Answer:
Range is {3,-1, 15}
Step-by-step explanation:
Answer:
{3, -1, 15} is the range.
Step-by-step explanation:
Evaluate the integral:
Substitute x = √7 sin(t) and dx = √7 cos(t) dt. Then
∫ √(7 - x²) dx = ∫ √(7 - (√7 sin(t))²) • √7 cos(t) dt
… = √7 ∫ √(7 - 7 sin²(t)) cos(t) dt
… = 7 ∫ √(1 - sin²(t)) cos(t) dt
… = 7 ∫ √(cos²(t)) cos(t) dt
We require that -π/2 ≤ t ≤ π/2 in order for the substitution we made to be reversible. Over this domain, cos(t) ≥ 0, so
√(cos²(t)) = |cos(t)| = cos(t)
and the integral reduces to
… = 7 ∫ cos²(t) dt
Recall the half-angle identity for cosine:
cos²(t) = (1 + cos(2t))/2
Then the integral is
… = 7/2 ∫ (1 + cos(2t)) dt
… = 7/2 (t + 1/2 sin(2t)) + C
… = 7t/2 + 7/4 sin(2t) + C
Get the antiderivative back in terms of x. Recall the double angle identity for sine:
sin(2t) = 2 sin(t) cos(t)
We have t = arcsin(x/√7), which gives
sin(t) = sin(arcsin(x/√7)) = x/√7
cos(t) = cos(arcsin(x/√7)) = √(7 - x²)/√7
Then
∫ √(7 - x²) dx = 7/2 arcsin(x/√7) + 7/4 • 2 sin(arcsin(x/√7)) cos(arcsin(x/√7)) + C
… = 7/2 arcsin(x/√7) + x/2 √(7 - x²) + C
QUESTION 4
Round the following number to two significant digits: 137,426.9
Which of the following equations has no solution?
3x + 1 = 3x + 1
3x+1= 3x + 2
3x+1= 2x + 1
Answer:
3x+1=3x+1
0x=0
no solution
3x+1=3x+2
0×=1
no solution
3x+1=2x+1
x=0
X IS THE SOLUTION BTW
A fabric store sells close-out fabrics for $2.14 a yard. A customer buys 8 yards of fabric. How much does the customer pay for the fabric? Show your work.
Answer:
$17.12
Step-by-step explanation:
2.14 · 8 = 17.12
746 divided by 40 with remainder
Answer:
Quotient: 18; Remainder: 26
Step-by-step explanation:
Please open the PDF file for work.
Hoped this helped.
[tex]GeniusUser[/tex]
Help me please I'm stuck on this question
Answer:
n= 2.9
1:2.9
Step-by-step explanation:
Divide by 15 on both sides
15 divided by 15 is 1
43 divided by 15 is 2.8666666666=>
It states "Give any decimals in your answer to 1 d.p.
Mean we round it to one decimal place
so it is 2.9
Thus the answer for n is 2.9
Hope this helps!
Which numbers complete the blanks when solving the equation cos(x+2π) = - √2/2 over the interval [0,2π]
Answer:
x = 3π/4, 5π/4
Step-by-step explanation:
cos(x+2π) = -√2/2, [0,2π]
cos(x)cos(2π)-sin(x)sin(2π) = -√2/2
cos(x) = -√2/2
x = 3π/4, 5π/4
Remember that the cosine function is periodic, so cos(θ+2π)=cos(θ).
10x + 7-x=3x + 8
Please give me answer!
Answer:
Solution: x = 1/6
Decimal form: 0.166667
Hope this helps :)
Answer:
x = 1/6
Step-by-step explanation:
10x + 7 - x : Combine like terms (In this case the x values)
9x+7 = 3x + 8 : Subtract 3x from both sides
6x + 7 = 8 : Now subtract 7 from both sides
6x = 1 : Divde both sides by 6
x = 1/6
Find the equation for a polynomial f(x) that satisfies the following:
- Degree 5
• Root of multiplicity 2 at x = 3
- Root of multiplicity 1 at x = 1
• Root of multiplicity 2 at x = 3
- y-intercept of (0, -162)
Root x= 3 of multiplicity 2, it means we can factor it with : (x-3)²
Root x = 1, of multiplicity 1, it means we can factor this polynomial with : (x-1)
Root x = -3, of multiplicity 2, it means we can factor this polynomial with : (x+3)²
Finally we get this expression : (x-3)²(x+3)²(x-1)
This expression is a polynomial of degree 5 but what is the y intercept of it ?
Basically, we need to replace x by zero and the value of the expression will be the y intercept :
let x = 0
then ,
(0-3)²(0+3)²(0-1) = 9*9*(-1) = -81 #-162
We need an y intercept of value = -162
Thus we simply need to multiply by 2, and finally f(x) = 2(x-3)²(x+3)²(x-1)
satisfies all the required condition
Good Luck
Which of the following trinomials can be factored using the square of the difference?
NO LINKS!!
