Mathematics High School

If f(x) = integral of 1/ (sqrt of t^3 +2)dt, then f'1 = ?
I'll write the equation with teh equation thing also ...?

Answers

Answer 1
Differentiating an integral removes the integral.

f(x) = integral of dt/sqrt(t^3 + 2)
f'(x) = 1/sqrt(x^3 + 2)
f'(1) = 1/sqrt(1^3 + 2)
f'(1) = 1/sqrt(3) = sqrt(3)/3.


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Related Questions

To travel 105 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 64 miles riding a bicycle. Sue travels 13 miles per hour faster than Doreen. Find the times and rates of both girls.

Answers

Let t=time Doreen travels; let r=rate of Doreen

                RATE * TIME = DIST.
        Sue | r+13      t-3       105
   Doreen |   r           t          64
 
Now solve the system:
(r+13)(t-3)=105
r*t=64
 
[tex]r= \frac{64}{t} \\ \\(\frac{64}{t} +13)(t-3)=105 \\ \\64- \frac{192} {t}+13t-39-105=0 \\ \\13t- \frac{192} {t}-80=0 \\ \\ 13t^2-80t-192=0 \\ \\t_{1,2}= \frac{80\pm \sqrt{(-80)^2-4\times13(-192)} }{2\times13}= \frac{80\pm128}{26} \\ \\t=\frac{80+128}{26} =8 \\ \\r=\frac{64}{t} =\frac{64}{8} =8[/tex]
             
Doreen: rate = 8 mph, time = 8 hours
Sue:  rate = 21 mph, time = 5 hours


Given: line segment AB≅line segment BC

Prove: The base angles of an isosceles triangle are congruent.

The two-column proof with missing statement proves the base angles of an isosceles triangle are congruent.

Statement     Reason
1. segment BD is an angle bisector of ∠ABC. 1. by Construction
2. ∠ABD ≅ ∠CBD 2. Definition of an Angle Bisector
3. segment BD ≅ segment BD 3. Reflexive Property
4.      4. Side-Angle-Side (SAS) Postulate
5. ∠BAC ≅ ∠BCA    5. CPCTC


Which statement can be used to fill in the numbered blank space?
A. ΔDAB ≅ ΔDBC

B. ΔABD ≅ ΔABC

C. ΔABC ≅ ΔCBD

D. ΔABD ≅ ΔCBD

Answers

In the given two column proof two sides and included angles are equal.

Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles .In the figure sides BD≅BD , AB≅ BC and <ABD ≅,BDD Therefore triangle ABD and triangle CBD are congruent by SAS property of congruence.

The correct  option for missing statement is D. ΔABD ≅ ΔCBD .


Answer:

ΔABD ≅ ΔCBD

Step-by-step explanation:

Guys this is the right answer,  ΔABD ≅ ΔCBD. I got it right on my test!

What is the equation for this slope question??

4.)The line whose slope is half as great as Its y-intercept. Their sum is 1.

Answers

I think the slope is 1/3 and the y-intercept is 2/3
Final answer:

We are given that the slope is half the y-intercept and their sum is 1. Using these conditions we can solve for b and m (which represent y-intercept and slope) and we find that b=2/3 and m=1/3. Therefore, the equation of the line is y = 1/3x + 2/3.

Explanation:

The question is about finding the equation of a line from given conditions. We know that the equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. We are given two conditions: the slope is half the y-intercept, and their sum is 1.

Let's assume that the y-intercept is b and the slope is m. Now we can substitute the value of m from the first equation into the second. This gives us: b + b/2 = 1. Solving this, we get b = 2/3 and therefore, m = 1/3.

So, the equation of the line is y = 1/3x + 2/3.

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Choose all correct answers. Which of the following ordered pairs are solutions of the system, y > 3 and y < 2x + 2

A. (0, 2)
B. (2, 4)
C. (3, 5)
D. (-2, 0)

Answers

B. (2,4) and C. (3,5) are your answers. I hope this helps and have  a good day!

10m - p = -n for m please help, I need help

Answers

10m-p=-n
10m-p+p=-n+p
10m=p-n devide by 10
m=(p-n)/10

Y=1.40x 14.25 solving for x

Answers

x= 0.5012531y
solve for X by simplifying both sides of the equation, than isolating the variables 

A _______________ is where a horizontal number line and a vertical number line intersect at their zero points.

Answers

The x intercept is what you are looking for. 
If you need help comment below!


