Compute the projection of u on v.

This equation is separable,

[tex]\dfrac{dA}{dt} = -6A \implies \dfrac{dA}A = -6\,dt[/tex]

Integrate both sides and solve for [tex]A[/tex] :

[tex]\displaystyle \int \frac{dA}A = -6 \int dt[/tex]

[tex]\ln|A| = -6t + C[/tex]

[tex]e^{\ln|A|} + e^{-6t+C}[/tex]

[tex]\implies A(t) = Ce^{-6t}[/tex]

Solve for [tex]C[/tex] using the initial value.

[tex]A(0) = 6 \implies 6 = Ce^0 \implies C=6[/tex]

Then the particular solution is

[tex]\boxed{A(t) = 6e^{-6t}}[/tex]

Answer:

y=-45x + 100

Step-by-step explanation:

The slope-intercept form is y=mx+b where m is the slope and b is the y-intercept or in other words the initial amount (when x is 0). Since you start off with 100 dollars the y-intercept is going to be 100 since after 0 weeks (when you opened the account) you put 100 dollars in... so you should have 100 dollars. The slope is going to be -45 since you are withdrawing 45 each week so the value is going to be decreasing by 45 every week. If you put that together you get y=-45x+100

The value of expression is n=3 and r= 16

An expression is a set of terms combined using the operations +, – , x or , /.

Given:

[tex](4k^{7})^{3} = 4^{n}* (k^{7})^{3} = 64 k^{21}[/tex]

[tex](64 k^{21}) = 4^{n}* k^{21} = 64 k^{21}[/tex]

[tex]4 ^{3} * k^{21}= 4^{n}* k^{21}[/tex]

On comparing

n=3

Now,

[tex](-3r^{-4})^{-4} = (-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}[/tex]

[tex](-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}\\1/ (-3)^{4} * 1/(r^{-4})^{4} = 1/81* r^{m}\\1/ (-3)^{4} * (r^{16}) = 1/81* r^{m}[/tex]

1/81 * r^16 = 1/81 * r^{m}

On compairing

r = 16.

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Answer:

answer in picture

Step-by-step explanation:

The tax paid by the condominium owner  is $2,632.88.

Tax is a compulsory levy that is paid to the government. The type of tax that is paid by the condominium owner is known as property tax.

Tax paid = (78,584 / 100) x $3.49 x (1 - 0.04) = $2,632.88.

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Answer:

Step-by-step explanation:

E. y = -3x

I can give you an explanation in the comments if you'd like

Answer:

1.  x = 55°

2.  x = 11°

3.  x = 30°

4.  x = 19°

Step-by-step explanation:

Trigonometric Identities

[tex]\sin(x)=\cos(90^{\circ}-x)[/tex]

[tex]\cos(x)=\sin(90^{\circ}-x)[/tex]

Question 1

[tex]\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}[/tex]

[tex]\implies x=55^{\circ}[/tex]

Question 2

[tex]\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}[/tex]

[tex]\implies x=11^{\circ}[/tex]

Question 3

[tex]\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}[/tex]

Question 4

[tex]\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}[/tex]

The area of the rhombus is 829.1562m².

A rhombus is a four sides quadrilateral with the four sides equal in length

The area of a rhombus =  [tex]\frac{1}{4}d[/tex] ×√(p² - 4d²)

where p is the perimeter and d is the diagonal

1/4(50) x √(120² - 4 x 50²) =829.1562m²

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Answer:

[tex]\sqrt{1}[/tex]

Step-by-step explanation:

We know that a rational number cannot have roots. All of the answer choices cannot be simplified except for [tex]\sqrt{1}[/tex], which can become 1. Therefore, our answer is [tex]\sqrt{1}[/tex].

