Matteo is following this recipe to make a cake.
He wants to make four of these cakes.
How much of each ingredient does he need?

Answer(s):

[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = 4cos\:2x[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

I've done this question: Its batch 5

Step-by-step explanation:

It has to be all equal proportions

Step-by-step explanation:

D batch 5

c. batch 4

so d and c

The solution set 3 and 7 are the true values of the absolute value equation

The absolute value equation that has a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]

The solution sets of the absolute value equation are given as:

x = {3, 7}

Calculate the mean of the solutions

[tex]x_1 = \frac{7 +3}{2}[/tex]

[tex]x_1 = 5[/tex]

Calculate the difference of the solutions divided by 2

[tex]x_2 = \frac{7 - 3}{2}[/tex]

[tex]x_2 = 2[/tex]

The absolute value equation is the represented as:

[tex]|x - x_1| - x_2 = 0[/tex]

Substitute known values

[tex]|x - 5| - 2 = 0[/tex]

Add 2 to both sides

[tex]|x - 5| = 2[/tex]

Hence, the absolute value equation that has the a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]

Read more about absolute value equation at:

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Answer:

f’(2) = -21/128

f’(-1) = -42

Step-by-step explanation:

We are given a function:

[tex]\displaystyle \large{f(x)=\frac{6}{x^7}}[/tex]

We want to evaluate f’(2) and f’(-1). Keep in mind that f’(x) denotes or means the derivative of f(x). So what we are going to do first is to find the derivative of given function.

Derive the function, there are two ways to derive it, either using power rules or quotient rules. For this, I’ll demonstrate two methods.

Power Rules

If [tex]\displaystyle \large{f(x)=x^n}[/tex] then [tex]\displaystyle \large{f\prime (x)=nx^{n-1}}[/tex] where n is any real numbers.

Since the function is written in a fraction form, we’ll have to convert it to the x^n form using law of exponent.

[tex]\displaystyle \large{f(x)=\frac{6}{x^7} \to f(x)=6\cdot \frac{1}{x^7}}[/tex]

Law of Exponent I

[tex]\displaystyle \large{\frac{1}{a^n} = a^{-n}}[/tex]

Therefore:

[tex]\displaystyle \large{f(x)=6x^{-7}}[/tex]

Then derive the function using power rules:

Property of Differentiation I

[tex]\displaystyle \large{y=kf(x) \to y\prime = kf\prime (x)}[/tex] where k is a constant.

[tex]\displaystyle \large{f\prime (x)=6\cdot -7x^{-7-1}}\\\displaystyle \large{f\prime (x)=6\cdot -7x^{-8}}\\\displaystyle \large{f\prime (x)=-42x^{-8}}[/tex]

Quotient Rules

[tex]\displaystyle \large{y=\frac{f(x)}{g(x)} \to y\prime = \frac{f\prime (x)g(x)-f(x)g\prime (x)}{[g(x)]^2}}[/tex]

If f(x) = k or a constant then:

Property of Differentiation II

[tex]\displaystyle \large{y=k \to y\prime = 0}[/tex] for k is a constant.

[tex]\displaystyle \large{y=\frac{k}{g(x)} \to y\prime = \frac{0\cdot g(x)-kg\prime (x)}{[g(x)]^2}}\\\displaystyle \large{y\prime = \frac{-kg\prime (x)}{[g(x)]^2}}[/tex]

Therefore:

[tex]\displaystyle \large{f\prime (x)=\frac{-6\cdot 7x^{7-1}}{[x^7]^2}}\\\displaystyle \large{f\prime (x)=\frac{-42x^6}{x^{14}}}\\\displaystyle \large{f\prime (x)=-42x^{6-14}}\\\displaystyle \large{f\prime (x)=-42x^{-8}}[/tex]

Laws of Exponent used above:

[tex]\displaystyle \large{(a^n)^m = a^{nm}}\\\displaystyle \large{\frac{a^n}{a^m} = a^{n-m}}[/tex]

Therefore the derivative of function is:

[tex]\displaystyle \large{f\prime (x) = -42x^{-8}}[/tex] or [tex]\displaystyle \large{f\prime (x)=-\frac{42}{x^8}}[/tex]

Next is to substitute x = 2 and x = -1 in the derivative.

[tex]\displaystyle \large{f\prime (2)=-\frac{42}{2^8}}\\\displaystyle \large{f\prime (2) = -\frac{42}{256}}\\\displaystyle \large{f\prime (2)= -\frac{21}{128}}[/tex]

And:

[tex]\displaystyle \large{f\prime (-1)=-\frac{42}{(-1)^8}}\\\displaystyle \large{f\prime (-1) = -\frac{42}{1}}\\\displaystyle \large{f \prime (-1) = -42}[/tex]

Therefore, f’(2) = -21/128 and f’(-1) = -42.

