help I'll give brainliest and 5 starts and heart thanks​

To prove the equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x), we can start by expressing the trigonometric functions csc(x) and cot(x) in terms of sine and cosine:

csc(x) = 1/sin(x)

cot(x) = cos(x)/sin(x)

Substituting these expressions into the equation, we get:

(1/sin(x))^4 - (cos(x)/sin(x))^4 = (1/sin(x))^2 + (cos(x)/sin(x))^2

Next, we simplify each term separately:

(1/sin(x))^4 = 1/sin^4(x)

(cos(x)/sin(x))^4 = cos^4(x)/sin^4(x)

Expanding the powers, we have:

1/sin^4(x) - cos^4(x)/sin^4(x) = 1/sin^2(x) + cos^2(x)/sin^2(x)

Combining the fractions on the left side:

(1 - cos^4(x))/sin^4(x) = (1 + cos^2(x))/sin^2(x)

Now, let's simplify the left side:

1 - cos^4(x) = sin^4(x)

Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:

sin^4(x) = sin^4(x)

The equation simplifies to an identity, showing that the original equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x) is true for all values of x.

Therefore, we have proved the given equation.

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Answer:

Step-by-step explanation:

The equation of an ellipse centered at the origin with height 8 units and width 16 units is (x² / 64) + (y² / 16) = 1.

To write the equation of an ellipse centered at the origin with height 8 units and width 16 units, we need to determine the semi-major axis (a) and the semi-minor axis (b). The width corresponds to the horizontal axis, and the height corresponds to the vertical axis.

In this case, the width is 16 units, so half of the width, or the semi-major axis, is 8 units. Thus, a = 8. The height is 8 units, so half of the height, or the semi-minor axis, is 4 units. Therefore, b = 4.

Now, we can use the standard equation for an ellipse centered at the origin:

(x² / a²) + (y² / b²) = 1

Plugging in the values of a and b, we get:

(x² / 8²) + (y² / 4²) = 1
(x² / 64) + (y² / 16) = 1

This is the equation of the ellipse centered at the origin with height 8 units and width 16 units.

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We can't use any of the pattern

Answer:

113 degrees

Step-by-step explanation:

2 and 7 are equal, so 0 and 2 will equal the same as 3 and 7, and both equal 180... Do 180-67=113

Answer:

the coefficient

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

In this problem, AC and BD should be set equal to each other.

3x + 15 = 4x - 5

You would then solve for x, which is x = 20.

Plug 20 back in the equation for AC, 3(20) + 15, to get 75.  

The length of AC is 75.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

AC = 3x + 15

BD = 4x - 5

AC and BD are diagonals of the rectangle.

The diagonals of a rectangle are equal.

Now,

AC = BD

3x + 15 = 4x - 5

15 + 5 = 4x - 3x

20 = x

Now,

AC = 3x + 15

= 3 x 20 + 15

= 60 + 15

= 75

Thus,

AC = 75

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The difference between the predicted value found in (c) and the actual winning height of 5.96 m is 2.66

We have to find the linear model of winning the height pole in the Olympics

This would given as

y = 4.7848 + 0.0265 (2008 - 1952)

y = 3.3008

Based on the equation the height is given as 3.3008

Then the difference would be  5.96 - 3.3008

= 2.6592

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Answer:

I am not sure which form you want.

Points slope: y -2  = 3(x -4)

Slope intercept:  y = 3x -10

Step-by-step explanation:

Point slope form for the line

y- y = m(x -x)  

slope of 3 and the point (4,2)  Use 4 for x and 2 for y

y -2  = 3(x -4)

Slope intercept form of a line

y = mx + b

2 = 3(4) + b

2 = 12 + b  Subtract 12 from both sides

2 - 12 = 12 - 12 + b

-10 = b

y = mx + b

y = 3x -10

Answer:

\(\large \boxed{\sf \ \ 70\% \ \ }\)

Step-by-step explanation:

Hello,

We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :

   \(1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})\)

For the second week

   \(1000\cdot (1+\dfrac{r}{5200})^2\)

After 52 weeks

   \(1000\cdot (1+\dfrac{r}{5200})^{52}\)

and we want to be equal to 2000 so we need to solve:

\(1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...\)

Rounded to the nearest percent, the solution is 70%.

If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4%

Step-by-step explanation:

Answer:

C. 7 hr

Step-by-step explanation:

On Friday, she ran for 16 miles at 8 Miles per hour. 16÷8=2, therefore on Friday she ran for 2 hours. On Saturday she ran for 15 miles at 7.5 Miles per hour. 15÷7,5=2, therefore on Saturday she ran for 2 hours. On Sunday she ran for 21 miles at 7 Miles per hour. 21÷7=3, therefore on Sunday she ran for 3 hours.

With a total of 2+2+3=7, we can say that Lori trained running throughout all 3 days for a total time of 7 hours. Thus the answer is C. 7 hr

Hope this helps!

Kind regards

Farah Syed

Answer:

yep it C

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The only choice that fits the provided statement is A.

A formula that expresses the connection between two phrases on each side of a symbol.It typically contains an equal symbol and one variable. Similarly, 2x - 4 equals 2. The variable x is present in the given case.

A. 3/4 − 1/2 = 1/4 is true.

B. 9/16 − 4/8 = 5/8 is false.

9/16 - 4/8 simplifies to (9/16) - (1/2) = (9/16) - (8/16) = 1/16, which is not equal to 5/8.

