Pls help with both...........

The evaluated integral is (1/7)sin(7x) + C, where C is the constant of integration.

Given the integral ∫cos(7x) dx and the substitution u = 7x, we need to find du and rewrite the integral in terms of u.
First, we find du by taking the derivative of u with respect to x:
du/dx = d(7x)/dx = 7
Now, we can solve for dx:
dx = du/7
Next, we substitute u = 7x and dx = du/7 into the integral:
∫cos(7x) dx = ∫cos(u) (du/7)
Now, we can evaluate the integral with the given substitution:
∫cos(u) (du/7) = (1/7)∫cos(u) du
To evaluate the integral, we recall that the integral of cos(u) is sin(u):
(1/7)∫cos(u) du = (1/7)sin(u) + C
Finally, we substitute back 7x for u:
(1/7)sin(7x) + C
So, the evaluated integral is (1/7)sin(7x) + C, where C is the constant of integration.

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The correct equation that can be used to find the number of bottles of water w that the club needs to sell to reach their goal is: 26+2w=100. Option B

Let w be the number of bottles of water that the club needs to sell to reach their goal of raising $100.

Total amount = $26 + $2w

To find the number of bottles of water w that the club needs to sell to reach their goal of raising $100 will be:

Total amount = Goal amount

$26 + $2w = $100

Simplifying the equation, we get:

$2w = $100 - $26

$2w = $74

Dividing both sides by 2, we get:

w = 37

Therefore, the club needs to sell 37 bottles of water to reach their goal of raising $100.

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There are 1008 different combinations of three chocolates that they can choose.

What is a combination?

Combination is a way of selecting objects from a larger set, where the order of the selected objects does not matter.

There are three separate choices to be made, so we need to multiply the number of choices for each step.

First, the daughter chooses one of the 8 milk chocolates. She has 8 options.

Next, the son chooses one of the 9 plain chocolates. He has 9 options.

Finally, Mrs. Sweet chooses one of the remaining 14 chocolates (8 milk and 9 plain chocolates have already been chosen). She has 14 options.

To find the total number of combinations, we multiply the number of choices for each step:

8 x 9 x 14 = 1008

Therefore, there are 1008 different combinations of three chocolates that they can choose.

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Answer:

x=−1−√112,−1+√112

Step-by-step explanation:

Move all terms to the left side and set equal to zero.

Answer:

Option B, \(13.32\ x\)

Step-by-step explanation:

Step 1:  Determine an equation

\(Last\ month\ +\ This\ month\)

\(3.75\ x + (0.85 * 3.75\ x * 3)\)

\(3.75\ x + (3.1875\ x * 3)\)

\(3.75\ x + 9.5625\ x\)

\(13.3125\ x\)

Answer: Option B, \(13.32\ x\)

Step-by-step explanation:

1/2 is equal to 0.5 and 5/4 is equal to 1.25

0.5_1.25

Which is greater?

1.25 by a long shot

Then we convert back to fractions.

The answer is 1/2<5/4

Hope it helps!

Answer:

1/2 is 50% and 5/4 = 125%

Step-by-step explanation:

Answer:

I think it's the first answer

Answer:

Bart sold 290

Step-by-step explanation:

if i did my math correctly it would be 290, i hope this helps

have a great day!

______________________________

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To determine the number of eggs needed to bake 12 cakes, we can set up a proportion based on the given information. Since every 4 cakes require 8 eggs, we can calculate that 12 cakes would require 24 eggs.

Based on the information provided, we know that for every 4 cakes, 8 eggs are needed. To find out how many eggs are needed for 12 cakes, we can set up a proportion:

4 cakes / 8 eggs = 12 cakes / x eggs

To solve for x, we can cross-multiply:

4 cakes * x eggs = 8 eggs * 12 cakes

Simplifying the equation:

4x = 96

Dividing both sides by 4:

x = 24

Therefore, to bake 12 cakes, you would need 24 eggs.

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Answer: You can't answer this without the graph

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

just out b i dont have time to explain

Answer:

C

Step-by-step explanation:

it is c because the x axis is 3 and three over and the y axis it is right on 4

Answer:

C )  ( x - 2 ) ( x + 4 ) ( x - 6 )

Step-by-step explanation:

.

Answer: You listed different numbers then in the picture since there is no 11  so this is based off of the picture.

Range: 20

Median: 15

Step-by-step explanation:

Range is just the highest number minus the lowest: 32-12 is 20

Median is the middle number after you put the numbers in order

12, 13, 13, 15, 16, 19, 32

The direction of the greatest increase in heat from the point (2, 5) is in the direction of the vector (-21, -20).

To find the direction of the greatest increase in heat from point (2, 5), we need to find the gradient vector of the temperature function T(x,y) at that point, and then determine the direction in which the gradient vector points.

The gradient vector of T(x,y) is given by:

∇T(x,y) = (∂T/∂x)i + (∂T/∂y)j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the partial derivatives of T(x,y) with respect to x and y, we get:

∂T/∂x = (x² - y²)/(x² + y²)²

∂T/∂y = -2xy/(x² + y²)²

Substituting x = 2 and y = 5, we get:

∂T/∂x = (4 - 25)/(29)² = -21/1681

∂T/∂y = -20/1681

Therefore, the gradient vector of T(x,y) at the point (2, 5) is:

∇T(2,5) = (-21/1681)i - (20/1681)j

The direction of the greatest increase in heat from points (2, 5) is in the direction of the gradient vector. We can normalize the gradient vector to get the unit vector in this direction:

u = (∇T(2,5))/|∇T(2,5)|

where |∇T(2,5)| is the magnitude of the gradient vector, given by:

|∇T(2,5)| = √((-21/1681)² + (-20/1681)²) = sqrt(841)/1681 = 1/41

Thus, the unit vector in the direction of greatest increase in heat from the point (2, 5) is:

u = (-21/1681i - 20/1681j)/(1/41) = -21i - 20j

Therefore, the direction of the greatest increase in heat from points (2, 5) is in the direction of the vector (-21, -20).

