Let g(t) denote the inner integral. By the fundamental theorem of calculus, the first derivative is
[tex]\displaystyle \frac{d}{dx} \int_0^x g(t) \, dt = g(x)[/tex]
Then using the FTC again, differentiating g gives
[tex]\displaystyle \frac{dg}{dx} = \frac{d}{dx} \int_1^{\sin(x)} \sqrt{1+u^4} \, du = \boxed{\cos(x) \sqrt{1+\sin^4(x)}}[/tex]
Need some help please!
Given that cos(theta) = 8/17 and that theta lies in Quadrant IV, what is the exact value of sin 2(theta)?
Answer: [tex]-\frac{240}{289}[/tex]
=========================================================
Explanation:
Use the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex] and plug in the fact that [tex]\cos(\theta) = \frac{8}{17}\\\\[/tex]
Isolating sine leads to [tex]\sin(\theta) = -\frac{15}{17}\\\\[/tex]. I'm skipping the steps here, but let me know if you need to see them.
The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.
Therefore,
[tex]\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\[/tex]
What is the product of x4y and 4x2
Answer:
4 x 2 (2WD) A 4x2 or 2WD is a vehicle that has a two-wheel drive (2WD) with four wheels.
Step-by-step explanation:
What is the volume of this oblique cone?
(A) 4321 cm?
(B) 2881 cm3
(C) 3240 cm
(D) 1441 cm3
Answer:
Its D I did my math
Step-by-step explanation:
Answer:
D. I worked the math out.
How would I solve I need to know Asap and what is the answer
Answer:
True; True; False; True
Step-by-step explanation:
Please explain. I'm a bit confused
The table shows the amount of red paint that can be added to different amounts of white paint while making a custom paint color:
Which statement is true about the ratio of red paint to white paint in the paint color?
A) It is 1:16.
B) It is 16:1.
C) It is 5:1.
D) It is 1:5.
Answer:
D) It is 1:5.
Step-by-step explanation:
[tex] \frac{4}{20} = \frac{1}{5} [/tex]
Mrs. Smith bought 3 pies for her family dinner. There were 10 people eating dinner. How much pie did each person get?
Answer:
Each person received 3/10 of pie
Step-by-step explanation:
3 dived by 10 equals 0.3 which is equivalent to 3/10
Need help with question 15 I did the work for it but the answer was wrong somehow it didn't work out question is on the photo
Answer:
336, (B)
Step-by-step explanation:
To find the surface area, find the area of each square and triangle
10x12 + 2(6x8)/2 + 12x6 + 8x12
This would then be,
120 + 48 + 72 + 96
Surface area = 336, (B)
You made a mistake on step 2.
When finding the area of triangle, you have to divide by 2.
Hope this helps!
Which of the following values are solutions to the inequality -1 + 4x < -1?
I.4
II. 1
III. 0
Answer:
4
Step-by-step explanation:
The net of a rectangular prism is shown below. The surface area of each face is labeled.
(Picture Below)
Answer:
option A is correct.
Explanation:
Total Area of the prism: 8 + 48 + 8 + 24 + 24 + 48 = 160 ft²
Area of rectangular prism: 2(LW+HW+HL)
Option A
2(2*4+4*12+12*2)
2(8+48+24)
2(80)
160 ft²
areas of all 6 surfaces of the rectangular prism are given just add them up for finding Total surface area
TSA:-
24+8+8+48+48+242(24+48+8)2(80)160ft²PQR is a right angled triangle. The area of the triangle is 6cm² and |QR|= 3cm.
find |PR|
Answer:
PQ = 4cm
QR = 3cm
PR = 5cm
Area = 6cm²
Step-by-step explanation:
Area of triangle = 0.5 × Base × Height
6 = 0.5 × 3 × PQ
Let PQ be = x6 = 0.5 × 3 × x
[tex] \frac{6}{0.5 \times 3} = x[/tex]
x = 4cm
PQ = 4cm
Since, it is a right angled triangle applying Pythagoras Theorem,
PR =
[tex] \sqrt{ {3}^{2} + {4}^{2} } \\ = \sqrt{9 + 6} \\ = 5cm[/tex]
PR = 5cm
Find the volume of the shape
Answer:
i think. 8 times 12 = 96 times 20 = 1,920
A circular flower bed is 19 m in diameter and has a circular sidewalk around it that is 4 m wide. Find
the area of the sidewalk in square meters. Use 3.14 for .