Answer:

4squared is 16 so 16×16=256

hope it help

Answer:

4^2=16 multiplyin 16 by 16 gets you 256

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use distributive property: a*(b - c) = (a*b) -(a*c).

Here, a = 2 ; b = 9p  & c = 1/2

[tex]2*(9p - \dfrac{1}{2})=2*9p-2*\dfrac{1}{2}\\\\\\ = 18p - 1[/tex]

Answer:

4

Step-by-step explanation:

had to look it up but do 20 x 0.2 (1/5) and u get 4

Answer:

Step-by-step explanation:

Draw the third point at (0, 0). This would make the distance from (3,0) to (0,0) equal to 3, and the distance from (0,4) to (0,0) be 4.

Answer:

54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

This probability is the pvalue of Z when X = 136 subtracted by the pvalue of Z when X = 128. So

X = 136

has a pvalue of 0.8849.

X = 128

has a pvalue of 0.3446.

0.8849 - 0.3446 = 0.5403

54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.

Answer:

[tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]

Step-by-step explanation:

Notice that [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=\frac{12(0)e^{0}-12(0)}{cos(5(0))-1}=\frac{0}{0}[/tex], which is in indeterminate form, so we must use L'Hôpital's rule which states that [tex]\lim_{x \to c} \frac{f(x)}{g(x)}=\lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]. Basically, we keep differentiating the numerator and denominator until we can plug the limit in without having any discontinuities:

[tex]\frac{12xe^x-12x}{cos(5x)-1}\\\\\frac{12xe^x+12e^x-12}{-5sin(5x)}\\ \\\frac{12xe^x+12e^x+12e^x}{-25cos(5x)}[/tex]

Now, plug in the limit and evaluate:

[tex]\frac{12(0)e^{0}+12e^{0}+12e^{0}}{-25cos(5(0))}\\ \\\frac{12+12}{-25cos(0)}\\ \\\frac{24}{-25}\\ \\-\frac{24}{25}[/tex]

Thus, [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]

The net square pyramid and its given dimension as shown has a total surface area of 1040 ft².

Surface area of a square pyramid = A + 1 / 2 ps

where

Therefore,

A = l²

where

A = 20² = 400 ft²

p = 4l = 4 × 20 = 80 ft

s = 16 ft

Therefore,

Surface area = 400 + 1 / 2 × 80 × 16

Surface area = 400 + 1280 / 2

Surface area = 400 + 640

Surface area = 1040 ft²

learn more on surface area here: https://brainly.com/question/2835293

Answer:

The answer to the problem is 4 1/2

Answer:

9/2

Step-by-step explanation:

the answer is 9/2 or 4.5,

the solution for that I have attached below

Answer:

12x−9y−12z

Step-by-step explanation:

1. 16x−12y−3z−4x−(−3y)−9z

2. Combine 16x and −4x to get: (12x−12y−3z+3y−9z)

3. Combine −12y and 3y to get: (12x−9y−3z−9z)

4. Combine −3z and −9z to get: (12x−9y−12z)

Answer: 12x−9y−12z Step-by-step

explanation: 1. 16x−12y−3z−4x−(−3y)−9z 2. Combine 16x and −4x to get: (12x−12y−3z+3y−9z)3. Combine −12y and 3y to get: (12x−9y−3z−9z) 4. Combine −3z and −9z to get: (12x−9y−12z)

Answer: 8/12

Step-by-step explanation:

1/4 times 3 will give you 3/12 and add 5/12

Radius of Circular Base Of Cone= 8m

Total Surface Area= 350m²

Considering Slant Height as l

We know,

Total Surface Area= Curved Surface Area of Cone+ Area of circular Base

i.e.,

[tex]350 { \text{m}}^{2} = \pi \times r \times l + \pi \times {r}^{2} [/tex]

[tex]350 = \pi \times r(l \times r) \\ \\ \implies 350 = 3.142 \times 8(l + 8) \\ \\ \implies \frac{350}{3.142 \times 8} = l + 8 \\ \\ \implies 13.924 = l + 8 \\ \\ \implies l = 13.924 - 8 \\ \\ \therefore l = 5.924 \: \text{cm}[/tex]

So, Slant Height= 5.924 cm

Answer:

91kg

Step-by-step explanation:

weight= mass × gravitational force

910kg = m× 10ms^-2

m= 910÷ 10

m= 91

Answer:

[tex]\frac{2}{k+2}[/tex]

Step-by-step explanation:

Simplify the expression and you will get this.

hope this helps

Answer:$940

Step-by-step explanation:

29%=$272.60

100%=

100%*$272.60/29%=$940

$940

Answer:

3t - t.t.t +3(-2t) + t

3t - t³ - 6t + t

3t - 6t + t - t³

-2t - t³

Option A is correct

Answer:

The answer is (-6 + √41), (-6 – √41)

Step-by-step explanation:

We are given an equation

Subtract 5 from both side we get,

x² + 12x – 5 = 5 – 5

x² + 12x – 5 = 0

we get the equation in the form of

Here, a = 1, b = 12, c = (-5)

Now, Add and subtract (b/2a)² we get,

x² + 12x + (12/2)² – (12/2)² – 5 = 0

x² + 12x + (6)² – (6)² – 5 = 0

(x + 6)² – 36 – 5 = 0

(x + 6)² – 41 = 0

Now, add 41 both side we get,

(x + 6)² – 41 + 41 = 0 + 41

(x + 6)² = 41

√(x + 6)² = √41

x + 6 = ±√41

x = -6 + √41, -6 – √41

Thus, The roots of the equation is

(-6 + √41) and (-6 – √41).

