Find the point of intersection of the tangent lines to the curve r(t) = 5 sin(πt), 6 sin(πt), 3 cos(πt) at the points where t = 0 and t = 0.5.

One radian is approximately 0.0175 degrees. To convert from radians to degrees, multiply the radians value by 57.3°. This conversion is commonly used in mathematics and physics.

One radian is equal to approximately 0.0175 degrees. To convert from radians to degrees, you can use the conversion factor of 1 radian = 57.3°. So, to convert an angle from degrees to radians, you can multiply the degrees value by 0.0175. This conversion can be used when working with angular measurements in mathematics and physics.

https://brainly.com/question/30033928

#SPJ2

The dimension of the rectangle should be 47cm and 26 cm respectively.

Given that,

Based on the above information,

We know that

The perimeter of the rectangle = 2(l + w)

w = width

(2w - 5) = length

So,

146 = 2(2w - 5 + w)

146  = 4w - 10 + 2w

156 = 6w

w = 26 cm

And, the length is

= 2(26) - 5

= 47 cm

Therefore we can conclude that the dimension of the rectangle should be 47cm and 26 cm respectively.

Learn more: brainly.com/question/16167300

The probability that exactly 4 out of 10 people given the medicine experience an allergic reaction is approximately 0.087 or 8.7%.

To find the probability that exactly 4 out of 10 people experience an allergic reaction to the new medicine, we use the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]

Where:

( n ) is the number of trials (in this case, 10 people)

( k ) is the number of successes (in this case, 4 people)

( p ) is the probability of success on each trial (in this case, the probability of having an allergic reaction, which is 2 out of 10, or 0.2)

Now let's calculate:

[tex]\[ P(X = 4) = \binom{10}{4} \times 0.2^4 \times (1 - 0.2)^{10 - 4} \][/tex]

[tex]\[ P(X = 4) = \frac{10!}{4!(10-4)!} \times 0.2^4 \times 0.8^6 \][/tex]

[tex]\[ P(X = 4) = \frac{10!}{4! \times 6!} \times 0.2^4 \times 0.8^6 \][/tex]

[tex]\[ P(X = 4) = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} \times 0.2^4 \times 0.8^6 \][/tex]

[tex]\[ P(X = 4) = 210 \times 0.2^4 \times 0.8^6 \][/tex]

[tex]\[ P(X = 4) = 210 \times 0.0016 \times 0.262144 \][/tex]

[tex]\[ P(X = 4) = 0.08704 \][/tex]

So, the probability that exactly 4 out of 10 people given the medicine experience an allergic reaction is approximately 0.087 or 8.7%.

Answer:

[tex]5x^{2}-2x=72[/tex]

Step-by-step explanation:

Let

y------> one integer number

x----> the other integer number

we know that

[tex]xy=72[/tex] ----> equation A

[tex]y=5x-2[/tex] -----> equation B

substitute equation B in equation A

[tex]x(5x-2)=72[/tex]

[tex]5x^{2}-2x=72[/tex]

Answer: 206

Step-by-step explanation:

22(4+16)-(78)(3)

(22)(20)-(78)(3)

440-(78)(3)

440-234=

206

°ω°

Answer: After t=1 hour the distance between the boat and the steamer be 1300 mi.

Step-by-step explanation:

Given the speed of boat = 1200 mph

the speed of steamer =500 mph

Distance traveled by boat in time "t"=[tex]\frac{distance}{time}=\frac{1200}{t}[/tex]

Distance traveled by steamer in time time "t"=[tex]\frac{500}{t}[/tex]

As boat head south and steamer heads east ∴ they will make a right angle triangle with hypotenuse=shortest distance between them =1300mi(given)

By Pythagoras theorem

[tex](Perpendicular)^2+(Base)^2=(Hypotenuse)^2\\\\\Rightarrow(\frac{1200}{t})^2+(\frac{500}{t})^2=(1300)^2\\\\\Rightarrow\frac{1440000}{t^2}+\frac{250000}{t^2}=1690000\\\\\Rightarrow\frac{1690000}{t^2}=1690000\\\\\Rightarrow\ t^2=\frac{1690000}{1690000}=1[/tex]

⇒t=1 hour

Thus, after t= 1 hour the distance between them be 1300 mi.

Answer:

Here,

4 × 8 = 32

Now,

using the doubles when multiplying with 4

2 × (4 × 4)

= 2 × 16

= 32

Hence,

we use the doubles this way as by doubling the result obtained on multiplying the 4 with 4

Step-by-step explanation:

Here,

4 × 8 = 32

Now,

using the doubles when multiplying with 4

2 × (4 × 4)

= 2 × 16

= 32

Hence,

we use the doubles this way as by doubling the result obtained on multiplying the 4 with 4

or

double the number 4 i.e 2 × 4 = 8

then again double the result i.e  2 × 8 = 16

and, again double the result i.e 2 × 16 = 32 which the required answer.

Answer:

the answer is false.

Step-by-step explanation:

This is called as the standard error of the mean. Standard error is a numerical term that calculates the accurateness with which a sampling embodies a populace or population. In statistics, a sample mean moves away from the real mean of a population; this deviancy is the standard error.

If x = 1, then the value of y in the equation [tex]\frac{4}{x}[/tex] + [tex]\frac{3}{y}[/tex] = 5 equals

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given equation is,

4 / x + 3 / y = 5

We have to find the value of y, when the value of x = 1.

Substitute x = 1 in the equation.

4/1 + 3/y = 5

4 + 3/y = 5

3/y = 5 - 4

3/y = 1

y = 3/1

y = 3

Hence the value of y is 3.

Learn more about Equations here :

https://brainly.com/question/10413253

#SPJ2

The question is incomplete. The complete question is as follows.