Answer:
289 m²
Step-by-step explanation:
First find the area of the flower bed
A=πr²= (3.14)(9.5)² = 283.385
Then get the area of everything including the sidewalk
A=πr²= (3.14)(13.5)² = 572.265
Then subtract and you'll get the area of just the sidewalk
572.265 - 283.385 = 288.88m²
The answer to this question is 289
what is the polynomial of (-3,0)(2,0)(2,0)(3,0)
Answer:(-2,0) and (3,0)
Step-by-step explanation:im not sure if its correct but it should be
True or False:
Gross income is the amount of money you make after deductions for taxes and other expenses have been taken out
Thank you so much!!!!!!
Answer:
False
Step-by-step explanation:
False.
Gross income is the total amount a person earns before any deductions are taken out.
Gross income is the amount of money you make after deductions for taxes and other expenses have been taken out. This statement is false.
What is gross income?Gross income is the income that is earned before any deductions are removed. For example, if a person sells a product for $20. The gross income is $20. Net income is the income after deductions have been taken out.
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What is x?
If necessary, round to the nearest tenth (one decimal place)
Please help, Thank you!
Answer:
4/x-8=8/2
4/x-8=4
4=4(x-8)
4=4x-32
4+32=4x
36=4x
dividing through by 4
x=9
converting to the nearest tenth will be 9.0
therefore x=9.0
how do i solve this?
The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?
The vertex of the graph of g is 1.5 units to the left of
the vertex of the graph of f.
B
The y-intercept of the graph of g is 1.5 units above the
y-intercept of the graph of f.
The graph of g is a reflection of the graph of f across
the y-axis.
The graph of g is a reflection of the graph of f across
the x-axis.
Answer:
Step-by-step explanation:
The graph of f(x) = x² was transformed to create the graph of g(x) = f(x) + 1.5. Which statement about the graphs is true?
The vertex of the graph of g is 1.5 units to the left of
the vertex of the graph of f.
B
The y-intercept of the graph of g is 1.5 units above the
y-intercept of the graph of f.
The graph of g is a reflection of the graph of f across
the y-axis.
The graph of g is a reflection of the graph of f across
the x-axis.
pls help
The perimeter of a rectangle is 24.
Write the function that describes its area in terms of one of the sides
The perimeter of a rectangle is 24. What is the maximum possible area of such rectangle?
The perimeter of a rectangle is 24. For what length of sides does the maximum area occur for this rectangle?
The function that describes the area of the rectangle in terms of one of the sides is A = 12L - L².
How to compute the area?The perimeter of the rectangle is given as 24. Therefore, the area in terms of one of its side will be:
A = L(24 - 2L)/2
A = L(12 - L)
A = 12L - L²
The length side for the maximum area will be 6 and 6. The maximum area of the rectangle will be:
= 6 × 6
= 36
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Rate Time = Distance
How many hours will it take to complete a 63-km bike ride if you go 20 km per
а
hour the whole time?
Answer here
SUBMIT
In 1999 the average cost of a house
was £91,199. In 2022 the average cost
of a house is £278,123. Find the
percentage change and state if this is
an increase or decrease.
The percentage change is 204.96% and it was increasing
Our percent calculator uses this formula:
[tex]((y2-y1)/y1)*100[/tex] = your percentage change
(where [tex]y1=[/tex] start value and [tex]y2=[/tex] end value)
[tex]((278.123-91.199)/91.199)*100=204.96%[/tex]
Therefore, The percentage change is 204.96% and it was increasing
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The maximum grain yield for corn is achieved by planting at a density of 37,000 plants per
acre. A farmer wants to maximize the yield for the field represented on the coordinate grid.
Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest
thousand, does the farmer need? (Hint: 1 acrt = 43,560 ft?)
у
500 fx
E
F
X
-500
0
500
G
-500
H
The farmer needs approximately
corn plants.