-TheUnknownScientist 72

Answer:

$710,000

Step-by-step explanation:

The computation of the owner’s equity at the end of the year is given below:

We know that

The accounting equation equals to

Total assets = Total liabilities + owners equity

where,

Total assets = $800,000 + $150,000 = $950,000

And, the total liabilities = $300,000 - $60,000 = $240,000

So, the owners equity at the end of the year would be

= $950,000 - $240,000

= $710,000

Answer:

132

Step-by-step explanation:

since they are 180 degrees subtract

Answer:

132

Step-by-step explanation:

since this is a 180 degree angle ABC will be

180-48

132

Answer:

In physics the standard unit of weight is Newton, and the standard unit of mass is the kilogram. On Earth, a 1 kg object weighs 9.8 N, so to find the weight of an object in N simply multiply the mass by 9.8 N. Or, to find the mass in kg, divide the weight by 9.8 N.Divide the object's weight by the acceleration of gravity to find the mass.

Step-by-step explanation:

this is what i think

Answer:

V(m) = [tex](4m+2)^3[/tex]

Step-by-step explanation:

The edge of the cube is increasing by 4 feet every minute

V(m) = [tex](4m + 2)^3[/tex]

Two is the starting sidelength of the cube, and 4m is how many feet the side of the cube has grown, depending on the number of minutes that have passed

Step-by-step explanation:

the inner angle of 2 crossing segment lines is half of the sum of the 2 arc angles.

55 = (arc angle IG + arc angle JH)/2 = (76 + JH)/2

110 = 76 + JH

arc angle JH = 34°

The required arc angle JH measures 34 degrees.

In geometry, a chord is a line segment that connects two points on the circumference of a circle. The two endpoints of the chord lie on the circle, and the chord divides the circle into two segments - the major segment and the minor segment.

Given the problem, we are given that the inner angle measures 55 degrees. Thus, we can set up an equation using the formula and solve for the unknown value.

The equation is given as follows:

55 = (arc angle IG + arc angle JH)/2

We know that the arc angle IG measures 76 degrees, so we can substitute this value into the equation:

55 = (76 + arc angle JH)/2

Multiplying both sides of the equation by 2 yields:

110 = 76 + arc angle JH

Subtracting 76 from both sides of the equation gives:

arc angle JH = 34°

Therefore, the arc angle JH measures 34 degrees.

Learn more about chords here:

https://brainly.com/question/30009947

#SPJ2

given ,

a circle of radius 12 inches

and [tex]\theta[/tex] = 45°

now we know that ,

[tex]\\{Area \: of \: sector = \frac{\theta}{360\degree} \times \pi \: r {}^{2} } \\ \\ [/tex]

let's now plug in the values of radius and theta as 12 inches and 45° respectively ,

[tex]\\\dashrightarrow \: \frac{45}{360} \times \frac{22}{7} \times 12 \times 12 \\ \\ \dashrightarrow \: \frac{1}{8} \times \frac{22 \times 12 \times 12}{7} \\ \\ \dashrightarrow \: \frac{22 \times 12 \times 12}{56} \\ \\ \dashrightarrow \: \frac{3168}{56} \\ \\ \dashrightarrow \: 56.57 \: inches {}^{2} (approx.)[/tex]

hope helpful :D

Answer:

Width = 12in, Length = 17in

Step-by-step explanation:

We can create two expressions from the given statements:

1) L (length) = 5 + W (width)

and

2) 58 = 2L + 2W (the equation for rectangular perimeter)

Substituting L from the first equation into the second equation yields:

58 = 2(5+W) + 2W

Distributing the 2 and solving for W yields:

12in = W

Plug this back into the first expression,

L = 5 + 12

L = 17in

Answer:

width = 12 in

length = 17 in

Step-by-step explanation:

Let width of rectangle = x

⇒ length of rectangle = x + 5

Given:

Perimeter = 2 × width + 2 × length

⇒ 58  = 2x + 2(x + 5)

⇒ 58  = 2x + 2x + 10

⇒ 58  = 4x + 10

⇒ 48  = 4x

⇒ x = 12

Therefore,

width = x = 12 in

length = x + 5 = 12 + 5 = 17 in