Answer:
d) 16x² -56x +49
Step-by-step explanation:
The square of a binomial difference will have the form ...
(ax -b)² = a²x² -2abx +b²
__
The sign of the linear term will be negative, which eliminates choices A and C.
The linear term will be double the product of the roots of the other two terms.
In choice B, the linear term has a factor of 5 that appears nowhere else, so that cannot be a perfect square.
Choice D factors as ...
16x² -56x +49 = (4x -7)² . . . . the square of a difference
a A rocket is launched from a tower The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground , the nearest 100th of second y=-16x^2+148x+128
Answer:t=10.05s
Step-by-step explanation:
Solve for X 3x - 5X + 8x + x = 42
7
8
6
Answer:
x = 6
Step-by-step explanation:
3x-5x+8x+x = 42
7x = 42
x = 6
A student downloaded a new game on her phone that was recommended by her friend. She wanted to show her friend how good
she was doing, so she wrote down all her scores on the game. Her first five scores on the game were 432, 543, 348, 788, and 823.
On the two questions below, round to the nearest whole number when relevant.
a. What is her mean, or average, score on the game?
b. What is her median score on the game?
Answer:
a. 587
b. 543
Step-by-step explanation:
a. Mean = sum / number of numbers
To find the sum, we can add the numbers up.
432 + 543 + 348 + 788 + 823 = 2934
There are 5 numbers. Our mean is thus
2934/5 = 586.8, or 587 when rounding up. We round up because we have a .8 at the end, and 8 ≥ 5
b. To find the median, we first must order the numbers. The numbers ordered are this:
348 , 432 , 543 , 788 , 823
To find the median, we can cross off one number on each side until we are left with one or two numbers.
348 , 432 , 543 , 788 , 823
cross out one number from each endpoint
432 , 543 , 788
cross out one number from each endpoint
543
Solve by factoring
5x2-8=-6x
Answer:
x= 4/5 or x = -2
Step-by-step explanation:
Step 1: Subtract -6x from both sides.
5x^2 -8 - -6x = -6x -6x
5x^2 + 6x - 8 = 0
Step 2: Factor left side of equation.
(5x - 4) (x + 2) = 0
Step 3: Set factors equal to 0.
5x - 4 = 0 or x + 2 = 0
Hense the Answer is x= 4/5 or x = -2
From 175 yards away, a marksman hit 14/50 of the targets last year.
GUYS PLEASE HELP ME ON THIS ONE!, i will give brainliest to the right answers
Aisha has $40 to spend for her ornithology club. She spends some of it buying birdseed and saves the rest. Her savings is given by f(x)=40−1.25x, where x is the number of pounds of birdseed she buys at $1.25 per pound.
Answer:
Step-by-step explanation:
Given f(x)=40-1.25x, where x=pounds of birdseed and 40=her saved amount, and birdseed costs 1.25/lb.
f(3)=40-1.25(3)
f(3)40-3.75
f(3)=36.25
If she buys (3 pounds) of birdseed, she saves ($36.25).
f(18)=40-1.25(18)
f(18)=40-22.5
f(18)=17.5
If she buys (18 pounds) of birdseed, she saves ($17.5)
f(36)=40-1.25(36)
f(36)=40-45
f(36)=-5
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given function f(x)=40-1.25x,
where x=pounds of birdseed and 40 is her saved amount, and birdseed costs is 1.25/lb.
f(3)=40-1.25(3)
f(3)40-3.75
f(3)=36.25
If she buys (3 pounds) of birdseed, she saves ($36.25) then;
f(18)=40-1.25(18)
f(18)=40-22.5
f(18)=17.5
If she buys (18 pounds) of birdseed, she saves ($17.5) then;
f(36)=40-1.25(36)
f(36)=40-45
f(36)=-5
If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.
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Your utility company charges 14 cents per kilowatt-hour of electricity. Complete parts (a) and (b) below.
a. What is the daily cost of keeping lit a 150-watt light bulb for 8 hours each day?
b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light using only 20 watts of power?
a. The daily cost of keeping lit a 150-watt light bulb for 8 hours each day is $
(Round to three decimal places as needed.)
b. The yearly savings of replacing the 150-watt light bulb with a 20-watt light bulb is
(Round to two decimal places as needed.)
Answer:
P = 150 W * 60 sec/min * 60 min/hr = 540000 W-sec/hr
1 kW = 1000 W * 3600 sec = 3.6E6 W-sec
E (8 hrs) = 8 * .54E6 W-s = 4.32E6 W-sec
or E= 4.32/3.6 = 1.2 kW = .168 $/day
20/150 = .133 as much for a 20-watt bulb
For a LED bulb cost/day = .168 * .133 = $.022/da
Note 1 W = 1 Joule/sec
harold bought 3 pounds of red apples
Answer:
what's your question?
evaluate 4/5 * for * =7
Answer:
16/5=7
Step-by-step explanation:
A police car drives 144 km in 240 minutes. what is its average speed in kilometers per hour?
sin^2 θ - secθcosθ + cos^2 θ =
Answer:
0
Step-by-step explanation:
sin²θ + cos²θ = 1
secθcosθ = (1/cosθ)cosθ = 1
1 - 1 = 0
Question
For every 3 kg of a child's weight, pediatricians prescribe 8 mg of fever reducer. If Nidhi weighs 15 kg, how many milligrams
of the fever reducer will the pediatrician prescribe?