"What is element a23 in matrix A

"

Answers

Answer: The answer is (A) -5.

Step-by-step explanation:  We are given to find the element [tex]a_{23}[/tex] in the following matrix:

[tex]A=\begin{bmatrix}8 & -4 & -3\\ 3 & -9 & -5\\ -8 & 8 & 8\end{bmatrix}[/tex]

We know that [tex]a_{mn}[/tex] is an element of a matrix present in the m-th row and n-th column.

So, [tex]a_{23}[/tex]  will be the element present in the second row and third column.

Since the element in the second row and third column is - 5, so we have

[tex]a_{23}=-5.[/tex]

Thus, (A) -5 is the correct option.

what is 2.999 rounded to the nearest hundreth?!!

Answers

If you would round it to the nearest tenth which is the third nine, you'd see that it would add up to the whole number 3. So the answer is 3!!
I believe the answer should be 3.00 if I'm not mistaken

What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 2]?

Answers

For this we need to take value of f(x) when x = -3 and value of f(x) when x = 2, sum them up and divide by distance between x = -3 and x = 2

f(-3) = -36

f(2) = 4

average rate of change is:

Avg = (36 + 4)/(3+2) = 8

Note that we have to use +36 and not -36 because we need distance from -36 and 4 and that is 36 + 4 = 40... same goes for -3


Which of the pairs of angles are complementary

Answers

the third choice. complementary angles add up to 90 degees

Estaban has a big jar of change in his room. he has 600 coins in total, 240 of them are pennies. what percentage of the coins are pennies

Answers

240/600= 24/60= 4/10 = 40%

Help!!! Question is attached. It is on Solving Equations.

Answers

Hi there!

Okay, so we are solving for s. This is pretty simple. Just follow the steps below!

-10s = -8 - 9s

Step 1) Simplify both sides of the equation.

-10s = -8 + - 9s
-10s = -9s - 8

Step 2) Add 9s to both sides.

-10s + 9s = -9s - 8 + 9s
-s = -8

Step 3) Divide both sides by -1.

-s/-1 = -8/-1
s = 8

Our final answer is s = 8.

Hope this helps!

Tomas orders a meal the costs $7.89.lisa's meal costs $9.05. about how much is combined cost if their meals?

Answers

$7.89 rounded is about $8
$9.05 rounded is about $9
8 + 9 = 17

Their meals together costed about $17

Toby just graduated from four years of college. At the beginning of each year, he took out a Stafford loan with a principal of $6,125. Each loan had a duration of ten years and an interest rate of 5.3%, compounded monthly. All of the loans were subsidized. Toby plans to pay off each loan in monthly installments, starting from his graduation. What is the total lifetime cost for Toby to pay off his 4 loans? Round each loan's calculation to the nearest cent.
a.
$7,904.04
b.
$31,616.16
c.
$10,393.82
d.
$36,490.25
Would appreciate if you could show the work for how this is done.

p.s. I later submitted this question and the answer is B.

Answers

The cost that's necessary to pay the loan will be $31,616.16.

How to calculate the cost of the loan

First, we need to calculate the effective monthly interest rate. This will be:

i = 0.053/12

= 0.0044

The effective annual interest rate will then be:

i = (1 + 0.0044)^12 - 1

I = 0.0543

Next thing will be to calculate the present worth of all the loans which will be:

P = 6125 + 6125 (1 + 0.0543) + 6125 (1 + 0.0543)² + 6125(1 + 0.0543)³

P = $22,671.40

The worth of the loans after four years will be:

P = 22671.40 (1 + 0.0543)⁴

= $31,616.16

In conclusion, the correct option is $31,616.16.

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To calculate the total cost of Toby's 4 Stafford loans, the monthly amount for one loan is first calculated and then multiplied by four and by the number of months. The correct total lifetime cost is approximately $31,569.60.

To determine the total lifetime cost that Toby will pay to pay off his 4 Stafford loans, each with a principal of $6,125, an interest rate of 5.3% compounded monthly, and a loan duration of ten years, we need to calculate the monthly payment for a single loan and then multiply by the number of loans and the duration. The formula for the monthly payment on an installment loan is:

P = P[r(1+r)^n] / [(1+r)^n - 1]

where:

P is Principle Amountr is rate of interestn is time in years

Using the data given:

P = $6,125 * [0.004417(1 + 0.004417)^120] / [(1 + 0.004417)^120 - 1]

Calculating this gives us a monthly payment of approximately $65.77 for each loan. Toby took out 4 loans, so his total monthly payment is 4 * $65.77 = $263.08.