If x = 1, then the value of y in the equation [tex]\frac{4}{x}[/tex] + [tex]\frac{3}{y}[/tex] = 5 equals ?

The simplest form of 8/10 is 4/5.

Given,

8/10

We need to write it in the simplest form.

It means that there is no common factor between the numerator and the denominator other than 1.

Example:

4/8

4 = Numerator

8 = Denominator

4 = 4 x 1

8 = 4 x 2

= 4 x 1 / 4 x 2

Cancel the common factor 4.

= 1/2 is the simplest form of 4/8

Find the simplest form of 8/10.

= 8/10

Look for a common factor.

= 2 x 4 / 2 x 5

Cancel the common factor 2.

= 4 / 5

Now we do not see any common factor.

= 4/5

Thus the simplest form of 8/10 is 4/5.

Learn more about converting given fractions into the simplest form here:

https://brainly.com/question/540029

#SPJ2

Answer:

First, keep good records to avoid overdraft fees. Second, be sure to check banks out carefully. Look at the services you will most likely need and see whether the bank charges fees for those services. Compare several different banks before opening an account in one of them.

Step-by-step explanation:

Plato answer

The two triangles are congruent, so the corresponding angles are the same, K is the mid-late phase of JKL, so K is the same as the mid-late phase of EFG. Therefore K = F = 62°.

What is compromise?

If a geometric shape can be placed on top of another so that all its points coincide, the geometry is said to be congruent or harmonious. >

Now that K is JKL, K will be similar to EFG's mid and late game.

Middle and late phase of EFG = F

M∠F = 62°

Therefore m∠K = m∠F = 62°

So "The two triangles are congruent, so the corresponding angles will be the same. K is at the end of JKL, so K will be the same as the end of EFG. So, K = F = 62°."

The probable question maybe:

In a triangle EFG and LJK, we are given angle G = 53 degree and angle F is 62 degree. △EFG≅△JKL. find the value of  m∠K ?

Correct answers to the statement that the price increased by 1/2 are: (B) The price is 150% of the price before and (E) The price is now 1.5 of what it was before. All other options either imply the price doubled, decreased, or was halved, which are not equivalent to an increase by half.

When it is stated that the price increased by 1/2, it means that the new price is the original price plus half of the original price. This is equivalent to multiplying the original price by 1.5. Let's evaluate the provided options:

Therefore, the correct answers to the statement "price increased by 1/2" are (B) The price is 150% of the price before and (E) The price is now 1.5 of what it was before.

The equivalent statements are (B) "The price is 150% of the price before" and (E) "The price is now 1.5 of what it was before".

To determine which statements are equivalent to the statement "price increased by 1/2", let's analyze each option:

(A) The price doubled:

This statement is not equivalent because doubling the price means multiplying it by 2, which is an increase of 100%.

(B) The price is 150% of the price before:

This statement is equivalent. Increasing by 1/2 is equivalent to increasing by 50%, which makes the new price 150% of the original price.

(C) The price was reduced by a quarter:

This statement is not equivalent because reducing by a quarter means subtracting 25%, not adding 50%.

(D) The price became a half of what it was before:

This statement is not equivalent because it implies a decrease to half, whereas the original statement implies an increase by half.

(E) The price is now 1.5 of what it was before:

This statement is equivalent. If the price is increased by 1/2, it becomes 1 + 1/2 = 1.5 times the original price.

(F) The price now is 66 2/3 % of what it was before:

This statement is not equivalent. 66 2/3 % represents a decrease, not an increase.

(G) The price now is 200% of what it was before:

This statement is not equivalent because 200% represents a doubling, not an increase of 1/2.

(H) The price is 75% of what it was before:

This statement is not equivalent because 75% represents a decrease, not an increase.

So, the equivalent statements are (B) and (E).

In binary tree there are n ancestor at level n.

Proof :

Take P(0): At node level 0, it has no ancestors since this is a roo tnode.

Take P(1): At node level 1, it has one ancestor. The ancestor is the root, its parents which is at level 0.

Take P(K): A node level K it has K ancestors. Its parent is at level K – 1.

Take P(K+1): At node K + 1 level have more than one ancestor than that of node at k level.

Thus there are n ancestor at level n in binary tree.

A node at level n in a binary tree has n ancestors. This is because there are n nodes on the path from the root to the node itself.


In a binary tree, the ancestors of a node are all the nodes that appear on the path from the root of the tree to that node. The level of a node is defined as its distance from the root node, with the root node being at level 0.

To determine the number of ancestors of a node at level n, consider the following:

Hence, the number of ancestors for a node at level n is simply n.

Answer:

You should place it 23 1/24 centimeters from each edge.

Step-by-step explanation:

The towel bar will be in the center in the door so the space between the edge of the door and each side of the bar is equal in the left and the right of the door. So lets define:

x: distance between edge of door and the towel bar edge.

We see that x is the distance left in both sides of the towel bar from the door so:

x+24 (1/4) +x = 70 (1/3)

2x + 24 (1/4)  =  70 (1/3)

2x=   70 (1/3) -  24 (1/4)

To operate the fractions , we need a common denominator that can be obtained simply by multiplying both denominators 4* 3=12

We then subtract the whole numbers and fractions

2x=   70 (4/12) -  24 (3/12) =  =( 46 1/12)

x= ( 46 1/12) / 2 = 23 (1/24)

Answer:

The maximum percentage of net Spendable income that should be set aside for housing is given by  [tex]\frac{28}{36}[/tex] rule,which states that ,if your total gross income after deduction is $ x, then you should use 28% of your income for housing finances and 36 % of your income for debt Purpose.

So, Maximum percentage of net spendable income that should be set aside for housing=28% of total gross income