According to the question, there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
Determining the area of a trapezium?The trapezium is a 2 -dimensional plane shape with the area calculated as shown below:
The formula for calculating the area of a trapezoid is expressed as:
Area = 0.5(a + b)h
Given the following parameters
a = 500 ftSubstitute the given parameters
Area = 1/2 (500 + 900) * 800
Area = 1/2 (1400) * 800
Area = 560000 square feet
Since 1 acre is equivalent to 43560 square feet, hence the total acre required is expressed as:
Total acre = 560000/43560
Total acre = 12.856 acres
Also since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
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In the regular decagon shown, what is the measure of angle 1?
Answer:
try 36 but im not quite sure
Step-by-step explanation:
im sry if im wrong have a good rest of your day :)
8. 1 hour 15 minutes
minutes
Answer:
1 hour and 15 minutes=75 mins.
Step-by-step explanation:
Employees who have retired from a company are placed in different benefit categories. The bar graph shows the percentages of the retired employees in different benefit categories. Which statement about the employees is supported by the data in the bar graph? The number of employees in Category II or Category III is greater than the number of employees in Category I. More than half the employees are in Category I. The number of employees in Category II is twice the number of employees in Category III. The number of employees in Category I is three times the number of employees in Category II.
please help!
Using the given bar graph, it is found that the statement that is supported by the data in the bar graph is given by:
The number of employees in Category I is three times the number of employees in Category II.
What does the bar graph state?Research the problem on the internet, it is found that:
45% of the employees are of Category I.15% are of Category II.30% are of Category III.10% are of Category IV.Hence the correct option is given by:
The number of employees in Category I is three times the number of employees in Category II, as 45% = 3 x 15%.
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This is the graph of y=x² + 4x + 7.
-5
What is the range of this function?
A. x²-2
B. y≤ 3
OC. y23
D. All real numbers
10- ly
(-2,3)
x45
Answer:
C y≥3
Step-by-step explanation:
Range is the y values that a function can be ...this one can be as low as 3 and up to infinity
Two men and a machine were picking oranges on a farm. One man picked x amount
oranges. The second man picked 12 less than the first. The machine picked three
times the second man. How many oranges did each pick if the total amount of
oranges picked is 332?
The equation to represent the situation is like so:
[tex]x+(x-12)+3(x-12)=332[/tex]
Simplify.
[tex]x+x-12+3x-36=332[/tex]
[tex]5x-48=332[/tex]
[tex]5x-380=0[/tex]
Solve for the variable x.
[tex]5x=380[/tex]
[tex]x=76[/tex]
[tex]first\ man =x\\second\ man =x-12\\machine=3(x-12)[/tex]
[tex]first\ man=76\\second\ man=64\\machine=192[/tex]
Verify.
[tex]x+(x-12)+3(x-12)=332[/tex]
[tex]76+(76-12)+3(76-12)=332[/tex]
[tex]76+64+192=332[/tex]
[tex]332=332[/tex]
[tex]LS=RS[/tex]
Liz leaning a total of 10 appetizers recipes over the course of 2 week of culinary school .
The number of appetizers that Liz would have learnt after 4 weeks given the unit rate is 20.
How many appetizers would Liz have learnt in 4 weeks?The first step is to determine the unit rate of appetizers that Liz learns.
Unit rate = total number of appetizers / total number of weeks
10 /2 = 5 appetizers
Number of appetizers Liz would learn in 4 weeks = 4 x 5 = 20
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Find the surface area of the cube with 2/3 units squared
Answer:
8/3 or 2.66.. units
Step-by-step explanation:
TSA of cube = 6a²
side = 2/3
= 6 x (2/3)²
= 6 x 4/9
= 2 x 4/3
=8/3
Ans = 8/3 units or 2.66.. units
HAVE A NICE DAY
STAY SAFE
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Find in the triangle. Round to the nearest degree.
a. 30°
b. 27°
c.21
d.34
The angles are 87ft
And 72ft.
Answer:
option d 34⁰
Step-by-step explanation:
Your Required Answer is 34⁰
I hope It helped you