The total lifetime cost for a single loan is the monthly payment * number of payments (120), which is:

Total cost for one loan = $65.77 * 120 = $7,892.40

And the total lifetime cost to pay off all 4 loans:

Total cost for all loans = $7,892.40 * 4 ≈ $31,569.60

Therefore, rounding each loan's payment to the nearest cent, the total lifetime cost to pay off all 4 of Toby's loans is roughly $31,569.60, making the answer option b the correct one.

Which of the following expressions could be used to represent "the difference between -17 and -8"?
-8 - (-17)
-17 - 8
-17 - (-8)
-8 + (-17)

Answers

-17 -(-8) should be the answer

Answer:

-17 - (-8)

Option 3 is correct.

Step-by-step explanation:

Phrase: "the difference between -17 and -8"

Expression: To write the phrase into algebraic form with a variable or constant.

Difference: write two number using subtraction between them.

"the difference between -17 and -8"

First number is -17 and second number is -8

Expression: -17 difference -8

Now using minus sign write as expression.

[tex]\Rightarrow -17-(-8)[/tex]

Hence, The correct expression is -17-(-8)

Solve the following equation: 2x - 3 = 17.

a. 5
b. 7
c. 10
d. 12

Answers

I hope this helps you




2x=17+3


2x=20


x=10



Select the postulate that is illustrated for the real numbers.

3 + 2 = 2 + 3

The commutative postulate for multiplication
Multiplication identity
The addition inverse postulate
Commutative postulate for addition
The distributive postulate
The addition of zero postulate
The multiplication inverse

Answers

3 + 2 = 2 + 3
the answer is Commutative postulate for addition

Maricella has a bag containing 35 nickles and quarters.The total value of these coins is less than $2.50. What is the maximum number of quarters that meets these conditions?

Answers

Ok this problem takes some problem solving skills!

Let's start. First, we need to divide 250 by 25. This is because each quarter is worth 25 cents, and $2.50 is worth 250 cents.

You can do this on a calculator.

You should get an answer of 10.

This means that 10 quarters can fit in the bag IF THERE IS NO NICKLEs!!!!!So we are not finished.


We have to subtract one quarter.


So the maximum amount of quarters that can fit is 9.

You would have 5 nickles.


Your answer would be 9 quarters.

Comment of you have any questions!
$0.05(35-Q)+$0.25Q=$2.50
$1.75-$0.05Q+$0.25Q=$2.50 Subtract $1.75 from each side.
$0.20Q=$0.75
Q=3.75 To have $2.50, you would have 3.75 quarters, so to have less, the maximum number of (whole) quarters would be 3

Which equation could be used to solve the following system?

x+y=11
4x^2-3y^2=8



A. 4(y + 11)2 – 3y2 = 8

B. 4(11 – y)2 – 3y2 = 8

C. 4(y – 11)2 – 3y2 = 8

D. 4(–11y)2 – 3y2 = 8

Answers

I hope this helps you




x=11-y




4. (11-y)^2-3y^2=8

we have

[tex]x+y=11[/tex]

[tex]x=11-y[/tex] --------> equation A

[tex]4x^{2} -3y^{2}=8[/tex] ----> equation B

Substitute equation A in equation B

[tex]4(11-y)^{2} -3y^{2}=8[/tex]

therefore

the answer is the option B

[tex]4(11-y)^{2} -3y^{2}=8[/tex]

10 with a small 6 on top is

Answers

Do you mean [tex] 10^{6} [/tex]?

Are you asking what that equals or what the 6 means?

I'll just answer both lol

[tex] 10^{6} [/tex]=1,000,000

The 6 is an exponent by the way, if you needed to know that
10to the 6th power is 1000000

multiply 3/7 x 14
...?

Answers

3/7 x 14/1
= 42/7
=6/1

6

The simplified product of 3/7 multiplied by 14 is 6.

To multiply 3/7 by 14, you can follow these steps:

Multiply the numerators: 3 x 14 = 42.

Multiply the denominators: 7 x 1 = 7.

Therefore, the product of 3/7 multiplied by 14 is 42/7.

However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 7.

= 42/7

= 6/1

= 6.

So, the simplified product of 3/7 multiplied by 14 is 6.

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What is 12 less than 15 times x?