Answer: 40 mg
Unitary method:
For 3kg --> 8mg
For 1kg --> 8/3 mg
For 15kg--> (8/3) * 15
--> 40 mg
The number of milligrams of the fever reducer the pediatrician will prescribe is 40 mg.
Given that, for every 3 kg of a child's weight, pediatricians prescribe 8 mg of fever reducer.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, for 1 kg of child's weight pediatricians prescribe [tex]\frac{8}{3}[/tex] mg of fever reducer.
If Nidhi weighs 15 kg, then the fever reducer = [tex]\frac{8}{3}\times15[/tex]
[tex]=8\times5[/tex]
[tex]=40[/tex] mg
Therefore, the number of milligrams of the fever reducer the pediatrician will prescribe is 40 mg.
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17. Solve for x: 3xyz
i need help i would be very grateful ty :)
Answer:
C. x = P/3yzStep-by-step explanation:
Given equation:
3xyz = PSolve for x, divide both sides by 3yz:
3xyz/3yz = P/3yzx = P/3yzCorrect choice is C
how do I solve it? I don't know how, I can't remember and I don't have my notes
Answer:
-2
Step-by-step explanation:
[tex]\frac{(-2)^3+3 (4)}{-8+6}[/tex]
[tex]= \frac{-8 + 12}{-2}[/tex]
[tex]= \frac{4}{-2}[/tex]
[tex]= -2[/tex]
Answer:
2.3
Step-by-step explanation:
First we must get rid of the exponent, which is that little 3 at the top.
To do this, we will do:
(-2) × (-2) × (-2) = -8
Now we have -8 + 3.4, which equals -4.6
Next we will combine the numbers in the denominator, to get -2.
Now, all together, we have -4.6/-2.
Last but not least, we will divide -4.6 by -2, to get 2.3
And that's your answer, hope this helps you :)
Sorry if it doesn't, though.
I need this answer answed ASAP please..work out the area of the shaded shape
Answer:
Step-by-step explanation:
A = 8(14) - 5(14 - 5 - 2) = 77 m²
Answer:
77m (squared)
Step-by-step explanation:
Michael paints a circular
tablc that has a diameter
of 19 inches. What is the
area of the table?
Answer:
90.25π
Step-by-step explanation:
The formula for solving the area of a circle is πr².
r is the radius. We can find the radius by splitting the diameter in half: 19/2 = 9.5.
We can apply the area formula and we get π9.5² and the answer is 90.25π.
The inequality is -2x > 30. What is the solution of the inequality?
Answer:
x < -15
Step-by-step explanation:
Divide both sides by -2.
Next you will reverse the sign because you are dividing by a negative number.
In an old photograph, the height of grandma's table is 3.8 cm. The table doesn't exist anymore; grandma doesn't know what happened to it. She does still have the vase in the photograph which is 0.8cm tall in the photograph and 30 cm tall in real life. Using the vase for a scale factor, how tall was the table? PLEASE ACTUALLY ANSWER AND DON'T JUST PUT I DON'T KNOW OKAY?
Answer:
5.67
Step-by-step explanation:
The scale factor of the height of the image is 7.89.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. The scale factor is the ratio of the actual size to the scaled size of the object.
Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
Given that In an old photograph, the height of grandma's table is 3.8 cm. The table doesn't exist anymore; grandma doesn't know what happened to it. She does still have the vase in the photograph which is 0.8cm tall in the photograph and 30 cm tall in real life.
The scale factor will be calculated as,
Scale factor = ( 30 / 3.8)
Scale factor = 7.89
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Howie wants to get a car loan with 4% simple interest rate. If the car costs $25,000, how much would Howie need to pay back at the end of one year, including the interest?
The amount Howie will pay back at the end of one year is $26000.00
The given parameters are:
[tex]P =25000[/tex] -- the principal amount
[tex]R = 4\%[/tex] -- the interest rate
[tex]T=1[/tex] --- the duration
The amount to pay back in this duration is then calculated using:
[tex]A = P(1 + RT)[/tex]
So, we have:
[tex]A = 25000(1 + 4\% \times 1)[/tex]
[tex]A = 25000(1 + 4\% )[/tex]
Express percentage as decimal
[tex]A = 25000(1 + 0.04)[/tex]
[tex]A = 25000(1 .04)\\[/tex]
Multiply
[tex]A = 26000[/tex]
Hence, the amount to pay back is $26000.00
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If one length of a board is 1 1/3 feet long, how many lengths of board is needed to cover 12 feet?
Answer:
9
Step-by-step explanation:
12÷1 [tex]\frac{1}{3}[/tex]=9