Answer:

Area: 15.53 square inches

Perimeter: 15.71 inches

Step-by-step explanation:

Area:

So the area of the rectangle is pretty easy to find and is just the width * height. In this case it's 4 * 3 which is 12. Now the area of a circle is [tex]\pi r^2[/tex]. But since this is a semi circle it's half of that which is [tex]\frac{\pi r^2}{2}[/tex]. The diameter of the semicircle is 3 as it sits on top of the rectangle. The radius is half of the diameter so the radius is 1.5. Now plug that into the equation and you get [tex]\frac{(3.14) (1.5)^2}{2} = 3.5325[/tex]. Now add that to 12 and you get 15.5325. Round that number to the nearest hundredth and you get 15.53. So that's the area.

Perimeter:

Pi is the ratio of any circle's circumference to the diameter. Or in other words the circumference is equal to the diameter * 3.14. The diameter is 3 which you multiply by 3.14 to get the circumference of a circle. This will get you 9.42 but since it's a semicircle, the circumference is half of this value which is 4.71. The perimeter of the rectangle is just 2 times the width + 2 times the height. This is not completely the case in this shape since one of the sides of the rectangle is not a side of the two shapes joined together. Which is the side that is parallel to the side of length 3 inches. So the perimeter is going to be 2(4) + 3. This gives you 11 which you add to the 4.71 and get 15.71

Answer:

56

Step-by-step explanation:

so 7 appetizers times 8 main courses

I do a easy trick where I multiple so

7×8=56

Answer:

a) A dozen= 24

3 dozen= 24 x 3

= 72

b) 1 dozen= 12 bananas

A dozen cost= 24

So, 1 banana cost= 24/12

= 2

So, 6 bananas would be 2 x 6 = 12

c) 1 dozen= 12 bananas

A dozen cost= 24

1 banana cost= 24/12

= 2

d) I need to know how many people are there in your class so please mention that first :)

Mark me brainliest pleaseee

Answer:

1 answer

The area of triangle with vertices A(0, 9), B(0, 4) and C( - 5, - 9) is

Answer:

43.96ft

Step-by-step explanation:

In the hint, you are given the equation [tex]C = 2\pi r[/tex].

Here, [tex]C[/tex] is the circumference, [tex]r[/tex] is the radius, and [tex]\pi[/tex] is a constant (a value that doesn't change). In this question, you are told to assume the value of [tex]\pi[/tex] is 3.14.

You are told the radius is 7, therefore, [tex]r[/tex] = 7.

Now we have these values, let's substitute them into the equation:

[tex]C = 2 * 3.14 *7[/tex]

For clarification, the stars mean multiplication.

So, the product of those values will give us our circumference, [tex]C[/tex].

In this case, you get an answer of 43.96ft.

The probabilities in the question are

we have

z< 70 - 100/12

= z < -30/12

= -2.5

Such that p (x<70) = 0.0062

Hence the probability that is is less than $70 = 0.0062

90 - 100/12. 120 - 100/12

= -0.8333 <z< 1.67

p(90<x<120) = 0.95224 - 0.20234

= 0.7499

0.7499 is the probability of  between $90 and $120.

140-100/12

= P(Z>3.3333)

= 0.000429

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Answer:

[tex]\textsf {p(-4) = -134}[/tex]

Step-by-step explanation:

[tex]\textsf {Given :}\\[/tex]

[tex]\mathsf {p(x) = x^{3} - 3x^{2} + 7x + 6}[/tex]

[tex]\textsf {Substitute x = -4 to find p(-4) :}[/tex]

[tex]\mathsf {p(-4) = (-4)^{3} - 3(-4)^{2} + 7(-4) + 6}[/tex]

[tex]\mathsf {p(-4) = -64 - 48 - 28 + 6}[/tex]

[tex]\textsf {p(-4) = 6 - 140}[/tex]

[tex]\textsf {p(-4) = -134}[/tex]

Step-by-step explanation:

el resultado le puedo ayudar si sabe Spanish

Answer:

see below

Step-by-step explanation:

White = 1 1/3   = 4/3 =  16/12

Color =   3/4 = 9/12  

white - color ==   16/12 - 9/12 = (16-9) / 12 = 7/12 of a scoop more for the white load

Answer:

360

Step-by-step explanation:

using the definition

n [tex]P_{r}[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]

where n! = n(n - 1)(n - 2)..... × 3 × 2 × 1

then

6[tex]P_{4}[/tex]

= [tex]\frac{6!}{(6-4)!}[/tex]

= [tex]\frac{6!}{2!}[/tex]

= [tex]\frac{6(5)(4)(3(2)(1)}{2(1)}[/tex] ← cancel 2(1) on numerator / denominator

=  6 × 5 × 4 × 3

= 360

Answer:

option B is correct

To write any equations in the form of matrix

first make a matrix of all coefficients of that equations.. here coefficients of first equation is 4 and - 2 and that of second is 0 ( as there is no value of X) and 3

then make second matrix of X and y

last of answer of the equations, here (-7 ) and 5

Answer:

n=1

Step-by-step explanation:

-n+4=8n-5

9=9n

n=1

hope that helps

The dog can roam 59.7 feet if the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have:

Rover the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall. The other end of the leash is tied to the top of an 8-foot pole.

After drawing a right-angle triangle from the above information.

Applying Pythagoras' theorem:

60² = 6² + x²

After solving:

x = 59.69 ≈ 59.7 foot

Thus, the dog can roam 59.7 feet if the dog is on a 60-foot leash. One end of the leash is tied to Rover, who is 2 feet tall.

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The better option will be at DiscountsRUs 40% off on any purchase.

The amount of money which is reduced on any product below its actual selling price is called the discount.

here we have two offers from the two stores Dominic had a coupon for 15 off his purchase at Save4You. At DiscountsRUs, there was a sale of 40% off on any purchase.

For a Dominic, the discount is fixed for any purchase that is if you purchase a $50 product or a $1000 product you will be getting only a $15 discount.

Now for the second store, the discount is given as 40% so if you purchase $50 your discount will be $20. If you purchase $1000 so 40% discount will be $400.

Therefore better option will be at DiscountsRUs 40% off on any purchase.

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Answer:

-2(10(-4))²

-2(-40)²

-2 × 1600

= -3200

Answer: = -3200

Step-by-step explanation:

took the test

We can use sine ratio in given right angled triangle.

The sine of ∠Q is represented by ratio 48/73.

Given data:

∠R=90°,

QP = 73,

PR = 48,

RQ = 55

We know that;

The sine of a given angle in a right angle triangle is the ratio of perpendicular and hypotenuse seen from the viewpoint of that angle.

Since, against ∠Q lies the side PR, thus, PR is perpendicular. The side PQ is hypotenuse.

Thus, we have:

sin Q = PR/PQ

        = 48/73

Thus, the sine of ∠Q is represented by ratio,

48/73.

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This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.

Given the following expression

32ab - 8

Find the factors of each terms

32ab = 8 * 4. * a * b

8 = 8 * 1

Since 8 is common to both factors, hence

32ab - 8 = 8(4ab -1)

This shows that the greatest common factor is 8, Hence Venita's error is that she incorrectly determined the GCF.

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Answer:

g(x) = sin(x)

f(x) = e^x

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]f(x)=e^x\\g(x)=sin~x\\y=f(g(x))=f(sin~x)=e^{sin~x}[/tex]

The exponential function decays at three-fourths the rate of the quadratic function.

The given inequality is -2≤x≤0.

We need to determine how do the decay rates of the functions compare over the interval.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

We calculate the average slope of each graph in the indicated interval, the slope can be calculated as [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

Now, for the exponential function:

[tex]m_{c} =\frac{4-1}{-2-0} =\frac{3}{-2}[/tex]

For the quadratic function:

[tex]m_{q} =\frac{4-0}{-2-0} =\frac{4}{-2}=-2[/tex]

Now, the ratio of both average slopes is[tex]\frac{m_{c} }{m_{q}} =\frac{\frac{3}{-2} }{-2} =\frac{3}{4}[/tex].

Therefore, the exponential function decays at three-fourths the rate of the quadratic function.

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