C. 7/8 − 3/4 = 1/8 is false.

7/8 - 3/4 simplifies to (7/8) - (6/8) = 1/8, which is not equal to 1/8.

D. 7/15 − 1/3 = 6/15 is false.

7/15 - 1/3 simplifies to (7/15) - (5/15) = 2/15, which is not equal to 6/15.

E. 1/2 − 1/20 = 10/20 is false.

1/2 - 1/20 simplifies to (10/20) - (1/20) = 9/20, which is not equal to 10/20.

Therefore, only option A is true.

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Answer:

AD=7.5

Step-by-step explanation:

If AB=15 and D is the midpoint that means AD=DB which is half of AD,

AD=AB/2

AD=15/2

therefore AD=7.5

Answer:

A 16

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the answer is 16 when you divide 96 by 6

The correct option is D. 100. The jet engine is 100 times more intense than the rock concert.

The decibel scale is logarithmic, which means that every increase of 10 decibels represents a tenfold increase in sound intensity. To determine how many times more intense the jet engine (140 decibels) is compared to the rock concert (120 decibels), we need to calculate the difference in decibels and then convert it into intensity ratios.

The difference in decibels is 140 - 120 = 20 decibels. Since every 10 decibels represent a tenfold increase in intensity, a 20-decibel difference corresponds to a 100-fold increase in intensity. Therefore, the jet engine is 100 times more intense than the rock concert.

Among the options provided: A. 20 (not correct), B. 2 (not correct), C. 1/100 (not correct), D. 100 (correct). The correct option is D. 100.

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One water tank can be rented for 160 dollars, according to the provided statement.

The radius of a circular is the separation between its centre and perimeter. Always, the circumference is twice the radius.

The volume of the cylinder-shaped water tank is given by the formula

V = πr²h, where

r is the radius

h is the height.

Substituting the given values, we get:

V = π(4 feet)²(2 feet) = 32π cubic feet

The cost of renting the water tank is given by the product of the volume and the cost per cubic foot:

Cost = 5 dollars/cubic foot × 32π cubic feet

Multiplying these values, we get:

Cost = 160π dollars

Therefore, it costs 160π dollars to rent one water tank.

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Yes, there is sufficient evidence to refute the publisher's claim that 20% of their readers own a Rolls Royce at the 0.01 level.

The hypothesis test result indicates that the p-value is less than 0.01, which means the null hypothesis can be rejected at a 0.01 level of significance. Therefore, there is evidence to suggest that the true percentage of Rolls Royce owners among the newsletter publisher's readers is less than 20%. This could have implications for the publisher's advertising strategy and target audience.

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The reported sky cover is one continuous overcast layer, its thickness is 5,780 feet.

To calculate the thickness of a cloud layer, you need to subtract the cloud base height from the cloud top height. In this case, the sky cover is reported as one continuous layer, and the cloud top is reported at 6,500 feet.

Aviation Routine Weather Reports (METARs) typically include cloud height information in increments of 100 feet above ground level (AGL). If the sky cover is reported as overcast (OVC) with no height information, it is assumed to be at or below 6,000 feet AGL.

Therefore, the thickness of the cloud layer in this scenario can be calculated as follows:

Cloud base height = 620 feet (field elevation) + 100 feet = 720 feet AGL

Cloud thickness = Cloud top height - Cloud base height

= 6,500 feet - 720 feet

= 5,780 feet

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Answer:

-----------------------

The total cost of repair is expressed by the function:

As we see,

Therefore the answer is option A.

Verify each equation

option A

For x=3 ------> y=216(3^3)=

Answer:

x = 5 and y = 22

Step-by-step explanation:

See attached image.

Answer:

v=18

Step-by-step explanation:

26=8+v

Swap sides:

8+v=26

Subtract 8 from both sides:

8+v-8=26-8

Group like terms:

v+8-8=26-8

Simplify the arithmetic:

v=26-8

v=18

Answer:

6/5 or 1 1/5

Step-by-step explanation:

Hope this helps. Please mark me Brainliest!

Answer:

c=3

Step-by-step explanation:

The absolute maximum value of f on the interval [-1, 1] is ln(2) and the absolute minimum value is ln(1/3).

To find the absolute maximum and minimum values of a function on a closed interval, we need to evaluate the function at its critical points and endpoints and compare the values.

First, let's find the critical points by finding where the derivative of f is equal to zero or undefined. The derivative of f(x) = ln(x^2 + x + 1) can be found using the chain rule:

f'(x) = (2x + 1) / (x^2 + x + 1)

To find the critical points, we set f'(x) = 0 and solve for x:

(2x + 1) / (x^2 + x + 1) = 0

This equation has no real solutions. However, since the interval is closed, we need to evaluate the function at the endpoints of the interval as well.

\(f(-1) = ln((-1)^2 + (-1) + 1) = ln(1) = 0\)

\(f(1) = ln(1^2 + 1 + 1) = ln(3)\)

So, we have the following values:

f(-1) = 0

f(1) = ln(3)

Comparing these values, we can see that ln(3) is the absolute maximum value and 0 is the absolute minimum value on the interval [-1, 1].

Therefore, the absolute maximum value of f on the interval is ln(2), and the absolute minimum value is ln(1/3).

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Step-by-step explanation:

(5-\/5)²

25-10\/5+5

30-10\/5

Here, a=30 and b=-10

Answer:

The dimensions are 5 and 7

Step-by-step explanation:

Answer:

1.) y = 4x - 3

2.) y = -3x + 2

Step-by-step explanation:

I'm not really sure how to explain it super well, but I do know the answers