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2 months ago

Value of sec Square 26 degrees - cot square 64 degrees is

Mathematics

1 answer:

Leona [12.6K]2 months ago

4 0

Answer:

The value equals 1

Step-by-step explanation:

Consider the expression

$sec^{2}(26\°)-cot^2(64\°)$

Recall that

$cot^2(64\°)=\frac{cos^2(64\°)}{sin^2(64\°)}$

$sec^{2}(26\°)=\frac{1}{cos^2(26\°)}$

For two complementary angles A and B (where A+B=90°),

the identity is

cos(A) = sin(B)

Here, 26° and 64° are complementary angles, so

$\frac{1}{cos^2(26\°)}=\frac{1}{sin^2(64\°)}$

Substituting values,

$\frac{1}{sin^2(64\°)}-\frac{cos^2(64\°)}{sin^2(64\°)}$

$\frac{1-cos^2(64\°)}{sin^2(64\°)}$

From this, we find

$1-cos^2(64\°)=sin^2(64\°)$

By substitution,

$\frac{sin^2(64\°)}{sin^2(64\°)}=1$

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The University of Central Florida's cheerleading team has eighteen males and twenty-one females. If h represents the height of a

Leona [12618]

Answer:

The range of cheerleaders' heights lies within the interval [58, 74)

It includes all real numbers from 58 inches and above, but below 74 inches.

Step-by-step explanation:

we have

$260 \leq 4h+28$

Separate the combined inequality into two distinct inequalities

$260 \leq 4h+28$ -----> inequality A

$4h+28$ -----> inequality B

Solve inequality A

$260 \leq 4h+28$

Subtract 28 from both sides

$232 \leq 4h$

Split by 4 on both sides

$58 \leq h$

Reformulate

$h \geq 58\ in$

Address inequality B

$4h+28$

Subtract 28 from both sides

$4h$

Split by 4 on both sides

$h$

consequently

The height range of the cheerleaders is the interval [58, 74)

It consists of every real number starting from 58 inches and less than 74 inches

3 0

1 month ago

Ill give a tip

PIT_PIT [12445]

To calculate the monthly interest, take the APR and divide it by 360, then multiply the result by 30 days. Typically, each loan is backed by the vehicle that was purchased, hence we will utilize the secured APR.

8. For an average secured APR of 5.85%, the calculation is: 5.85% divided by 360 multiplied by 30 gives a monthly rate of 0.4875%.
The vehicle cost is 19,725; with a sales tax of 4.75% and a down payment of 2,175.

19,725 multiplied by 1.0475 results in 20,661.94, and after subtracting the down payment, the loan amount is 18,486.94.
To find the accrued interest for the first month: 18,486.94 multiplied by 0.4875% equals 90.12.

9. An excellent secured APR of 4.80% results in a monthly rate of 0.40% when 4.80% is divided by 360 and multiplied by 30.
Price of a different vehicle: 15,867; a sales tax of 5.25%; down payment equals 10% of the total.

Calculating, 15,867 multiplied by 1.0525 gives 16,700.02; taking 90% results in a principal balance of 15,030.02 at the loan's beginning.

10. For a fair secured APR at 7%, dividing by 360 and multiplying by 30 provides a monthly rate of 0.5833%.
Cost of a new vehicle is 19,072; sales tax stands at 4.5%; down payment of 1,200.
Cost for a used vehicle is 15,365; same tax and down payment as the new one.

Calculating for new: 19,072 multiplied by 1.045 results in 19,930.24, with down payment deducted gives 18,730.24.
Accrued interest for new is 18,730.24 multiplied by 0.5833% equating to 109.25.

For the used vehicle: 15,365 multiplied by 1.045 results in 16,056.43, then down payment leaves 14,856.43.
Accrued interest here is 14,856.43 multiplied by 0.5833% equaling 86.66.

The difference in interest accrued by the first month's end is 109.25 minus 86.66, which is 22.59.

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15 days ago

CORINA INDRAGESTE FOARTE MULT ANIMALELE IN DAR DE ZIU EI A PRIMIT O CARTE DESPRE LUMEA LOR MINUNATA IN PRIMA ZI EA A CITIT 36 DE

babunello [11817]

The answer I arrived at is related to paging.

7 0

17 days ago

Last week, your delivery runs took 7 hours 12 minutes on Monday, 6 hours 46 minutes on Wednesday, and 6 hours 53 minutes on Frid

zzz [12365]

7 hours 12 minutes
6 hours 46 minutes
6 hours 53 minutes
--------------------------sum
Total: 19 hours 111 minutes, which converts to (19 × 60) + 111 = 1140 + 111 = 1251 minutes

Calculate average time by dividing by 3: 1251 / 3 = 417 minutes, equivalent to 6 hours 57 minutes, which is the average delivery duration.

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2 months ago

555 grams of wool were needed to knit a sweater, a hat, and a scarf. The hat required 5 times less wool than the sweater and 5 g

Zina [12379]

Answer:

The amount of wool required for a sweater was 400 grams.

A hat needed 80 grams of wool.

A scarf required 75 grams of wool.

Step-by-step explanation:

Let

x ------> grams of wool necessary for a sweater

y -----> grams of wool necessary for a hat

z -----> grams of wool necessary for a scarf

From the information given

x+y+z=555 -----> equation A

y=x/5 ----> x=5y -----> equation B

y=z+5 ---> z=y-5 ----> equation C

By substituting equations B and C into equation A, we can solve for y:

(5y)+y+(y-5)=555

7y=560

y=80 grams

Now, find x

x=5(80)=400 grams

Next, determine z

z=80-5=75 grams

In conclusion,

400 grams of wool was required for the sweater,

the hat needed 80 grams of wool, and

the scarf required 75 grams of wool.

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1 month ago