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This is karma for doing this to some one else :)

regdcd gvfd vcds xgrcd xre dse dxf crdx vcfx gvf c fcvr fvcrdgbv

Answer:

here are four main types of transformations: translation, rotation, reflection and dilation. These transformations fall into two categories: rigid transformations that do not change the shape or size of the preimage and non-rigid transformations that change the size but not the shape of the preimage

Step-by-step explanation:

pls make me brainiest

The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.

Answer:

Step-by-step explanation:

Given :

45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44

Using technology, the box and whisker plot generated for the data is attached below.

The 5 - number summary is also given below :

Minimum: 39

Median: 45

First quartile: 42

Third quartile: 47

Interquartile Range: 5

Maximum: 49

Outliers: none

Answer:

Step-by-step explanation:

Answer:

Susan pays $2220 more interest than Robert

Step-by-step explanation:

Interest = principle times rate times the time

I = PRT

Robert:  I = 30000(.049)(4) = $5880  

Susan:   I = 30000(.045)(6) = $8100

8100 - 5880 = $2220

Answer:

\(5.40\)

Step-by-step explanation:

The work:

\(x=(\frac{2}{5} )(13.50)=\frac{(2)(13.50)}{5} =\frac{27}{5} =5.40\)

Hope this helps.

The correct answers are :

Part A = £10.50

Part B = £5.40

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

1/4 of £42

and, 2/5 of £13.50

'of' means multiply here. So, we will simply multiply the numbers.

A. what is 1/4 of £42

1/4 * 42

=10.50

or, 10 1/2  = £10.50

B.  what is 2/5 of £13.50

2/5 * £13.50

= £5.40

Hence, The correct answers are :

Part A = £10.50

Part B = £5.40

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Complete question:

What is 1/4 of £42

and what is 2/5 of £13.50

Answer: x = 10

Step-by-step explanation: hope this helps

The solution to the equation, 4 + x = 7, is given as x = 3.

The solution for the variable of an equation is the value of the variable, which can be determined by applying the necessary properties of equality in order to isolate the variable to one side of the equation.

Given the equation, 4 + x = 7, the variable we want to solve for is x. Follow the steps below to find x.

4 + x = 7 [given]

Subtract 4 from both sides:

4 + x - 4 = 7 - 4 [subtraction property of equality]

x = 3

Therefore, the solution is, x = 3.

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Answer:

∠9 and ∠12

Step-by-step explanation:

Supplementary angles are two angles that add up to 180. Looking at all the answer choices, A, C, and D have either Big-Big angle or Small-Small angle. What we need is Big-Small angle that is next to eachother, which is ∠9 and ∠12.

Hope this helped.

(Also sorry!)

Answer:

1

+t

3

+t

5

=39

t

2

+t

4

+t

6

=51

To find:

t

10

=?

Solution:

Let a be the first term and d be the common difference.

t

1

+t

3

+t

5

=39

or, a+a+2d+a+4d=39

or, 3a+6d=39

or, a+2d=13 .............(i)

t

2

+t

4

+t

6

=51

or, a+d+a+3d+a+5d=51

or, 3a+9d=51

or, a+3d=17

Subtracting eqn. from eqn. we get,

d=4

Putting value d=4 in eqn.(i) we get,

a+2×4=13

or, a=13−8

or, a=5

Now, t

10

=a+9d

t

10

=5+9×4

t

10

=5+36

t

10

=41

The elapsed time between a start time of 6:28 am and an end time of 10:08 am is 3 hours and 40 minutes.

To calculate the elapsed time between a start time of 6:28 am and an end time of 10:08 am, we need to subtract the start time from the end time. First, let's consider the minutes. The end time is 08 minutes past the hour, and the start time is 28 minutes past the hour. Subtracting 08 minutes from 28 minutes gives us 20 minutes.

Next, let's consider the hours. The end time is 10:08 am, and the start time is 6:28 am. Subtracting the hours, we get 10 - 6 = 4 hours. Therefore, the elapsed time between the start time of 6:28 am and the end time of 10:08 am is 4 hours and 20 minutes. In other words, from 6:28 am to 10:08 am, there is a total of 4 hours and 20 minutes that have passed.

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The exponential growth function's estimate of the monthly percentage rate is; log 3/ 3.

We will employ the exponential function, as indicated, to determine the monthly percentage rate;

P(t) = P(0)e∧(rt)

Enter the following parameters into the calculation to obtain the rate "r".

P(t) = P(0)e∧(rt)

3P(0) = P(0)e∧(rt)

3 = e∧(rt)

Taking log both sides.

log 3 = (rt)

r = log 3 / 3

r = 0.366

r = 36.6%

Consequently, the exponential growth function's estimate of the monthly percentage rate compounded continuously is; log 3/ 3.

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Answer: the answer is ln(2)/3

Step-by-step explanation:

Answer:

Rock bundles:

950R+250

pop bundles:

1200P+300

Step-by-step explanation:

R=amount of rock bundles

P=amount of pop bundles

Rock bundles:

950R+250

pop bundles:

1200P+300

Answer:

Pop equation:1200C + 300 = D

Rock equation:950A + 250 = B

Step-by-step explanation:

Answer:12

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Answer:

The answer is 20 ft