the intercept is (0, 0, -5)</h3>

Thus, intercept of equation 2x + 3y - 6z = 30 is (15,0,0) ,(0,10,0) and (0,0,-5)

6 0

3 years ago

Somebody please help me!

GREYUIT [131]

Answer:

second option, IQR = 13-6 = 7 and Range = 17-6 = 11

Step-by-step explanation:

7 0

2 years ago

Someone please help me with problem #7 !!!

ser-zykov [4K]

Answer: b and d

Step-by-step explanation:

Since the roots are x=2 and x=6, we can write the equation as

$f(x)=a(x-2)(x-6)$

Substituting in the coordinates of the vertex,

$-4=a(4-2)(4-6)\\\\-4=-4a\\\\a=1$

So, the equation is $f(x)=(x-2)(x-6)$

On expanding, we get $f(x)=x^2 - 8x+12$

3 0

1 year ago

How do u turn 67÷100 into a fraction need help plz

Deffense [45]

Answer:

67/100

Step-by-step explanation:

67÷100 Divide the numbers

0.67 then move the decimal point to the right

6.7 *10 this will give you the fraction

3 0

3 years ago