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3 years ago

Simplify the trigonometric expression. sin4(α) − cos4(α) + cos2(α)

Mathematics

1 answer:

natulia [17]3 years ago

5 0

Answer:

sin²(α)

Step-by-step explanation:

sin⁴(α) − cos⁴(α) + cos²(α)

sin⁴(α) − cos²(α) (cos²(α) − 1)

sin⁴(α) − cos²(α) (-sin²(α))

sin⁴(α) + sin²(α) cos²(α)

sin²(α) (sin²(α) + cos²(α))

sin²(α) (1)

sin²(α)

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If you order 3 hamburgers, 2 orders of fries, and 3 milkshakes for your friends, how much do they owe you?

Amiraneli [1.4K]

Answer:

31.55

Step-by-step explanation:

5 0

2 years ago

A grocery store manager notices that this month her store sold a total of 623 gallons of ice cream, which represents a decrease

kotykmax [81]

Answer:

- The store sold 733 gallons of ice cream last month.

- The store sold 748 pounds of broccoli last month.

Step-by-step explanation:

Given

$Ice\ Cream = 623$

$\%\ Ice\ Cream = 15\%$

$Broccoli = 912$

$\%\ Broccoli = 22\%$

Solving (a): Gallons of Ice Cream

<em>Let Gallons sold last month be G1; Gallons sold this month be G2;</em>

The relationship between both is:

$G2 =G1 - 15\% * G1$

Substitute 623 for G2

$623 =G1 - 15\% * G1$

$623 =G1 - 0.15 * G1$

$623 =G1 - 0.15 G1$

$623 =0.85 G1$

Divide through by 0.85

$G1 = 623/0.85$

$G1 = 732.941176471$

$G1 = 733$

Solving (b): Pounds of Broccoli

<em>Let Pounds sold last month be P1; Pounds sold this month be P2;</em>

The relationship between both is:

$P2 =P1 + 22\% * P1$

Substitute 912 for P2

$912 =P1 + 22\% * P1$

$912 =P1 + 0.22 * P1$

$912 =P1 + 0.22 P1$

$912 =1.22 P1$

Divide through by 1.22

$P1 = 912/1.22$

$P1 = 747.540983607$

$P1 = 748$

6 0

3 years ago

error uses 1/3 can of wet dog food for his dog,muddy,each day.how many servings will he get from 5 cans of dog food?

Vesnalui [34]

First convert 5 cans of dog food to a fraction
(5*3)/3 = 15/3
15/3 - 1/3 = 14/3
he uses 1/3 a can and so he then has 14 servings.

7 0

2 years ago

Write two equations for two perpendicular lines that have the same y intercept and do not pass through the same origin 15Points

Zanzabum

Two equations for two perpendicular lines that have the same y-intercept and do not pass through the same origin are; y = x + 1 and y = -x + 1

<h3>What is the equation of the two lines?</h3>

The general formula for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, when we talk about two perpendicular lines, it means that their slopes are negative reciprocals of each other.

Secondly, we are told that they both do not pass through the origin. Thus, it means that the y-intercept cannot be zero.

Therefore, two possible equations here can be;

y = x + 1 and y = -x + 1

Read more about Equation of lines at; brainly.com/question/13763238

#SPJ1

8 0

1 year ago

in CAT the measure of the largest angle is 10 less than 5 time the smallest angle. The measure of the middle angle is 6 more tha

Vsevolod [243]

Answer:

The measure of middles angle is 113.5° .

Step-by-step explanation:

Given as :

The measure of the largest angle is 10 less than 5 time the smallest angle.

The measure of the middle angle is 6 more than twice the measure of the largest angle

Let The largest angle = L

Let The middle angle = M

Let The smallest angle = S

As per statement

Largest angle = 5 times smallest angle - 10

i.e L = 5 × S - 10 .....1

Again

Middle angle = twice largest angle + 6

i.e M = 2 × L + 6 ......2

Since for any Triangle sum of three angles = 180°

i.e ∠L + ∠M + ∠S = 180°

Or, ( 5 × S - 10 ) + ( 2 × L + 6 ) + S = 180°

Or, ( 5 × S - 10 ) + [ 2 × (5 × S - 10 ) + 6 ] + S = 180°

Or, 5 S - 10 + (10 S - 20 + 6) + S = 180°

Or, 5 S - 10 + 10 S - 20 + 6 + S = 180°

Or, (5 + 10 + 1) S - 24 = 180°

Or, 16 S = 180° + 24

Or, 16 S = 204

∴ S = $\dfrac{204}{16}$

i.e S = 12.75

So, The measure of smallest angle = S = 12.75°

And

L = 5 × 12.75 - 10

i.e L = 53.75

So, The measure of Largest angle = L = 53.75°

And

M = 2 × L + 6

Or, M = 2 × 53.75 + 6

i.e M = 107.5 + 6 = 113.5

So, The measure of middles angle = M = 113.5°

Hence, The measure of middles angle is 113.5° . Answer

3 0

3 years ago