Answers

15x - 12 Then you got X= 12/15

Use the SAS Congruence Axiom to prove the ASA criterion ...?

Answers

Given the SAS, we can use the CPCPT (congruent parts of congruent triangles are congruent) and get the ASA.

What is "the ratio of a line's rise over its run?"

Answers

The ratio is y/x and it is referred to as the slope or the rate of change

how do I solve : COT pi/4 ...?

Answers

cot x = cos x / sin x
cot π/4 = cot 45° = cos 45° / sin 45°
We know that sin 45° and sin 45° have the same value:
cos 45° = sin 45° = √2 / 2;
cos 45° / sin 45° = √2/2 : √2/2 = 1
Answer:
cot π/4 = 1

The graph of a line gets _____ as the absolute value of the slope gets bigger.
A. longer
B. shorter
C. steeper
D. less steep

Answers

the answer is C
The graph of a line gets steeper as the absolute value of the slope gets bigger.
The slope of a line is defined as rise by run i.e. how much y value changes with respect to the change in x value. So the slope gives the steepness of the line.

Slope 0 indicates there is no change in y when the x value is changed and so the line with slope 0 is a horizontal line. A line with slope 1 shows with 1 unit change in x, y changes by 1 unit. Likewise slope equal 2 indicates with 1 unit change in x, y changes by 2 units.

We can see as the absolute value of slope is increasing, the change in y with respect to x is increasing i.e. the line is becoming more tilted or steep.

Hence, we can conclude that:
The graph of a line gets Steeper as the absolute value of the slope gets bigger.
C is the correct answer.

1. A local pizzeria sold 65 pizzas yesterday.
(a) The owner offers the employees a bonus if the number of pizzas sold increases by 20% today. How many pizzas must the pizzeria sell for employees to receive the bonus? Explain your reasoning.

(b) Suppose the actual number of pizzas sold today was 60. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth. Show your work.

Answers

65 + 0.20(65) = 65 + 13 = 78..they would have to sell 78 to get the bonus

(65 - 60) / 65 = 5/65 = 0.0769 x 100 = 7.69 rounds to 7.7 % decrease compared to the 65 pizza's sold yesterday

Answer: 1) Pizzeria must sell 78 pizzas for receiving the bonus.

2) The number of pizzas sold is decreased by Approximately 7.69 %.

Step-by-step explanation:

1) The number of pizza sold yesterday = 65,

The target for receiving the bonus = 20% more than the number of pizza sold yesterday

= 20% more than 65,

= 65 + 20% of 65    ( 1% = 0.01 ⇒ 20% = 0.2 )

= 65 + 0.2 × 65

= 65 + 13 = 78.

Hence, they must sell 78 pizzas for receiving the bonus.

2) If the actual number of pizza sold today = 60

⇒ Total reduction in the number of pizza = 65 - 60

= 5

Thus, the percentage decrease in the number of pizza

[tex]=\frac{\text{Total reduction}}{\text{The number of pizza sold yesterday}}\times 100[/tex]

[tex]=\frac{5}{65}\times 100[/tex]

[tex]=\frac{500}{65}=7.69230769\approx 7.69\%[/tex]

A six-sided fair die and an eight-sided fair die are rolled together. What is the probability of getting numbers whose sum is a multiple of 3?

Answers

There are 48 possible outcomes in this situation, and of those outcomes, the ones whose sums are a multiple of three are;
12, 21, 15, 51, 24, 42, 33, 18, 27, 36, 63, 45, 54, 48, 57, and 66. So, that is 16 out of 48 possibilities, or 16/48, which simplifies to 1/3. Written as a percent, the probability of getting numbers whose sum is a multiple of three is 33.33%.

Hope this is helpful! :)

To solve this problem, we have to find the multiples of 3 and then find the probability of selecting them. The probability of having a multiple of 3 is 1/3.

Probability of tossing a fair dice.

The probability of tossing a six-sided dice and a eight-sided dice.

When we toss them together, the maximum value will be

[tex]6 * 8 = 48[/tex]

The multiplies of 3 will be

Data;

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

The probability of having a multiple of 3 will be

[tex]P(multiple of 3) = \frac{16}{48} = \frac{1}{3}[/tex]

The probability of having a multiple of 3 is 1/3

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Fractions that are equivalent to1/2

Answers

3/6, 2/4, 5/10, 10/20, 15/30..
As long as the numerator (top number) is half of the denominator (bottom number), it is the same as 1/2
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